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This report was prepared as an account of work sponsored by an agency of the United State*Government. Neither the United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer*ence herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.

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TABLE OF CONTENTS

Page

PROGRAM ABSTRACT xii

ABSTRACT , 1

1. INTRODUCTION 2

2. NEUTRONICS EQUATIONS AND SOLUTION METHODS 5

2.1 Derivation of the Mesh-Centered Finite-Difference Equations . 5

2.1.1 The Multidimensional Multigroup Neutron DiffusionEquations 5

2.1.2 The Orthogonal XYZ Geometry Derivation 62.1.3 Comments Regarding All Geometry Options . . . . . . . 102.1.4 The Matrix Equations and Their Properties 16

2.2 Solution Strategies i 19

2.2.1 The Chebyshev Accelerated Outer (Fission Source)Iterations 20

2.2.2 The Line Successive Overrelaxation of the InnerIterations 25

2.2.3 Outer Iteration Computational Considerations 282.2.4 Inner Iteration Computational Considerations 302.2.5 Data Management Considerations 382.2.6 Adjoint Solution Strategy 392.2.7 Upscatter Iteration Strategy 402.2.8 The Inhomogeneous Problem 41

2.3 The Criticality Search Option 43

2.3.1 Statement of the Problem 432.3.2 Method of Solution .a 442.3.3 Comments on the Concentration Search Option 45

2.4 Summary 47

3. A GUIDE FOR USER APPLICATIONS 48

3.1 Setting Up a DIF3D Job - An Overview 48

3.1.1 Input Binary Files 483.1.2 BCD Card-Image Model Input 483.1.3 BCD Card-Image Calculation Parameter Input 493.1.4 Edits 49

3.2 BCD Input Conventions « . . . 49

3.2.1 BLOCK" 503.2.2 DATASET-, UNFORM-, NOSORT- 503.2.3 BLOCK-OLD 523.2.4 MODIFY-, REMOVE*, nn-DELETE . . . . 523.2.5 Sample Input S33.2.6 Output from BCD Input Card Preprocessors . . . . . . . 53

ill

TABLE OF CONTENTS (cont.)

Page

3.3 General Philosophy on Input Data 53

3.4 Free-Format (FFORM) Syntax Rules . 55

3.4.1 Delimiters 553.4.2 Data Forms 553.4.3 Implied Blanks and Zeroes 563.4.4 nR, the Repeat Option 563.4.5 $, End of Card 563.4.6 UNFORM and Card Type Numbers 57

3.5 Microscopic Cross Sections - ISOTXS, XS.ISO and A.ISO . . . . 57

3.5.1 Reaction Versus Production Based (n,2n) Cross

Sections 57

3.6 Number Densities, Cross Section Homogenization and Edits . . . 58

3.6.1 Compositions, Zones and Subzones - A.NIP3 13 and14 Cards , 58

3.6.2 Isotope Sets - A.NIP3 39 Cards • 593.6.3 Homogenization of Principal Cross Sections 593.6.4 Homogenization of the Scattering Cross Section . . . . 603.6.5 Discussion of the Removal Cross Section 623.6.6 Homogenization Options for the Fission Spectrum -

A.HM64C 02 Card 623.6.7 Edit Options and Container Storage - A.HMG4C 02 Card . 633.6.8 Directional Diffusion Coefficient Factors -

A.NIP3 35 and 36 Cards 643.6.9 Fission and Capture Energy Conversion Factor Data -

A.NIP3 37 and 38 Cards 643.7 Geometry Input and Edits - A.NIP3 and GEODST 64

3.7.1 Geometry Types - A.NIP3 03 Card 653.7.2 Boundary Conditions - A.NIP3 04, 05, 10, 11 and

31 Cards 653.7.3 Regions and Areas - A.WIP3 06, 07, 15, 30 and

31 Cards 663.7.4 Mesh-Spacing - A.NIP3 06, 09 and 29 Cards 663.7.5 Buckliags - A.NIP3 12 and 34 Cards 663.7.6 Geometry Edits - A.NIP3 02 and 43, A.DIF3D 04 Cards . 67

3.8 Distributed, Inhomogeneous Sources - A.NIP3, FIXSRC andA.DIF3D . 67

3.8.1 By Group, By Region or Mssh - A.NIP3 19 Cards . . . . 673.8.2 Synthesis Trial Function Source - A.NIP3 40 Card . . . 673.8.3 Natural Decay Source - A.NIP3 41 and 42 Cards . . . . 673.8.4 Source Edits - A.NIP3 40 Card 68

3.9 Code Dependent Input - A.DIF3D 68

3.9.1 Data Management Options and Container Sizes -A.DIF3D 02 Card 68

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Page

3.9.2 Solution Options and Control Parameters -A.DIF3D 03 Card 72

3.9.3 Convergence Criteria - A.DIF3D 05 and 06 Cards . . . . 723.9.4 Edit Options and Interface File Output -

A.DIF3D 04 Card . 733.9.5 Restart Option - A.DIF3D 03, 06 and 07 Cards 753.9.6 Acceleration of Near-Critical Source Problems -

A.DIF3D 08 Card 753.9.7 Neutron Transport Option - A.DIF3D 09 Card 75

3.10 Guidelines for the Efficient Use of the CIIS 75

3.10.1 Optimal ECM Size Estimation - A.DIF3D 02 Card . . . . 76

3.11 Criticality Search Input and Edits 79

3.11.1 Parametric Modifiers M - A.NIP3 23-26 Cards 803.11.2 Search Parameter Estimates x - A.NIP3 22 Card . . . . 803.11.3 Search Pass Control Parameters - A.NIP3 21 Card . . . 803.11.4 Search Restarts - A.NIP3 21 and 22 Cards 813.11.5 Search Edits - A.NIP3 21 Card 81

3.12 Running DIF3D 81

3.12.1 Input and Output Interface Datasets 813.12o2 Sample Input 813.12.3 IBM Considerations - ARCSP021 Symbolic Parameters . . 833.12.4 CDC 7600 Considerations 873.12.5 Multiple Problems and Restarts - RTFLUX and DIF3D . . 89

3.13 LASIP3 CCCC Standard Interface File Processor 90

3.14 Definitions of Output Integral Quantities 90

3.14.1 Iteration History Quantities . 903.14.2 Preliminary Definitions of Integral Forms 923.14.3 Region and Mesh Cell Flux Integrals 953.14.4 Region-Averaged Flux Integrals 973.14.5 Zone-Averaged Flux Integrals (RZFLUX) 973.14.6 Region and Mesh Power Density Integrals (PWDINT) . . . 983.14.7 Region and Group Balance Integral Components 99

3.15 Signs of Trouble 103

3.15.1 Error Messages . . . . . 103

3.15.2 Non-monotonic Convergence 103

3.16 Special 0IF30 Applications 107

3.16.1 Perturbation Theory - VARI3D 1073.16.2 Fuel Cycle Analysis - REBUS-3 1073.16.3 Calculating Higher Harmonics . . 1073.16.4 Calculating Electrostatic Potential Distributions . . 1083.16.5 Neutron Transport with Isotropic Scattering 108


Page

4. PROGRAMMING INFORMATION 109

4.1 Role and Function of Subprograms . 109

4.1.1 Module and Overlay Driver - STP021 (D3DRIV) 1094.1.2 Input Preprocessors - SCAN and STUFF 1104.1.3 CSE010 (ANL only) , 1124.1.4 LASIP3 (ANL only) 1124.1.5 The General Input Processor - GNIP4C 1134.1.6 Cross Section Homogenization - HMG4C 1154.1.7 MODCXS . . . . . 1154.1.8 BCDINP , . . . 1174.1.9 SRCH4C 1174.1.10 DIF3D 1184.1.11 Summary (ANL only) 1244.1.12 UDOIT1-UDOIT3 124

4.2 Data Set Classification and Use by Code Block 124

4.3 Data Management Considerations 127

4.3.1 Data Management Concepts . . . . . 1274.3.2 Multilevel Data Management Strategy 128

4.3.2.1 The One-Group-Contained Strategy 1314.3.2.2 Concurrent Inner Iteration Strategy . . . . 1324.3.2.3 Two-Level Machine Data Management

Considerations 135

4.3.3 DIF3D Data Management Routines 136

4.3.3.1 DEFICF 1364.3.3.2 OPENCF . . . * 1364.3.3.3 CLOSCF 1374.3.3.4 PURGCF , , 1374.3.3.5 BLKGET, FINGET, BLKPUT and FINPUT 1374.3.3.6 DEFIDF 1384.3.3.7 OPENDF and CLOSDF 1384.3.3.8 PNTGET and IPTGET 1394.3.3.9 PCRED, ICRED, PCRIT and ICRIT 1394.3.3.10 STATCF « . . . 139

4.3.4 CCCC Utility Routines 139

4.3.4.1 SEEK 1404.3.4.2 REED/RITE 1414.3.4.3 DOPC and DRED/DRIT 1424.3.4.4 CRED/CRIT 1434.3.4.5 ECMV 144

4.3.5 BPOINTER, a Dynamic Storage Allocation Program . . . . 144

4*3.5.1 Programming Considerations . . . . . . . . . 1444.3.5.2 IGTLCM/IGTSCM/IGTXCM 1474.3.5.3 IBM Allocation . . . . . . . . . 1474.3.3.4 CDC Allocation 1494.3.5.5 Cr AY Allocation (CTSS) 1494.3.5.6 CRAY Allocation (COS) 149

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4.4 Machine Dependence, Hardware and Software Requirements . . . . 152

4.4.1 General Considerations . > 1524.4.2 Storage Requirements 1524.4.3 Data Access Modes . . . . . 152

4.4.3.1 SIC, a random access, asynchronous I/Opackage for IBM systems 153

4.4.3.2 Implementation Considerations on theCDC 7600 154

4.4.4 Vectorization on the CRAY-1 154

5. THE NATIONAL ENERGY SOFTWARE CENTER VERSIONS OF DIF3D 156

5.1 The DIF3D Package 156

5.1.1 File 1 - DIF3D FORTRAN Source Images 1565.1.2 Machine Dependent Source Code 1585.1.3 Loader Instructions 1585.1.4 Sample Problem Input and Output . . . . 1595.1.5 ARCSP021, An Instream JCL Procedure for IBM

370 Systems 1595.1.6 CCCC and Code-Dependent Interface File

Descriptions , 159

5.2 Implementation of the NESC DIF3D as a Stand-Alone Program . . 159

5.2.1 Code Structure and Loading Instructions 1595.2.2 SIO 1605.2.3 File Number Assignments 160

5.2.4 Running the NESC version of DIF3D 162

5.3 Sample Problems 163

5.3.1 The SNR Benchmark Problem . 163

5.3.1.1 The Two-Dimensional Model 163

5.3.1.2 The Three-Dimensional Model 167

5.3.2 The IAEA Benchmark Problem 167

5.3.2.1 The Two-Diuiensional Model 167

5.3.2.2 The Three-Dimensional Model . 167

5.4 Suggested Local Modifications * 167

5.4.1 SEEK Initialization 1675.4.2 Storage Allocation Routines 1705.4.3 TIMER 1705.4.4 GNIPAC Graphics 1705.4.5 Random Access I/O Routines DOPC, DRBD and DRIT . . . . 170

ACKNOWLEDGEMENTS 171

REFERENCES 172

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Page

APPENDIX

A. ARCSP021 INSTREAM JCL PROCEDURE FOR IBM 370 SYSTEMS A-l

B. DIF3D BCD INPUT FILE DESCRIPTIONS B.l-1

B.I A.DIF3D B.l-1

B.2 A.HMG4C B.2-1B.3 A.ISO (See ISOTXS File Description) B.3-1B.4 A.NIP3 B.4-1

C. DIF3D CCCC BINARY INTERFACE FILE DESCRIPTIONS C. 1-1

C.I ISOTXS C. 1-1C.2 GEODST . . . . . . C.2-1C.3 NDXSRF C.3-1C.4 ZNATDN C.4-1C.5 FIXSRC C.5-1C.6 RTFLUX C.6-1C.7 SEARCH C.7-1C.8 ATFLUX ' C.8-1C.9 RZFLUX . C.9-1CIO PWDINT „ C.10-1

D. DIF3D CODE-DEPENDENT BINARY INTERFACE FILE DESCRIPTIONS D. 1-1

D.I COMPXS . D. 1-1D.2 DIF3D D.2--1Dv3 LABSLS D.3-1D.4 NHFLUX D.4-1

D.5 NAFLUX D.5-1

E. LINK EDIT INSTRUCTIONS FOR IBM 370 SYSTEMS E-l

F.I. SEGMENTED LOADER INSTRUCTIONS FOR SEGLINK ON THE CDC 7600 F.l-1

F.2. TYPE 01 OVERLAY DIRECTIVES FOR THE LDR LOADER ON THE CRAY-1 . . . . F.2-1

G. SAMPLE PROBLEM OUTPUT „ G. 1-1

G.I Sample Problem 1 (entire output) . . . G.l-1S.2 Sample Problem 2 (selected pages) G.2-1G.3 Sample Problem 3 (selected pages) . * . . » . G.3-1G.4 Sample Problem 4 (selected pages) . . . . G.4-IG.5 Sample Problem 5 (selected pages) . . . . . . . . . * . . . . . G.5-1G.6 Sample Problem 6 (selected pages) . * . G.6-1

viil

LIST OF FIGURES

No. Page

1.1 Major Modules In the DIF3D Standard Path STP021 . . . 4

2.1 X-Y-Z Volume Element 13

2.2 9-R-Z Volume Element 13

2.3 Triangular-Z Volume Elements 14

2.4 Parallelogram Boundary Domain (120° planar symmetry) 14

2.5 Parallelogram Boundary Domain (60° planar symmetry) . . . 15

2.6 Rectangular Boundary Domain (90°, 180° or 360° planar symmetry). . . 15

3.1 Illustration of Input Conventions '54

3.? A Data Management Page Edit for Sample Problem 4 71

3.3 Iteration History Page Edit for Sample Problem 1 74

3.4 CIIS ECM Storage Requirements Guide 78

3.5 ANL DIF3D Input Skeleton for Sample Problem 1 82

3.6 Minimal Input Data Example 84

3.7 LASIP-3 Input Skeleton . . 84

3.8 Structure of Job Deck for CDC 7600 at LBL 88

3.9 Structure of Job Deck for CDC 7600 at BNL 88

4.1 An Example of the Use of SCAN and STUFF Ill

4.2 Subroutine Map for the GNIP4C Code Block „ 114

4.3 Subroutine Map for the HMG4C Code Block , 116

4.4 Subroutine Map for the DIF3D Code Block » . . . . t 119

4.5 Multilevel Data Transfer Paths . . . . . . . , 129

A.6 Concurrent Inner Iteration Algorithm . . . . . . . . . . . 133

4.7 Concurrent Inner Iteration I/O Cycle Description (L-3, U"2) . . . . 134

4.8 A BPOINTER Example 1A6

4.9 IGTSCH/FRESCH/LOCFWJ) Exanple «. 148

ix

LIST OF FIGURES

No.

4.10 Fast-Core Allocation on IBM and CDC 7600 Machines 150

4.11 Fast-Core Allocation on a CRAY Machine 151

5.1 Input Data for the Four SNR Benchmark Problem Models 165

5.2 Input Data for the IAEA Benchmark Problem Models 168

I

LIST OF TABLES

No.

2.1 Mesh-Centered Finite-Difference Formulas 11

2.2 Areas and Volumes for Each Geometry Option 12

3.1 Microscopic Cross Section Assignments to 7>Iacroscopic Cross Sections. 61

3.2 A.DIF3D FCM and ECM Minimum Container Size Estimation 70

3.3 ECM Size Estimation for the CIIS 77

3.4 DIF3D Interface Files (CCCC and code dependent) 82

3.5 Job Region Size and Dataset Space Estimation for ARCSP021 . . . . . 85

3.6 Inner Iteration Error Reduction Effects for the SNR

Benchmark Problem 104

3.7 Inner Iteration Error Reduction Effects for the LCCEWG

Benchmark Problem 105

3.8 Inner Iteration Error Reduction Effects for a ZPPR 11(B) Model . . . 106

4.1 Data Set Classification and Description 125

4.2 Interface File Usage by Module 126

4.3 Random Access File Dejcriptions 130

4.4 Correspondence Between ECM and Disk Files . . . . . . . . 130

4.5 Execution Rates for the 2D IAEA Benchmark 155

5.1 DIF3D Tape Characteristics and its BCD File Contents 156

5.2a Contents of NESC Export Tape for IBM 370 Systems 157

5.2b Contents of NESC Export Tape for CDC 7600 Systems 157

5.2c Contents of NESC Export Tape for CRAY-1 Systems 157

5.3 DIF3D Code Blocks • . 158

5.4 Data Set Classification for the NESC DIF3D 161

5.5 Resource Estimates for Sample Problems 1-6 164

xi

PROGRAM ABSTRACT

1. Name of Program; DIF3D 4.0

2. Computer for which Program is Designed and Other Machine VersionPackages Available; IBM 370 series, CDC 7600 and CRAY-1 computers.

3. Description of Problem Solved; DIF3D solves multigroup diffusiontheory eigenvalue, adjoint, fixed source and criticality (concentrationsearch) problems in 1-, 2- and 3-space dimensions for orthogonal (rec-tangular or cylindrical), triangular and hexagonal geometries.Anisotropic diffusion coefficients are permitted. Flux and power den-sity maps by mesh cell and regionwise ilance integrals are provided.Although primarily designed for fast reactor problems, upscattering andinternal black boundary conditions are also treated.

4. Method of Solution; Mesh-centered finite-difference equations aresolved by optimized iteration methods1'2. A variant of the Chebyshevsemi-iterative acceleration technique is applied to outer (fission-source) iterations and an optimized block-successlve-overrelaxationmethod is applied to the within-group iterations. Optimum overrelaxa-tion factors are precomputed for each energy group prior to the initia-tion of the outer iterations. The forward sweep of the LU decomposi-tion algorithm for the resulting tridiagonal matrices is computed priorto outer iteration initiation in orthogonal non-periodic geometrycases.

In two- and three-dimensional hexagonal geometries the neutron dif-fusion equation is solved using a nodal scheme^"^ with one mesh cell(node) per hexagonal assembly. The nodal equations are derived usinghigher order polynomial approximations to the spatial dependence of theflux within the hexagonal node. The final equations, which are cast inresponse matrix form, involve spatial moments of the node-interior fluxdistribution plus surface-averaged partial currents across the faces ofthe node. These equations are solved using a fission source itsrationwith coarse-mesh rebalance acceleration.

5. Restriction on the Complexity of the Problem; Problem dimensions areall variable. The number of mesh cells in a mesh plane is limited onlyby the available dynamic storage (see "Machine Requirements" below).In three-dimensional finite-difference problems a concurrent inneriteration strategy permits the specification of an unlimited number ofmesh planes. Scattering is Po only and only CHI vectors are permitted.

xli

The nodal option does not permit fixed-source problems. Enough coremust be available on IBM machines to contain all data for at least oneenergy group. On the CDC 7600 machine, problem size may be limited bythe requirement that one-group data for a single axial mesh plane fitin the available fast core memory. .

6. Typical Running Time; Running time for the finite-difference calculationis roughly proportional to: flux work units (FWU) = number of spacemesh cells x number of energy groups x number of iterations per group.Depending on the options selected, rates of 4 to 8 million FWU perminute on the IBM 370/195 are typical in three-dimensional problems.CPU times on the IBM 3033 are 35 to 50% greater, than those obtained onthe IBM 370/195. CPU times on the CDC 7600 are 10 to 25% less thanthose obtained on the IBM 370/195. CPU times on the CRAY-1 with thenon-vectorized SLOR algorithm are about one-third those on the IBM370/195. The vectorized SLOR algorithm times are nearly one-fourththose on the IBM 370/195.

A three-dimensional nodal calculation with 4 energy groups and 14axial mesh planes for a fast reactor model with sixth core planar sym-metry and 17 rings of hexagons required approximately 1 CPU minute onan IBM 370/195 machine. The 6 triangle/hex finite-difference calcula-tion for this same 14-plane problem required almost 2 epu minutes. Foraccuracy comparable to the nodal option, the finite-difference calcula-tion requires 42 mesh planes and 10 epu minutes.

7. Unusual Features; The DIF3D nodal option uses a single meshpoint perhexagon instead of the six triangular meshpoints per hexagon typicallyemployed in fast reactor finite difference calculations. The higher-order axial approximation^*5 permits the use of coarse axial mesheswithout sacrificing accuracy. The nodal coupling coefficients are pre-computed and stored only for unique nodes.

DIF3D strictly adheres to the CCCC (Ref. 6) code standards and readsand writes CCCC interface datasets. For the finite-difference optionmore accurate peak power and peak flux edits are obtained by optionallycalculating average power and flux values on mesh cell surfaces. Thesurface fluxes are obtained in a manner consistent with the mesh-centered finite-difference approximation.

8. delated or Auxiliary Programs; This is a stand-alone version of theDIF3D module described in Ref. J.-5. DIF3D is included in the REBIJS-3(Ref. 7) code package, and can thus be used to provide the neutronicssolutions required in the REBUS-.l depletion calculations.

9. Status: The modular version of the code is in production use atArgonne. The standalone CDC 7600 and CRAY-1 versions of DIF3D are inproduction use at other laboratories.

10. References:

1. D. R. Ferguson and K. L. Deratine, "Optimized Iteration Strategiesand Data Management Considerations for Fast Reactor FiniteDifference Diffusion Theory Codes," Nucl. Sci. Eng., 64, 593 (1977).

xili

2. K. L. Derstlne,"DIF3D: A Code to Solve One-, Two-, andThree-Dimensional Finite Difference Diffusion Theory Problems,"ANL-82-64,Argonne National Laboratory, 1984.

3. R. D. Lawrence, "A Nodal Interface Current Method for MultigroupDiffusion Calculations in Hexagonal Geometry," Trans. Am. Nucl.Soc, _3J9, 461 (1981).

4. R. D. Lawrence, "A Nodal Method for Three-Dimensional Fast ReactorCalculations in Hexagonal Geometry," Proceedings of the TopicalMeeting on Advances in Reactor Computations, Vol. II, p. 1030, SaltLake City, American Nuclear Society, March, 1983.

5. R. D. Lawrence, "The DIF3D Nodal Neutronics Option for Two- andThree-Dimensional Diffusion Theory Calculations in HexagonalGeometry," ANL-83-1, Argonne National Laboratory, 1983.

6. R. Douglas O'Dell, "Standard Interface Files and Procedures forReactor Physics Codes, Version IV," UC-32 Los Alamos ScientificLaboratory (September 1977).

7. B. J. Topyel, "The Fuel Cycle Analysis Capability, REBUS-3,"ANL-83-2, Argonne National Laboratory, 1983.

11. Machine Requirements: At least 325K-bytes of core storage are recom-mended for program and file buffer storage on the IBM 370 series.Between 30000 and 40000 words of SCM are required on the CDC 7600depending upon the operating system employed. Additional (LCM on CDCmemory requirements expand linearly with the number of cells (N) in amesh plane. The finite-difference option requires at least 9N (8-byte)words in 2-D problems and at least 25N words are required in 3-D prob-lems. At least 19 mesh lines of data and one group of cross sectiondata must be stored in SCM on the CDC 7600. External data storage mustbe available for approximately 40 scratch and interface files.Fourteen of these are random access scratch files (grouped into 6 filegroups), the remainder are sequential access files with formatted orunformatted record types.

12. Programming Languages Used; The standard FORTRAN described in ANSSTD.3-1971 is used. The program can be executed entirely in FORTRAN,except for dynamic memory allocation routines on IBM and CDC computers,random access I/O routines on IBM computers4 and LCM/SCM transfer rout-ines on the CDC 7600. The exceptions noted above are either written inassembly language or supplied from the CDC or CRAY system libraries.Thus non-Fortran code is about 2* of the IBM package an1 about .2% ofthe CDC and CRAY package.

13. Operating System; No special requirements are made of the operatingsystem. The IBM linkage editor and the CDC or CRAY-1 overlay or seg-mented loading facilities may be used. Random access I/O data filesshould be supported for efficient operation, but they are not necessaryfor correct operation*

xiv

DIF3D: A Code to Solve One-, Two-, and Three-dimensionalFinite-difference Diffusion Theory Problems

by

K. L. Derstine

ABSTRACT

The mathematical development and numerical solution of the finite-differenceequations art; summarized. The report provides a guide for user applicationand details the programming structure of DIF3D. Guidelines are included forimplementing the DIF3D export package on several large scale computers.

Optimized iteration methods for the solution of large-scale fast-reactcfinite-difference diffusion theory calculations are presented, along withtheir theoretical basis. The computational and data management considerationsthat went into their formulation are discussed. The methods utilized includea variant of the Chebyshev acceleration technique applied to the outer fissionsource iterations and an optimized block successive overrelaxation method forthe within-group iterations.

.•>•'

A nodal solution option intended for analysis of LMFBR designs in two- andthree-dimensional hexagonal geometries is incorporated in the DIF3D packageand is documented in a companion report, ANL-83-1.

lo INTRODUCTION

This report is a user's manual for DIF3D, a computer code which uses themesh-centered finite-difference approximation to obtain numerical solutions ofthe multigroup diffusion equations in one-, two- or three-dimensions for fastreactor applications. Although two mesh-centered finite-difference codes 3DB(Ref. 8) and VENTURE (Ref. 9) were already in existence, DIF3D (Ref. 1) waswritten to employ the more rigorous strategies of the well-known PDQ-7(Ref. 10) code. This decision was based on a thorough intercomparl,?on of sev-eral iterative strategies, the results** of which indicated the iterativemethod employed by PDQ-7 (Refs. 12 and 13), when modified to take advav;r ge ofseveral unique aspects of fast reactor diffusion theory calculation, lo alsohighly efficient when applied to fast reactor calculations. Significantefforts were concurrently expended to provide efficient, yet flexible, datamanagement and data structures in DIF3D. The numerical results in Ref. 1demonstrate the efficiency achieved by these methods.

User interaction with the DIF3D acceleration and data management strategiesprincipally involves only two parameters; e^n, the inner iteration errorreduction factor, and ECMSIZ, the ECM container size. For most problems thee i n default is suitable and ECMSIZ is readily estimated. Optimizing thejob cost for a class of similar problems involves only a simple adjustmentto e i n and ECMSIZ.

Incorporated in DIF3D for the solution of two- and three-dimensionalhexagonal geometry problems is a nodal option that uses input data virtuallyidentical to that of the finite-difference option. Reference 5 discusses themathematical development and numerical solution of the nodal equations; somenumerical comparisons between the nodal and finite-difference options fortypical heterogeneous core LMFBR designs have shown that the accuracy of thenodal solution is superior to that of a standard (6 mesh cells per hexagon,5 cm axial mesh) finite difference calculation, and that this improved accuracyis achieved with a potential order-of-magnitude reduction in computationalcost for a three-dimensional calculation.

DIF3D was developed at Argonne National Laboratory and is operational onboth the IBM 370/195 and the IBM 3033 computers, and is a principal module inthe ARC System providing eigenvalue and flux calculations for the burnup codeREBUS-3 (Ref. 7), the perturbation theory code VARI3D1(t and the fluxsynthesis code SYN3D" in addition to performing standalone neutronlcs cal-culations including nuclide concentration searcnes. The programming adheresstrictly to the conventions set forth by the Committee on Computer CodeCoordination6 (CCCC). Most of the data for a calculation must be supplied inthe format of the Standard Interface Files6 defined by the CCCC. BCD inputdata (when it is required) is limited to data that is essential for theproblem (i.e. redundant information is not required), and this data may bereadily specified in free format. Particular attention has been paid tomaintaining a single unified source in which language flag comment cardssegregate code by particular and generic machine environments. A simplepreprocessor code activates or deactivates language flags appropriate to thetarget machine environment. The portability afforded by this approach isdemonstrated by the relative ease to which OIF30 is now exported and currentlyoperational in standalone form on IBM 370 series computers, on CDC 7600computers and on CRAY-i computers.

The computational efficiency and data management flexibility (achievedwith minimal user control), the user-oriented input data philosophy and thehighly portable export package combine to make DIF3D an efficient computationaltool that is a standard for the LMFBR community. Thermal reactor applicationsare routinely solved with DIF3D, also.

An overview of the major code block (modules) in the DIF3D package is pro-vided in Fig. 1.1. DIF3D features are summarized in the code abstract on pagexii. This report is organized into 5 sections. Section 2 provides users withthe mathematical and computational aspects that strongly influenced the imple-mentation of the optimized iteration strategies in DIF3D. Sections 3 and 4respectively provide user and programmer information. Section 5 is intendedfor users who have just received DIF3D from the National Energy SoftwareCenter (NESC) and who are faced with the task of making the code operationalon their machine ; it describes the contents of the NESC tapes and outlinesthe steps necessary to implement DIF3D in stand-alone form on the IBM 370series, the CDC 7600 and the CRAY-1 computers.

Fig. 1.1. Major Modules In theDIF3D Standard Path STP021

2. NEUTRONICS EQUATIONS AND SOLUTION METHODS

In this section, the "mesh-centered" finite-differenced form*6»l^ of themultigroup neutron diffusion equations is presented and is accompanied by areview of the properties of these equations that permit the application of theiterative methods chosen to solve these equations. Theoretical aspects of theiterative methods are described and the computational and data management'•onsiderations that strongly influence the implementation of the iterativemethods are discussed in turn. The equations which form the basis of thecriticality search are also discussed.

2.1 Derivation of the Mesh-Centered Finite-Difference Equations

The mesh-centered form of the finite-difference equations rather thanthe mesh-edged form10'13'18 is traditionally used in fast-reactor analysisbecause of the computational savings afforded in the calculation of theremoval and source terms in Eqs. (2.1) and (2.2).

2.1.1 The Multidimensional Multigroup Neutron Diffusion Equations

In the mesh-centered finite-difference approximation the problem domain Ris subdivided into a regular array of mesh cells such that all material inter-faces lie on mesh cell surfaces. Within any mesh cell, say R^, the materialproperties are assumed homogeneous and the time-independent multigroup neutrondiffusion equation19 for mesh cell R^ can then be written:

-V-Dfv<j,|(r) + Ej'g^(r) - Q.f(r), reR£f g = 1,2, ...,G (2.1)

where

OP

X denotes an eigenvalue, S?(r) denotes an optional distributed source, and the

remainder of the notation is standard. 3»

Equation (2.1) is solved subject to the conditions that the flux andsurface-normal component of the net current be continuous across cell inter-faces, i.e.

•f(r) - •£(£) (2.3)

(2.4)

*Homogenization formulas defining the macroscopic cross section quantitiesappearing in Eq. (2.1) and Eq. (2.2) are defined in Section 3.6. Note thatDIF3D permits x~vectors, only; x~oatrices a re not permitted.

for r on the interface between cells Ro and R . Similar relations hold for~" * TO

the interfaces between R^ and its remaining adjoining mesh cells.

Boundary conditions of the general form

<x8n'T)fi$Z(r) + e g^(r) = 0, r e 3R, (2.5)

are specified on cell surfaces which form part of the external boundary 3R ofR. Standard boundary conditions (e.g. zero flux, zero incoming partial currentand extrapolated) are obtained via appropriate specification of the surface-

dependent boundary constants a and 3 in Eq. (2.5).

When sf(r) s 0 for all I and g, Eq. (2.1), Eq. (2.2) and Eq. (2.5) definethe eigenvalue problem for which the fundamental eigenvalue (k-effective) and

eigenvector (neutron flux) are sought. Fixed source problems arise when sf $ 0and A is fixed at a user specified value ensuring reactor subcriticality. Thecorresponding flux solution is then sought.

Adjoint eigenvalue and fixed source problems determine the sclution tothe adjoint system associated with Eq. (2.1), Eq. (2.2) and Eq. (2.5).

2.1.2 The Orthogonal XYZ Geometry Derivation

The mesh-centered finite-difference equations will be derived in XYZgeometry for R^, an arbitrary mesh cell chosen from the IxJxK parallelepipedmesh cells defined by the coordinates x.,i=l,2,...,1+1, y.,j=l,2,...,J+1 and

z, ,k=l,2,...,K+1. The dimensions of R are denoted by

~ si f o r siL = (xi'yj o r *k> • (2-6>

Using a local coordinate system with the origin at the centroid of the meshcell, R^ is defined by

\ a Rijk = *- = (x,y,z> Is = (x»v or

The group index will be henceforth omitted and whenever possible the singlesubscript notation SL and m will denote R... and adjacent cell, say,

ljKRTO = Ri+ljks respectively.

We start by integrating the neutron diffusion equation over the volume ofR^, i.e. we operate on Eq. (2.1) with

IJreR

d3r • = 1 dz I dy / dx • . (2.7)

Zk yj Xi >.

Application of Gauss' Theorem to the integrated leakage term yields

6

V - V jjAj (2.8)

where A£ denotes the surface areas of E.£ with outwardly directed surface normaln (i.e. n.. = - u , n o = u , . . . , n , = u ) and u denotes a unit vector in direc-P x x . x o z stlon s. The resulting neutron balance equation may be written for each energygroup in the form

6o "*• '•o't'oVo = QoV 0 (2.9)E

P=I

where the cell-averaged values of the flux and multigroup source terms aredefined by

and

J^. the surface-averaged component of the net current in direction n atP

surface A^ is defined by

The solution of Eq. (2.9) clearly requires additional relationshipsbetween the leakages and the cell-averaged fluxes in R^ and its six neighbors.Such relationships are obtained by assuming:

(1) the flux varies linearly from the center of the mesh cell to themidpoints of any of its six surfaces;

(2) along each surface, A^, variations in the normal derivative to thesurface may be neglected.

These assumptions are equivalent to introducing a multidimensional Taylorseries expansion of the flux about the cell midpoint and truncating terns ofQ(h2) and higher.20

Application of assumptions (1) and (2) to Eq. (2.10), Eq. (2.11) andEq. (2.12) lead to Che following approximations:

= 4>£(0,0,0), (2.13)

Q£ E

where

p = 1

p = 2

= -D,3x

(x,0,0)x = Ax±/2

(2.14)

(2.15a)

(2.15b)

(2.16)

Similar equations hold for the remaining directions y (p = 3 or 4) andz (p = 5 or 6). The derivative in Eq. (2.16) is approximated by usingassumption (1). We obtain the following expression for the component ofthe net current in direction x at the boundary of cell R^:

(2.17)

Evaluating and equating two expressions for the x-directed current component

across the interface betwean cells Ro and R (e.g. J.(Ax./2) and J (-Ax. ,./2))& ni x, x is i+x

and then applying the interface conditions, Eq. (2.3) and Eq. (2.4), leads tothe following expression for the interface flux

Dm/Axi+1 (2.18)

Substitution of Eq. (2.18) into Eq. (2.17) leads to the desired expression forthe net current components

(2.19a)

or

(2.19b)

where

Similar equations are obtained for directions y and z.

When Ax./2 corresponds to an external boundary in cell R. or if cell

R = R

i +i-k *

s a blackness theory region, then Eq. (2.5) provides the relation

needed ifor determining the boundary coupling coefficient Y^, = Y* . Rewriting

Eq. (2.5) in terms of the net current we obtain

( M (2.21)

The flux at the cell boundary is obtained by eliminating J.(tAx./2) from

Eq. (2.17) and Eq. (2.21), and solving for

•£(±A,

1/2,0

10> -

D /Ax%(

g

1/a)/2 h'

(2'

22>

The general expression for the leakage term at the boundary is obtained by

substituting Eq. (2.22) into Eq. (2.21), e.g.

Iix,/2)

(2.23)

)

where

Y* - Y?A = -r- — • (2.24a)

25^+Te7^0

Rearrangement of terms 3 and a oermit evaluation of Eq. (2,24a) when a « 0 orβ - o , i.e.

10

Equation (2.13), Eq. (2.14), Eq. (2.19) and Eq. (2.23) can now be combined )to form the mesh-centered finite difference approximation to Eq. (2.9), i.e.

2 , m * m + V * =q* (2'25)

p=1 p pm ?b

where R is the cell adjacent to R. at surface A^ andmp * *

<2'26>

\ = S£V£ + y a£m (2*27)

(2.28)

2.1.3 Comments Regarding All Geometry Options

The terms Y? and the formulas for calculating the indices m < . the Pxm • pcells R adjacent to R. are tabulated in Table 2.1 for all geometry options

nip *in DIF3D. Table 2.2 tabulates the corresponding area and volur i elements thatare illustrated in Figs. 2.1-2.3. Not included here are the two- and three-dimensional hexogonal geometry options associated with the PIF3D nodal option.5

Mesh cell numbering proceeds in a poi t ^duL, row by row and plane byplane fashion for both orthogonal and trian&. geometries. Figures 2.4-2.6illustrate the mesh cell numbering for the two basic triangular geometryoptions (i.e. parallelogram or rectangular boundary domains). Includingalternately upward and downward pointing triangles in a single row, permitsthe same data structure to be used for both rectangular and triangular geometry.

The periodic boundary conditions offered by DIF3D are limited. The op-posite face periodicity option, models a repeating lattice in the "X"-directionin orthogonal geometries (i.e. R,., is coupled to R... ). The periodic coupling

i J 1C Xj KIn the ©-direction of O-R-Z geometry also fits this model.

The rotational periodicity option applies to only the lower x- and lowery-face combination which intersect at the origin in either theorthogonal or the triangular (parallelogram boundary domain only) geometryoptions. This option models the case in which the A3, surface of cells R.,,

are connected to the A™ surface of R... wheretn ijK. v

11

Table 2.1 Mesh-Centered Finite-Difference Formulas

Orthogonal Triangular8

Geometry Option1,: X,XY,XYZ T,TZ

'Am Asi

2Dm

As. As9. m

3D. 3DZ m

[Ab

3Dfl T (3/a)

: (S JH-1

p = 1 or 2d: mp = (i + 1, j, mp = <i + 1, j, k)

p = 3 or 4d: m , j + 1, k) m = (i + 6, j + 1, k) e

5 or 6d: m » (i, j, k + 1)

aAxial (z-direction) formulas In TZ geometry are identical to theorthogonal case.

Coordinates are ordered as listed (e.g. 0RZ implies "X"-0, "Y"»Rand "Z"»Z.

c^St is triangle height or 1/2 hex pitch, (2Ax = triangle side

length).dSign convention for m=mp: odd numbered p take minus '••.{-) sign,even numbered p take plus <+) sign.

eTriangular geometry offset index:(-1 parallelogram boundary domain, 60° symmetry,

6 » I 0 rectangular boundary domain,t 1 parailelogram boundary domain, 120° symmetry.:

Geometry

12

Table 2.2 Areas and Volumes for Each Geometry Optiona

I ijk

i=1.2,...,1+1

Al - Aijkj=1,2 J+l

A5 =A ZAi ijk

K=l,2 K+l

'ijk

XY

Ax.

XYZ

R

RZ

AyjAZk

2ur i

27rr1Azj

QR

QRZ

TZbe

Ar,

A rj A zk

2Ax

}j(i)2Ax

n(t)2Ax

n(t)2AxAz

n(t+j-l)?(i)2Ax

( ri+r ri ) , r A zj

\ \ (rf+rrj)A0iA2k

Ax2Az

TZbd y(i)2AxAz n(t+j-l)C(i)2AxAz Ax2Az,

aUnless otherwise noted, indices (i,j,k) take the values l=1,2,...,I,

A p - A^p

j=l,2,...,J and k»l,2,...K. Note that A p - A^, p • 1,3,5 where m is givenD * Pin Table 2.1.

b"T" denotes the triangulai geometry option. n(t) « mod(t,2) accounts for thefact that alternate "y-direotion" surface areas are non-existant.

cParallelogram domain boundary option with 60° (t • 1) or 120°(t • i+1) symmetry.dRectangular domain boundary option with 90° symmetry (t « i+1), 180* symmetry(t - i-ttlTHPT) or full core option (m - i-rtITHPT) where NTHPT » (1 or 2) isdefined in the GEODST description (Appendix C). The functions

account for the fact

that K... and Rj>k are always half triangles.

13

Fig. 2.1. X-Y-Z Volume Element

Fig. 2.2. 6-R-Z Volume Element

14

Fig. 2.3. Triangular-Z Volume Elements

Fig. 2.4. Parallelogram Boundary Domain (120° planar symmetry)

15

Fig. 2.5. Parallelogram Boundary Domain (60° planar symmetry)

Fig. 2.6. Rectangular Boundary Domain (90°, 180*or 360° planar symmetry)

16

j"i, i=1,2,...,I in orthogonal geometry;

je(i+l)/2, 1=1,3,5,... in triangular geometry (60° symmetry);

j=i/2, 1=2,4,6,... in triangular geometry (120° symmetry).

Conversely, cells R-,*. are connected to R.-,. where

i=j, j=1,2.,..., J in orthogonal geometry;

i=2j-l, j=1,2,...,J in triangular geometry (60° symmetry);

i=2j» j=l»2,...,J in triangular geometry (120° symmetry).

2.1.4 The Matrix Equations and Their Properties

The mesh-centered finite-difference equations (Eq. (2.25) in eigenvalueform) for the cell-averaged fluxes can be written in matrix form as

" V + Izg])*g - E [Tgg,1V = i [ V £ [ V ] V (2-29>

where £ is the N-dimensional vector of (approximate) fluxes on the finite

difference mesh. The matrices [Z ], [T , ] , [F ] and [x ] are NxN diagonal, o So S §

matrices defined by

[Sg] = diag (^,gV£) (2.30)

[T .] = diag (£j,gg'Vj) (2.31)

[Fg] - diag <vz£,gV£) (2.32)

6diag (xf) (2.33)

*

where N is the number of cells in the finite-difference mesh. The unknownsin $ are ordered in a linear fashion, row by row and plane by plane. Given

this linear ordering, the NxN matrix [D ] contains three, five or seven

nonzero stripes for one-, two- or three-dimensional geometries, respectively.It operates on 6 to yield the net leakage across the faces of each mesh cell

O

17

The GEqs. (2.29) can be condensed into the single matrix equation

(2.34)

where [M] and [B] are square and of order N*G and $

The matrix [M] is given by

= col , <|> , ...,

[M]

[0]

[0] [AG]

[T1G]

I T G,G-1 ]

[0]

(2.35)

where [A ] (= [D ] + [2 ]) is the leakage-plus-removal matrix operator and [0]

is the null matrix. As shown in Eq. (2.35), the ln-group scatter term is ignoredin DIF3D. The symmetric matrix A is defined by

J-lkJ JkJ

JkJ

(symmetric)

[0]

fAgZ 1l A J - l k + l J

FAgzl AJk+l

lk+2

(2.36)

where the submatric.es in Eq. (2.36) are defined in terms of coefficients

a® = a , p-1,3 or 5 and b . = b from Eqs. (2.26) and (2.27):

b l ~

"a b2 "a3

a

(2.37)

(2.38)

and

18

IA^J » dlag CaJ)Jkg. (2.39)

By defining the N*G by N matrices

[P] = col [[F^, [F2], ..., [FG]] (2.40)

l ] , [X2J, ..., fX

the matrix [B] can be written as

[B] = [X][F]T, (2.42)

where T denotes the transpose of a matrix.

The matrices used in Eqs. (2.34)-(2.42) possess a number of propertieswhich provide a sound theoretical basis for the iteration methods which arediscussed in Sec. 2.2. For any physically realistic set of assumptions, thediagonal matrices [T , ] , [x ] and [F ] are non-negative matrices. It has

been shown21 that the matrices [A ] are irreducible Stieltjes matrices and that

the inverse of each fA ] has all positive entries, i.e., [A ] >0. Because ofg cr

0 0 v

these properties, the matrix [MJ is nonsingular and the eigenvalue problemEq. (2.34) can be written as

X • = [M]-1[B] ». (2.43)

Under quite general conditions, Froehlich23 has shown that Eq. (2.43) has aunique positive eigenvector $„ and a corresponding single positive eigenvalue

XQ greater than the absolute value of any other eigenvalue of Eq. (2,43).

Furthermore, any positive eigenvector of [M] [B] is a scalar multiple of [$]*

The properties of [B] permit a reduction of the matrix eigenvalue problemwhich must be solved to obtain XQ from one of order N*G (Eq. (2.43)) to one ofonly order N.12 Advantage is taken of this fact in obtaining the outeriteration method presented in Sec. 2.2 which is used to obtain A. and *-.

This reduction is accomplished by first noting that [Mj-ifB] is of order N*Gand therefore has N*G eigenvalues. However, the rank of [F] is only N, thusmaking the rank of [M]~*[B] only N. Hence, (G-1)*N of its eigenvalues arezero. The nonzero eigenvalues can be determined by considering the reducedbut equivalent problem of order N.

Following Ref. 12, but considering r full scattering matrix, this reduc-tion is accomplished by first defining the fission source vector, £, as

G

4 i [FjT * - ] £g-f

and the K*G x N matrix [L] as

19

[L] = col [L^, [L2], .... [LG] [M]-1 (2.45)

where the N x N matrices [L ] are defined asg

(2.46)

These definitions plus Eq. (2.34) permit the group g flux vector £ , to bewritten as **

(2.47)

Premultiplying Eq. (2.43) by [F] and using Eqs. (2.42) and (2.44) yields thereduced problem

(2.48)

where

[0] = II] - (2.49)

,-1IB],If £ and A. are an eigenvector and corresponding nonzero eigenvalue of [M]then ](; and X must be an eigenvector and eigenvalue of [Q] and vice versa.Furthermore, by making use of a similarity transformation, it has been shown12

that the nonzero eigenvalue spectrum of [0] is identical to the nonzero

spectrum of [M] [B] and that any non-negative eigenvector of [Q] is either ascalar multiple of £_ or else corresponds to a zero eigenvalue, whera jJ/_

corresponds toare equivalent.

u. Thus the two eigenvalue problems, Eq. (2.43) and Eq. (2,48),

2.2 Solution Strategies

The finite-difference equations are solved by the well-known fission sourceiteration method2** accelerated by the Chebyshev semi-iterative method.25*26

At each fission source (or "outer") iteration, the vector of neutron fluxesfor each group is computed by solving the finite-difference equations with aknown group-dependent source term. This solution is accomplished via sucessivesweeps through the spatial mesh. Each such inner iteration sweep iterativelyinverts the leakage-plus-removal matrix operator using the line-successive-overelaxation procedure.2?

The acceleration strategies for DZF3D are linear, well-founded and proven,and they relieve users of the burden of specifying optimum parameters for largeclasses of reactor models. Theoretical aspects of the two acceleration methodsare presented in Sections 2.2.1 and 2.2.2, respectively. Computational anddata management aspects of each method are described in Sections 2.2.3-2.2.5.The adjoint problem is discussed in Section 2.2.6. Problems with upscatteringare solved using the iteration strategy reported in Section 2.2.7. Section2.2.8 describes aspects of the inhomogenaous problem.

20

2.2.1 The Chebyshev Accelerated Outer (Fission Source) Iterations

The outer iterations seek to determine the fundamental eigenvector, ty^,and corresponding eigenvalue, A , of Eq. (2.48) or the fundamental eigenvector,*„, and A- of Eq. (2.43). Most few-group codes, such as PDQ-7, treat the fluxproblem, Eq. (2.43). This is due to two factors. First, most thermal powerreactors of interest have large reflecting regions which contain no fissionablematerials. For any outer iteration method which utilizes an outer iterationacceleration procedure such as the one described in this report, accelerationof the fission source does not markedly improve acceleration of the solutionin these reflecting regions unless much additional effort is invested in theinner iterations. This point is elaborated in Sec. 2.2.4. Second, for thetwo to four energy group structures which are typically used for thermalreactor calculations, the data storage and transfer requirements associatedwith acceleration procedures based on the fluxes are not prohibitively largerthan if the fission source were used.

In fast reactors, on the other hand, the data management requirementsassociated with accelerating the flux vector are at least an order ofmagnitude greater than those associated with the fission source for the ten tothirty energy groups which are typically used for fast reactor calculation.In addition, the fast reactor cores under consideration at the time of DIF3D'sdevelopment tended to be more tightly coupled with relatively small non-fissionable regions. Consequently, the cost of the increased number of outeriterations resulting from the fission source acceleration is more than com-pensated by the savings in I/O resources. These conclusions are borne out bythe numerical results presented in Ref. (1). Later, application to large-scale heterogeneous fast reactor core designs^ also proved highly efficient.

In the method reported here, approximations to A and \jjn, the fundamental

eigenvalue and eigenvector of [Q]> are obtained by the well-known power itera-tion method. It is assumed that the eigenvalue spectrum of [Q] satisfiesA0>|A >| A J >.. . > IA . I and that ijj. is the eigenvector associated with A .

The power method proceeds as

(2.50a)

and

(2.50b)

where n is the outer iteration index and . ||* || . denotes the Ln norm. The

actual computation of the product [Qljjj in Eq. (2.50a) involves, anotherlevel of iteration, the inner iteration, and is discussed in the next section.A later section describes a third level of iteration, the upscatter iterationwhich occurs outside the inner iteration ir all groups when upscatteringsource terms are present.

21

Because the largest (in modulus) eigenvalue of [Q] is real and simple,the power method is guaranteed to converge for any arbitrary non-negativeinitial vector ^ to Xo and c^0, where c is some positive constant. If itis assumed that the eigenvalue estimates X are sufficiently well convergedto X~ and that £ can be expanded in terms of the J|J. , the eigenvectors of[Q], then the rate at which |j; converges to ^ depends on the separation ofA n from the other eigenvalues of [Q].*2 This convergence rate depends on thedominance ratio, a, given by

lila = max —-— , (2.51)

±1*0 A0

with the convergence rate ultimately being controlled by (a) .

The dominance ratios of large thermal power reactors typically are of theorder of 0.95 or larger, implying relatively slow convergence of the iterativeprocess given by Eq. (2.50). This fact led to the search for methods toaccelerate this convergence for thermal reactor codes, of which the accelera-tion method based on Chebyshev polynomials used by PDQ-712>13 and the classof methods known as coarse-mesh rebalance23'21* methods are the best known.Dominance ratios for large heterogeneous fast reactors can also be as large as0.95. In addition, typical fast reactor multigroup energy structures arecharacterized by nearly full downscattering matrices. The group-by-groupcalculation of the scattering source required for each outer iteration becomesa costly, input/output-bound calculation when such energy structures are usedin large multidimensional calculations. Both of these factors motivate the useof ? efficient outer iteration acceleration technique in fast reactor diffusiontheory calculations.

A Chebyshev acceleration strategy similar to that used in PDQ-7 isutilized in the solution method presented here. The primary difference isthat while PDQ-7 accelerates the flux vector, $, DIF3D accelerates the fissionsource, ty . The motivations for this have been presented above. Its applica-tion is based on the assumptions that the eigenvalues of [Q] are real and non-negative and are ordered as Xfl>X,>X2>...>XN_.>0 and that the eigenvectors

\K of [Q] form a basis for the N-dimensional vector space. Following thederivations in Refs. 12 and 13, the basic power iteration is accelerated bychoosing a linear combination of the eigenvector iterates ^ such that

where n* is the outer index where this acceleration begins and p succet "ivefission source iterates are employed. The objective is to choose the coefficients such that jji ^ approximates $u more closely than does \ji ^* .

22

(n*)Based on the assumption of completeness, ip can he written as

N-l

j<»*> = V c f . (2.53)^ — * ± • * •

i=0

For a sufficiently converged eigenvalue estimate X/n , Eqs. (2.50a) and (2.53)imply that Eq. (2.52) can be written as

N-l ^ /x .

*""* i,_ l-r) #*• (2.54)

Letting P (x) = \ ^ a. xP, Eq. (2.54) becomes

j=0

\ N-lci p

P ("r jh- (2,55)

The sum on the R.H.S. of Eq. (2.55) is the error. This error is minimized ina practical sense by choosing P (x) such that P (1)=1 and max P (x) is

P P o<x<a Pminimized. This is accomplished by choosing P (x) in terms of Chebyshevpolynomials as25 p

c (¥ - i)P (x) = -P-l —, (2.56)p C it-

p\0

where the C (y) = cosh (p cosh~^y), y > 1 . Given the well known recurrence

relationships for Chebyshev polynomials, the recursion relationship for P (x) is

_ /cO8h[(p-l)Y]\\cosh[(p+l)Y] i p-l P

23

where

P,(x) = " ' , (2.58)

(I "I)and

Y = cosh "(I -11. (2.59)-(«-)•

This leads to the accelerated iterative procedure for p > 1 :

\ (2.60O

~(n*+p) = ~(n*+p-l)1 1 «pi

(2.6,0b)

(n*+p) _ (n*+p-l)

where

'2a l = 2:::a

_ 4 /cosh[(p-l)Y]ap - f \

To apply the iteration schemes given by Eqs. (2.50) and (2.60), thedominance ratio o must be obtained and a suitable convergence criterion must

be applied to measure convergence. It has been shown21 that if $r ' is a non-

negative vector, then lim A • Ao and lim jjr • cin* *n addition, if the

i-th components of ij; ""*1^ and ^n^ are written as ^ n 1 ^ and / n^ and if X

and A are defined

24

X ( n ) = max ——=-7 , X ( n ) = min * .. , (2.62)(n'1) ~ (n"1)

then

X ( n ) > Xo > X( n ) , X ( n ) > X ( n ) > X ( n ) , (2.63)

and

lim X ( n ) = lim X ( n ) = X,

Thus,. X •' and X^n^ provide upper and lower bounds on the eigenvalue estimatebased on the behavior of the cellwise fission source components. Because theyare related to the behavior of the individual components, they also provide

insight into how well the individual components of ty are converged. By

defining the relative point error, e , as

.(n) =evl' = max-Pt

1KOi

(2.64)

where ^n is the i-th component of i|>n, the true result, and

, x r(n) ,(n), A - A(2.65)

it has been shown13 that, for n sufficiently large, G is approximatelybounded as

! - ; + « ~ V ~ x . ; . 2e(n+l> • (

This relationship provides a measure of maximum relative error in any of the

components of ijj * The precise manner in which this measure is applied tocheck fission source convergence here is discussed in Sec. 2.2.4,

An estimate of the dominance ratio 9 is required both in the fissionsource extrapolation process given in Eq. (2.60b) and in Eq. (2.66) above.

One such estimate can be determined by defining the error vector R as

R<n> = <,<«> . #(n-D (2.67)

25

and the decay rate of the error, E , as

<R(n)>R(n)> I 1/2(2.68)

where <,> denotes an inner product.

For the power method of iteration,13

lira En *»

(n) (2.69)

Several key algorithmic details associated with the application of thepower iteration and Chebyshev acceleration procedures remain to be discussed.These include (a) determining when to start the first acceleration cycle,(b) obtaining improved estimates of the dominance ratio as the accelerationcycles proceed and (c) determining when to start a new acceleration cycle.These are discussed in Sec. 2.2.3.

2.2.2 The Line Successive Overrelaxation of the Inner Iterations

The inner iterations are required in carrying out the operation [Q]ij;on the R.H.S. of Eq. (2.50a) and (2.60a). From Eqs. (2.46) and (2.47),[Qjjjj can be written as

(n-1)

(n-1) _ (n-1) = x(n-l) (2.70)

where

(2.71)

Given the n \ [Qljfe and hence $rof [L 1, Eq. (2.46), defines a series of linear equations

can be easily obtained. The definition

[A J4 • b , g-1, Z, ...» G,o o o

(2.72)

which can be solved for the gx;oup flux vectors

26

The source b is given by (see Eq. (2.112b) for the upscatter problem)

g V ^ + I R T 1 ^ ' (2-73)

For multidimensional problems, the direct: inversion of [A ] matrices in

Eq. (2.72) is not practical. The iterative inversion of [A ] for each group

comprise the inner iterations.

Because of its sound theoretical basis and computational simplicity (seeSec. 2.2.4), the line successive overrelaxation method has been chosen for thesolution strategy reported here. The matrix [A] in Eq. (2.72) (dropping thegroup subscript) is split as 2 7

[A] = [D] - [E] - [F], (2.74)

where [D] contains the diagonal of [A ] plus those off-diagonal coefficients

which represent coupling between cell fluxes in each row, [E] contains thoseblocks of [A] which lie below the diagonal blocks placed in [D], and [F]contains those blocks which lie above the blocks in [D]. The line successiveoverrelaxation procedure is then given by

= [Lu]£v ' + k , (2.75)

where

[LJ = ([D] - a)[E])~1(a)[F] + (l-a))[D]) (2.76)

and

kg = ([D] - to[E]) 1ta bg. (2.77)

The matrix [L ] is the line successive overrelaxation iteration matrix and <u

is the overrelaxation factor; both are group-dependent. Because [A] (for eachgroup) is an irreducible consistently-ordered 2-cyclic Stieltjes matrix forthe finite differencing schemes used here, the iteration procedure given byEq. (2.75) is convergent for Ku><2.29 Furthermore, there is an optimum valueof a>, say u , for which the convergence is the most rapid. This group-dependent value of u>, is given by2^

w - 1 -nr , (2.78)b 1 + [1 - P U L ] ) ] 1 ^

where p( [I*. ] > is the spectral radius of [L,}, the associated Gauss-Seidel

Iteration matrix, which can be obtained from Eq. (2.76) by setting u>1,

27

Following the procedure outlined in Ref. 30, the value of o> c a n e

determined to arbitrary accuracy because the [A] matrix for each group has the

properties listed above. For such matrices, if x >0 and if

x(H) s [Ljx^-^ I (2.79a)

and

<x(m) (m)

5 = ~<™\ ~(m 1) ' (2.79b)( m ) ( m _ 1 )

then

lira 6 ( m ) = p([L ] ) . (2 .80)

Furthermore, if x^","1^ £ 0 and if

x 0 > x ( )5<m) = max - i ^ p - ; 6 (m) = min 4 r T Y ' <2'81>

^ " 1 } " ^ " 1 J

then

and

lim,6(n5) = lira 6(m) = P([L]). (2.82)

The spectral radius p([L.]) can be computed by carrying out the iteration given

by Eq. (2.79a), computing 6 , 6 W and 6 , and monitoring their convergence

to one another. The computational details involved by implementing thisprocedure for computing a>. are discussed in Sec. 2.2.4.

28

2.2.3 Outer Iteration Computational Considerations

The obvious ultimate goal of the outer iteration procedure is to be ableto apply the Chebyshev acceleration procedure given in Eqs. (2.60) withaccurate estimates of both Aft and o. However, since neither An and a are known

when the outer iterations are commenced, a "boot-strap" process is required.As reported in Refs. 12 and 13, it has been found advantageous to perform alimited number of power iterations, Eq. (2.50),_initially to provide a reason-able estimate of A_ and an initial estimate of a, which is generally quite low.

A series of low-order extrapolation cycles are then utilized, during which the

higher overtones are rapidly damped out and raore accurate estimates of a areobtained. Only when all but the first overtone mode are essentially damped

out are high-order cycles based on accurate estimates of a utilized.

The precise algorithm can be described in terms of four basic parts asfollows:13

1. A minimum of three power iterations using Eq. (2.50) are performedinitially. The first Chebyshev acceleration cycle is begun on outeriteration n*+l, where n*+l is the smallest integer such that n*>3 forwhich the dominance ratio estimate, a satisfied the criterion

0.4 < a < 1.0,

where Eq. (2.68) is used to estimate a. That is,

,(n*)(2.83)

2. Using 0 as the dominance ratio estimate for a in Eq. (2.61), theaccelerated iterative sequence given by Eq. (2.60) is carried out foriterations n*+p, p>1. At first, low degree polynomials are appliedrepeatedly, with the estimates of the dominance ratio being updatedcontinuously according to

I {cosh

where

cosh-1(Y)p-1

+ 1 (2.84)

(2.85)

En*,p-1(2.86)

29

3.

4.

and C , is the Chebyshev polynomial of degree p-1. The polynomials areat least of degree 3 and are terminated when the error reduction factor

n*,p-l is greater than the theoretical error reduction factor:

En*,p-1 >

!2 - o1

-p-1'

-1(2.87)

The theoretical error reduction factor is the error reduction which wouldhave been achieved if o were equal to o", the true dominance ratio. IfE -i is greater than this, the acceleration cycle has not been asn*,p—1effective as it should have been, so a new cycle is started using theupdated dominance ratio estimate, a', from Eq. (2.84).

It has been found^judicious to limit the rate of growth cf the dominanceratio estimates, o,, during the early stages of the iterative process.Denoting the dominance ratio estimate to be used to start a new polynomialcycle (p=1) at iteration n*+l as cr, o is constrained as

min (a,, 0.9) , n*+l < 6

(2.88)min (a,, 0.95) , n*+l < 9

min (a\ 0.985), n*+l < 12

min (a,, 0.99) , n*+l > 12

Though seldom needed in fast reactor problems, these constraints helpsmooth the convergence process in problems characterized by largedominance ratios.

After the estimates for 5 have converged, higher degree polynomials areapplied. In fact, the process described in part 2 above is appliedcontinuously. The length of the cycles increases naturally due to theimproving estimates of 3,

The outer iterations are terminated at outer iteration n if the followingthree criteria are met:

.(n) (2.89)

(2.90)

(n) _ <keff eff e k •

(2.91)

30

where e., e. and e, are input parameters. The test specified in Eq. (2.89)

is a measure of the pointwise eigenvector convergence and is based on thebounds placed on the relative point error in the relationship (2.66). In

computing e , only cells in which the fission source has some minimum(user-specified) relative size are considered. The test (2.90) is ameasure of the average rate of convergence of the eigenvector (the fissionsource), while test (2.91) is a measure of the eigenvalue convergence.The k estimate at the end of n iterations is taken from

eff eff , v , ,. 1/2

Experience has shown that if e and e are assigned equal values, the test

(2.89) almost always controls convergence. The same tests (2.89)-(2.91)are applied after each outer iteration is completed, regardless of whetherthe iteration just completed was a power iteration or an acceleratediteration.

2.2.4 Inner Iteration Computational Considerations

Computational considerations arise concerning three aspects of theinner iterations. These are the computation of the optimum overrelaxationfactor ui, for each group, the determination of the number of inner itera-tions which should be carried out for a given group at a particular outeriteration and the actual procedure used to solve the tridiagonal matrixequations which characterize the line successive overrelaxation method.

It has been shown in Sec. 2.2.2 that the optimum overrelaxation factorfor a given group can be computed if the spectral radius of the, line Gauss-Seidel matrix, p([L-]), is known. The procedure outlined in Eqs. (2.79)-

(2.81) provides a rigorous method for determining p([L ]), With the coding to

carry out the inner iterations using the line successive overrelaxation methodalready in place, the implementation of this procedure is trivial, since [L-]

is equal to [L ] with u) set to unity. The vector k in Eq. (2.75) also has

to be set to the null factor.

In order to Insure that the actual outer and inner iterations are asefficient as possible, this computation of the overrelaxation factors is doneprior to commencing the first outer iteration. Starting with an arbitrary

non-negative initial guess x > the iteration in Eq. (2.79a) is carried out

for m » 1 to 10. Following each iteration for m > 10, the quantities 6*

and 6^m' are computed. The related quantities urn , u> ^ and w ,

defined by12

31

«<•> =

?-(ml 1/2*

1 + (1 - A^- ,) 1

and

,(tn) -0)

are also computed. The iterations for a given group are terminated when either

« -4 , (2.94)w - w

or m = M, where M is a user controlled iteration limit; u, for that group is(m)

set to 0) . The test given by Eq. (2.94) forces tighter convergence as p([L ])

increases. The amount of CPU time required to precompute the o> is typicallyon the order of one or two outer iterations.

The theory presented in Sec. 2.2.1 on the Chebyshev acceleration methodimplicitly assumes that the matrix equation for each group, Eq. (2.72), issolved exactly during each outer iteration. For multidimensional problems,this is not the case. It has been shown^ that the effect of solving Eq. (2.72)iteratively to less than infinite precision for each group is to modify some-what the system of equations being solved. Although both systems share thesame fundamental eigenvalue and eigenvector, the dominance ratio of themodified syst'em is larger than the original system, Eq. (2.48). Some of theeigenvalues of the modified system may be negative or complex, which wouldslow convergence of the outer iterations.

The most practical solution to this problem is to do a sufficient numberof inner iterations for each group during each outer iteration so that theeffect on the dominance ratio is not appreciable, yet no more than this. Ithas been determined experimentally for a range of typical fast reactorproblems11 that this can be achieved most economically by doing a fixed numberof iterations, m , for each group during each of the outer iterations. Thisgeliminates the need for any convergence checking during the inner iterationsand thus eliminates the costly divides which would have to be done to determinerelative convergence on a component-by-component basis.

This number mg Is determined for each group by requiring that the normof the continued product of the iteration matrices for that group during eachouter iteration be less than some desired (user controllable) error reductionfactor. This assures that the norm of any of the components of the errorvector is greater than or equal to this error reduction factor during each

32

outer iteration. For a variant of the line successive overrelaxation methodof Eq. (2.75), where a single Gauss-Seidel iteration precedes (m-1) successiveoverrelaxation iterations, the norm of the continued product of the iterationmatrices is given by26 ,

m i n 9 \ o 1/2L*"1] [L 1 = [tf, U t M , m > 1, (2.95)

co|j J- II2 Zra-1 u&

where

tm - [a^ - l ] ( m " 1 ) / 2 - [ p ( L 1 ) ] 1 / 2 U +. (m - 1)(1 - [pO-p] 1 7 2 ) ] . (2.95b)

The single Gauss-Seidel iteration is applied because the norm in Eq. (2.95a) isthen strictly decreasing for m > 1. Letting e be the desired error reduction

factor and given e, and p(L.. ) for a group from the optimum overrelaxation

factor calculation just described, Eq. (2.96) is solved to determine that valueof m such that

The value of m so obtained is the fixed number of inner iterations, m , that

are done for group g for every outer iteration. There is no direct user controlover m ; it is always computed from e. .

"'Experience has shown that choosing e < 0.04 will result in no adverse

impact on the outer iteration convergence rate for typical fast reactorproblems. For problems with dominance ratios larger than 0.85 (large reactors),a value cf e as small as 0.01 is sometimes necessary. It is quite obvious

when a value of e which is too large for the problem at hand has been chosen.

The dominance ratio estimates being obtained from the outer iteration grow toolarge, and oscillatory behavior of the acceleration cycles generally results.

A great percentage of the total CPU time required to solve large problemswith this solution method is spent in the inner iterations. In implementingthe algorithms used to carry out these iterations, it is essential that thefull capabilities of the large-scale scalar scientific computers for whichDIF3D was designed be utilized. A feature shared by some of these computersis the high speed instruction stack, from which significant gains in executionspeed can be obtained when repetitive instruction sequences can be contained inthis stack. Multiple functional units and instruction segmentation permitparallel execution of several arithmetic operations, loop indexing and thestoring and fetching of data.

The requirements for utilizing these features efficiently include thefollowing: (a) compact coding for loops, (b) no conditional branchingperformed within the loop, and (c) avoiding divisions whenever possible. Theone-line successive overrelaxation method was chosen in part because it issimple and can be coded compactly. Performing a fixed number of inneriterations for each group eliminates the need for the divides and conditional r-branching which usually accompanies convergence checking. Finally, by utilizing

33

the procedure outlined below, it is possible to eliminate all divides andconditional branching from the innermost loops of the inner iterationalgorithm and reduce those loops to a few lines of machine language codingwhich easily fit within the instruction stack on, say, an IBM 370/195 or aCDC 7600.

For a particular line of fluxes which are computed simultaneously duringeach inner iteration, the equations which must be solved are of the form

where j and k are the row and plane indices of this line, [A®, ] are the

matrices given by Eqs. (2.37)-(2»39) and the flux values Qn, and <t>TJ,,,>UK. J iJ.it

k=l,2,...,K, and £ n and £-K+1» j=l»2,...,J are null. The solution ofEq. (2.97) utilizes a variant of Gaussian elimination to perform the LUfactorization of the tridiagonal matrix [A* ].

jk

The forward elimination on the matrices [A , ] is performed only once,

prior to the beginning of the outer iterations, in such a fashion as to elimi-nate the need for further divides in computing the <{>., . The backward sweep

and overrelaxation are then combined in a single loop to save memory fetchesand stores.

We define I. = a* in Eq. (2.37) then the forward elimination on [A3?,] is

d. - J, (2.100a)1 bj

Ui(2.100b)

„ i = 2, 3, .... I.

(2.100c)

The d. values are saved for subsequent use in the inner iterations by storing

over the b, values, which are no longer needed. Given s . for one inner

Iteration, the forward sweep on it is given by

yx » s ^ , (2.101a)

34

2>3» •••» I> (2.101b)

where s. is the i-th component of s.,. A second loop then performs thei —J *t

remainder of the work on line j,k according to

(m)), (2.102a)

1.

(2.102b)

(2.102c)

This procedure permits very efficient use of the arithmetic capabilities ofhigh speed scalar computers.

When periodic boundary conditions (e.g. next-adjacent-face periodicity oropposite-face periodicity) are present, the solution procedures given byEqs. (2.97)-(2.102) require modification. The changes are minimized bypermitting periodicity with respect to the domain boundary coincident withcoordinate x., only. Consequently, next-adjacent-face periodicity couples the

x1 and y1 faces; opposite-face periodicity couples the x. and xT faces. Thechanges are summarized for two cases.

Case 1: Next-adjacent-face Periodicity

The following modifications are required:

(1) Replace diagonal element b^ in (see Eq. (2.37) by

x ybi - ai " a r

(2.103)

The elements of are unchanged for j > 1

(2) Replace transverse leakage terms s. = s... in s , (Eq, (2.101)) by

ijk

.On)TLik

(2.104)

j>1, 1-1

35

Case 2: Opposite-Face Periodicity

The matrix IA°£] associated with the opposite-face periodicity option has

the special form (i.e. tridiagonal with two additional entries as indicated)

bl "a2

where

-a. b2" a3

X

*1

X , X

"ai-ibi-rai

(2.105)

x _ gxa l = a (2.106)

The LU decomposition of this matrix is straightforward to derive. The resultingsolution algorithm is summarized in the following equations.

x

given by

90

Define A = a^, then the forward elimination sweep on [A?i] and on s., is

ai - 2> ze« - ° (2.107a,b,c1)

u yl = 8ldl (2.107d,e1,f2)

0 i - l = Gi-2ui-l

ex.

u.i - 2,3,...1-1

(2.107g)

(2.107h)

(2.10711)

(2.1O7J)

(2.107k1)

(2.107A2)

36

*I = *I + ©I-2UI-1 (2.107m)

UI = (*I+*I-lUI-l)dI-l (2.107n)

dj = (bj -jijuj -r e a>_ 1 (2.1070*)

1-2

°iI ) dI (2.107p2)i=1

Equations (2.107) may be arranged into two overlapping subsets so that thediagonal terms arising from the LU decomposition may be preinverted prior tothe start of the outer iterations. Equations (2.107) with superscripts 1 or 2apply to the preinversion step or the forward elimination of s ,, respectively.The non-superscripted Eqs. (2.107) apply to both steps. •*

The back substitution to complete the work on line j,k proceeds accordingto

Xi = yi

0 x = v A y = A + (x - AV ') (2 108a)

(2.108b)

•l(m+1) _ (m) , (m)

i = 1-1,...,2,1.

(2.108c);

The matrices [A?, ] obtained for triangular geometry options with non-3

periodic and periodic (next-adjacent-face periodicity only) boundary conditionsare nearly identical to those obtained in the orthogonal geometry case. Conse-quently, the same general solution algorithms and data structures are applied.

Two aspects in which triangular geometry problems differ from orthogonalgeometry problems lead to the two modifications detailed below.

First, because realistic reactor core models do not fully encompass eitherthe rectangular or parallelogram problem domains required in the triangulargeometry option, provision is made for the specification of background(unoccupied) mesh cells. Computational and physical considerations lead tothe stipulation that the projection of the region of solution of the K planesbe identical. Therefore, the majority of the background cells may be excluded

from the calculation if iterations over line jk are over cells i » I®, 1^+1,

...,I^ where I^ and I^ are the first and last "active" mesh cells on a line*

Occasionally, the reactor outer boundary is so Irregular that one or moreS 6

background mesh cells appear within the active mesh limits I < i < I of aJ J

line. The leakage coefficients afjj. and the initial flux guess ^ . are setto zero In such a mesh cell, thereby permitting computations to proceeduninterrupted for the entire active mesh line.

37

The second difference between orthogonal and triangular geometry concerns

the structure of the matrices [A?£]. Like their orthogonal geometry counter-

parts, the matrices [A^] have a single stripe. In the rectangular boundary

domain option, this stripe is located on the main diagonal. In the parallel-ogram boundary domain option, however, the stripe is located either on the

first super- or sub-diagonal of [A?£] depending on the symmetry option (120° r.

or 60°). In triangular geometry alternate elements of the diagonal stripeare zero corresponding to the fact that alternate y direction surface areasare nonexistent in the mesh ordering chosen here (see Figs. 2.4-2.6).

Thus in general the matrix [A°-J is defined (for I odd, say) by

90

60

120

0

0

0

90a 3

60a.

a 1 2 0

0

60 0

0

0

90

(2.109)

t ywhere a. denotes the coupling coefficient a;f

corresponding to geometry option

t. When option t is active all elements a. , tVt are zero.denotes all rectangular domain symmetry options (e.g. 90°

Note that t=90180*? or 360°).

When t^90, the pattern of null super- or sub-diagonal elements is fixed. Whent=90, the null entries begin on odd or even mesh cell indices depending uponthe orientation of the first triangle in a given row. Knowledge of this

special substructure of the [A^] leads to the following general algorithm for

calculating the transverse leakage source in triangular geometry:

sijk ijk*ijk-l + f o r a U

where the same conditions apply to Eq. (2.110) as apply to the orthogonalgeometry algorithm Eq. (2.99). The term BY.. is defined by

? r v 2 (2-ma)

38

%, ±~t

-2.3.....J J,,t +z,...,1^ra

(2.111c)

ei,j.k * •l,Jik*i-*.j-l,k J-2.3.....J, i-lj, m.=2 (

sf . . = 0 otherwise t (2.111e)i j K

where

I 1 : parallelogram boundary domain (60° symmetry)J 2 : parallelogram boundary domain (120° symmetry)jmod(j+NTHPT,2)+l: rectangular boundary domain (NTHPT*-1 or 2)

m = mod (I - t - 1, 2)

J 0 : rectangular boundary domain-1 : parallelogram boundary domain (60° symmetry)+1 : parallelogram boundary domain (120° symmetry).

2.2.5 Data Management Considerations

Strong consideration must be given to data management implications ofany solution method that is contemplated for use in a code capable of treatingproblems where the number of space-energy unknowns can exceed 106, From theprevious sections, it is obvious that such considerations have influenced theform of the solution method presented here. These considerations aresummarized in this section.

The prime goal of the solution strategy described here is to reduce thenumber of outer iterations to a minimum, even at the expense of investingrelatively greater effort in the inner iterations performed during each outeriteration. By minimizing the number of outer iterations, the number ofscattering source calculations (one per group per outer iteration) is kept ata minimum. These scattering source calculations necessitate the transfer oflarge amounts of data from peripheral storage to core memory for problemsutilizing 10 or more energy groups, yet there is little arithmetic to be donewhile these data transfers are taking place. As a result, CPU utilization canbe quite low during the scattering source calculations, even if efficientasynchronous data transfer methods are utilized.

Data management considerations also led to the decision to apply theChebyshev polynomial acceleration technique to the fission source vector £rather than the flux vector *. Three complete fission source or flux vectors.

*NTHPT denotes the orientation of the (1,1,1) triangle in the region ofsolution, uee the GEODST file description in Appendix C.2.

39

depending on which are to be accelerated, have to be stored on peripheralstorage devices and transferred to memory to carry out the accelerationprocedure for each outer. Again, there is little arithmetic associated withthis acceleration method, so that CPU utilization can again be low if largeamounts of data have to be transferred. Since the fission source vectors areonly (1/G) as long as the flux vectors, a significant reduction in datatransfer requirements is achieved by accelerating the ij; vector.

Because fast reactor models are generally characterized by significantlyfewer space mesh cells than thermal reactor models for reactors of the samethermal rating, relatively less effort is required to carry out the inneriterations for a given group in a typical fast reactor calculation. It isonly for relatively large three-dimensional problems that all of the datarequired for the inner iterations for one group cannot be contained in thememory of the large scale computers available today. The spectral radii ofthe inner iteration matrices for the groups in a typical heterogeneous fastreactor problem are generally lower than those that arise from typical thermalreactor problems. Thus fewer iterations are required to achieve a given amountof error reduction in typical fast reactor problems. This lessens the pricepaid for demanding tighter convergence of the inner iterations in order tominimize the number of outer iterations.

Many relatively large three-dimensional problems that cannot be corecontained may be solved with no appreciable increase in data transfer cost byemploying the concurrent inner iteration strategy. Instead of calculating

<(>., serially for all lines j,k, this strategy serially computes £., for

(m+2)the block of mesh planes currently core-contained, then computes all <|>., , «••,

3<j>., where B is the "active bandwidth" of core-contained mesh planes. IfB > nig, the number of inner iterations in group g, then the inner iterationsrequire a single I/O pass comparable in cost to the one group core-containedoption, but usually at a significantly reduced memory size requirement.Details of the concurrent inner iteration strategy are found in Section 4.3.2.2.

2.2.6 Adjoint Solution Strategy

The adjoint problem is solved using the same solution algorithm as thereal problem. The self-adjoint property of the continuous and discretizedwithin-group leakage-plus-removal operator only requires a transformation ofdata in order to utilize the iteration methods just discussed.

The transformation consists of:

(1) Reversing the order of the group structure of the principal

macroscopic cross section data (e.g. E +

(2) Transposing the scattering matrix (i.e.T . «• T , ) and then revers-ing the order 'f the group structure (i.e. T , •*• TG+1__ Q+1-B ,^*

The corresponding arrays indicating the up and down (in)scatterbandwidth are converted to the corresponding up and down (out)scattcrbandwidths.

40

f(3) Interchanging v£ , and x terms in the fission source calculation.

The resulting flux eigenvector is then obtained in reverse group order,g=G,G-l,...,1 and the fundamental eigenvalue is identical to the real problemdue to the self-adjoint property of [Q] in Eq. (2.48). Likewise the symmetricwithin group matrices have identical spectral radii p([L ]), hence the o>are identical. wg g

2.2.7 Upscatter Iteration Strategy

DIF3D provides an upscatter iteration for application to problems in which[T ,]>0 for g'>g in Eq. (2.29). The essence of this strategy is to perform (in

each outer iteration) U-l additional group (inner) iterations for those groupswithin the upscatter bandwidth. Let G denote the group index of the firstenergy group that receives a nonzero upscattering source. Then the inner

iterations for the groups without upscatter, g=1,2,...,G-1, follow Eq. (2.72)and Eq. (2.73). The group g inner iteration at outer iteration n and upscatteriteration u is

r» u(n,u) _ , (n,u) „ - F n j. i n f> no^\

iA J = b , g = G, G + 1, ..., G (Z.LLla)© o o

where

g'<g g'>g Xxg i

0,"" (2.u2b)

(2.112c/

The calculation for the group contributions to the fission source ijj resumein the last upscatter iteration pass, U.

The cost of performing U upscatter iterations is approximately equivalent

to solving a problem with (U-1)*(G-G+1) additional groups. If a scattering

band B of fluxes is core contained and if (G-G+1)<B, then the upscatter itera-tions requires no additional I/O transfers for the flux data. Finite differencecoefficients and cross section data transfers will still be required.

Experience with several Safety Test Facility configurations with thermaland epithermal drivers indicates that user-supplied U values between 5 and 10are comparable in performance for the thermal case. U-l is sufficient forthe epithermal case.

The procedure in Eqs. (2.112) is reversed for adjoint calculations with

upscatter. The upscatter iterations are performed in groups g«G,G-l,...G.

Then the remaining groups, g«G-l,G-2,...,1 are calculated.

41

2.2.8 The Inhomogeneous Problem

The matrix equations describing the fixed distributed source problem naybe written in the form

(IM] - y[B])$ = s (2.113)

where [M] and [B] are defined by Eqs. (2.35) and (2.42), and S is the externalsource vector. The constant u is specified to ensure the subcriticality ofthe reactor in the absence of an external source. An exception occurs, forexample, in generalized perturbation theory adjoint calculations where thereactor is critical, but the adjoint source S is orthogonal to the fundamentalmode; in this case a solution is guaranteed by the alternative theorem.31 Forthis discussion y=1 suffices, since [B] may be redefined. The flux <£ is subjectto the boundary and interface conditions of Eqs. (2.3)-(2.5).

Equation (2.113) may be written as

$ = ([I] - [MJ'^B])"1!! (2.114)

where u = [M] S. The properties of [M] and [B] discussed in Section 2.2.1

together with the assumption of reactor subcriticality requires p([M] [B])<1.

Therefore, ([I]-[M]-1[B])_1 exists which in turn implies that ([M]-[B])-1 =

([I]-[M] [B]) exists. Because [M] is nonsingular, the iterative process

n ^ 1 (2.115)

for the flux j> generated from the regular splitting18'32 of ([M]-[B]) willconverge.

The flux iteration is reduced to a fission source iteration by followingthe procedure outlined for the eigenvalue problem, provided the definition of<J> is appropriately modified for the fixed source problem, i.e.

v ' v v - (2-u6)T

Then multiplying Eq. (2.113) by [F] and using Eqs. (2.42) and (2.44) we obtainthe reduced problem

rV (2.H7)T

where v = [F] u and [Q] is defined by Eq. (2.49). Because the nonzero eigen-values of [01 and [M]"1^] are identical, p([Ql)<l and therefore (fI]-[Qj)-1

exists. Consequently, the iterative process

42

j 1 + v (2.118)

generated from a regular splitting of ([I]-[Q]) will converge and the fissionsource vectors obtained from the flux problem and the fission source problemwill be identical.

The rate of convergence in fixed source problems is dependent on p([Q]).The Chebyshev acceleration method detailed in Section 2.2.1 can therefore beapplied to the iterations in Eq. (2.118) provided that suitable estimates ofp(0) are obtained. One such estimate may be obtained using Eq. (2.68), whichfor the fixed source problem is easily shown to satisfy the relation

(n)lim E = p([Q]). (2.119)

The previously described Chebyshev acceleration procedures may be used directly

in fixed source problems, provided we redefine the meaning of the symbol a tomean p([Q]), the spectral radius of the iteration matrix.

The inner iteration process in fixed source problems differs from itscounterpart in eigenvalue problems only by the presence of an additional sourceterm contribution to £., in Eq. (2.99).

When the fixed source problem is near-critical (i.e. p(lQ]) approachesunity), convergence rates, even with Chebyshev acceleration are unacceptablyslow. Application of a single asymptotic extrapolation" »31* prior to thefirst Chebyshev acceleration significantly reduces the required number ofiterations. This reduction is achieved by an approximation procedure thatattempts to correctly scale the contribution of the fundamental eigenvectorto the flux solution. This approach is motivated by the fact that in near-critical source problems the fundamental eigenvector term dominates the solu-tion.

If we assume, therefore, that the n-th iterate of Eq. (2.118) convergesto the exact solution IJ;00 with asymptotic behavior

f = $ ( n ) + pn([Q])cj|j0. (2.120)

where cty- is an arbitrary multiple of the fundamental eigenvector of [Q]

corresponding to p([Q]), then it follows that an improved n-th iterate is

J(n) m 4(n) + T(n)(J(n) _ di-Dj {2

where the extrapolation factor x is defined by

43

T ( n ) . (2.i

1-p

Here, p = E is the estimate for p([Q]) at the n-th unaccelerated poweriteration.

As alluded to earlier, the effect of the extrapolation is to rescale thecontribution of the fundamental vector to the solution. The extrapolationfactor also increases31+ the magnitude of the higher harmonics. However, theseare readily attenuated by the Chebyshev acceleration procedures that (after asingle unaccelerated outer iteration) are applied to subsequent iterations.

To ensure that an asymptotic behavior has been achieved, the singleextrapolation is performed when the following conditions are met:

/•'

1. e ( n ) < .1 (2.123a)

2. e ( n~ 1 ) < .1 (2.123b)

P

3. n > 5 (2.123c)

where

x ( n ) - T ( n _ 1 )(n)

The asymptotic extrapolation procedure typically leads to a factor of 2 ormore reduction in the number of outer iterations required to achieve compar-able fission source accuracy with the standard acceleration method.

2.3 The Criticality Search Option

2.3.1 Statement of the Problem

The criticality search17 seeks to achieve a desired reactor k-effective,k,, by adjusting certain parametric vectors which are constrained to lie

along a given straight line. The parametric vectors considered here aresubzone volume fractions which are discussed later in section 2.3.3. Othercommonly used parametric vectors (not implemented in DIF3D) include buckling,dimension and reactor period (a).

If £ = (Pi»P?>•••»PD) denotes a parametric vector, then the desired

vector is constrained to lie on the line given by

g(s) = £ + s*iE (2.124)

44

where £2 = (6p 6p ,..,5p ) denotes the parametric modifiers (the directioncosines for the line), and 2 denotes the initialized state of the parametervector when s=0.

For reasonable* values of s and £2* the parametric vector p_(s) generates

matrices [M(s)J and [B(s)] having the same general properties as the matrices[M] and [B] in Eq. (2.34). Then associated with each vector g(s) is k ff=k(s),

the solution to the eigenvalue problem

[M(s)]£ - ~ y [B(s)]£ . (2.125)

The object of any search then is to solve the equation

k(s) = k,. (2.126)d

2.3.2 Method of Solution

The solution of Eq. (2.126) is achieved by repeatedly solving Eq. (2.125)for a series of carefully selected estimates sn. This iterative process hasthree principle steps. The first step estimates sn; Step 2 solves Eq. (2.125)for k(sn) and Step 3 performs the convergence check on k(sn).

Step 1: Estimation of sn

s. and s? are derived from user data, s, is determined by linear

interpolation or extrapolation of data from search passes 1 and 2:

s - s . + e ,/(dk/ds) , (2.127)n n—1 n—j. in—1

where

When

e = k.-k(s ) (2.128)n d n

(dk/ds)n - (k(sn) - k(s H))/(s n - s n_ 1). (2.129)

n>3, the three most recent estimates Cs .,s »,s ») determine a parabolan—l xv~£ n—o2

p(s.) « p-s. + pos. + p» - k(s.), i • n-l,n-2,n-3. Then, s is the root of

p(s)-k,»0 that is closest to s ,.a n—l

*The user is expected to specify an initial configuration [M(O)J and [B(O)Jthat is reasonably close to the desired solution, and is expected to specifysearch parameter constraints that avoid non-physical configurations*

45

If the parabola is degenerate (a straight line) or if the roots ofp(s)-k(j=O are complex, then linear extrapolation is applied. The estimatehaving the largest e^ and which upon removal leaves two estimates that bracketthe solution k^ will then be discarded (This is the regula falsi algoritm35).

If the parabola is not degenerate, a similar root bracketing procedureis used to discard in favor of s the least useful estimate among s ,, s „~A n n-1' n-2

and s ~.n-3

Step 2: Solution of Eq. (2.125)

The eigenvalue problem Eq. (2.125) is solved using the methods discussedfor Eq. (2.43). The matrices [M(s)j and [B(s)J are defined by

[M(s)] = [M(O)J + A[6M] (2.130a)

[B(s)J = [B(0)] + X[6B] (2.130b)

whert [M(0)] and [B(0)] denote the matrices obtained with no contributionsfrom the search ("modifier") subzones and A[SM] and X[6B] denote the matrix ofperturbations resulting from the inclusion of the search modifier subzones.[<SM] and [<SB] have the same general structure as [M] and [B], but the formerare quite sparse due to the limited number of compositions usually modifiedduring a search.

Step 3: Termination Tests

Search passes are terminated by any one of the following events:

1. k - k(s ) < e, where e, is a user-supplied threshold;

a n d d

2. n = n where n is a user-supplied iteration limit:max max

3. s < s . and s > s where s . and s are minimum and maximumn m m n max min maxlimits on the range of s. The first time s exceeds the search range

say. s < s . , it is set to s . . A subsequent violation of theJ n nan min ^limits cause termination.

4. Insufficient time remains to perform the next eigenvalue calculation.

2.3.3 Comments on the Concentration Search Option

On each search pass the SRCH4C module rewrites the subzone6 volume frac-tions on the CCCC file NDXSRF and the HMG4C module calculates the correspond-ing macroscopic cross sections for the code-dependent file COMPXS. This ap-proach is attractive for two reasons. First, the creation of "modifier" sub-zones (i.e. collections of isotopes or materials which are to be varied duringthe search) requires minimal effort on the part of the user. During the search

46

process it is a trivial matter for SRCH4C to rewrite the subzone volume frac-tions on the NDXSRF file. The second advantage of this approach is modularity.Arbitrary neutronics computation modules that use the CCCC interface files maybe employed to solve the eigenvalue problem.

The alternative to subzone volume fraction modification requires atom den-sity modification for all nuclides in the CCCC file ZNATDN, a job of consider-ably larger magnitude that yields a marginal improvement in user convenience.

The economics of incurring the overhead associated with repeated exitsand reentries to the neutronics module might argue against the mo.dular approach.The net gain from avoiding such overhead was considered marginal compared tothe benefits of modularity.

Except for the prompt fission spectrum cross section type, the modifica-tion of subzone volume fractions in "modifier" subzones yields the followinghomogenization equation

. - o?'gn. V^ + s /J a?» Bn. (2.131)m ' i xm im n T" - •* ~ —

iem o o iemo s

where

X 2E is the macroscopic cross section of type x for group g in zone m;

o\ is the microscopic cross section of type x for group g for isotope i;

m denotes the set of isotopes in the primary zone assignment and subzone° assignments of zone m (modifier subzones are excluded);

m denotes the set of isotopes in modifier subzone assignments of zone m;5

n. is the atom density of isotope i in the appropriate set m or m ;

V. is the zone or subzone volume fraction assigned to isotope i in the set

m = m or m .o s

Equation (2.131) may be viewed from a macroscopic standpoint as

*• s <52X,g (2.132)m tn n tn

o s

where

u. — m^^ o. * n. V. (2.133a)m T^ i im imo iem o o

o

47

andSE

m = Z- i °,- n,-_ • (2.133b)s

Modification of the prompt fission spectrum cross section depends uponwhich of the three available homogenization options are selected.

Option 1: Use set x vector for all zones

= (X g). (2.134)

Option 2: Use isotope fission vectors with total fission source weighting

- « | j (2.135)> n V (vo )f * im im f iiem

where V. = s for those isotopes in search modifier subzones.im n ^

Option 3: Use isotope fission vectors with (vof) weighting

(^>n = 'V 1 n Vf (vo ) g * (2"136)

iem

There are no restrictions on subzone modifiers or on the zone being modifiedwith regard to fissionable or nonfissionable cross section types or with regardto scattering bandwidths.

2.4 Summary

The mesh-centered finite-difference approximation introduces a three-,five- or seven-stripe symmetric matrix of coupling coefficients that are com-puted using Eqs. (2.25)-(2.27) ; Tables 2.1 and 2.2 summarize formulas associatedwith each geometry option. The required source term is computed using Eq. (2.28)and Eq. (2.2). During each inner iteration a particular line of fluxes issimultaneously computed by solving Eqs. (2.97)-(2.99).

For a wide class of LMFBR problems m> user input is required by theacceleration strategies described in Sections 2.2.1-2.2.4. On option the usermay override e^n, the inner iteration error reduction factor in Eq, (2.96),which influences the fixed number of inner iterations to be performed during thewithin-group calculations in each outer iteration. Section 3.15.2 addressesperformance issues in this regard. Performance (i.e. job cost) is also directlyrelated on many host installations to the user-specified ECM storage containersize, ultimately the job memory size. Sections 3.9.1 and 3.10.1 address thisissue.

48

3. A GUIDE FOR USER APPLICATIONS

3.1 Setting Up a DIF3D Job - An Overview

As mentioned in the introduction, the code described in this report is,in fact, a collection of quite independent code blocks. DIF3D actually isonly one of these code blocks ; the others process input data required bythe diffusion-theory calculation. It is a common, though sometimes confusing,practice to apply the name "DIF3D" to both the complete set of code blocksand the specific diffusion-theory calculation code block.

The DIF3D code block itself reads only binary files. Otler code blocksread card input and convert the data to binary files. The input to thecode, therefore, is generally a mix of binary files written by code blocksand card-image files composed by users. Users have a variety of optionsavailable in choosing the mix; their choice then determines which code blocksare actually executed.

This section is a brief overview of the input requirements. Latersections go into greater detail. Information regarding specific input datasets or conventions may be rapidly located by using the table of contents withits detailed subsection headings.,

3.1.1 Input Binary Files

In practice the input to DIF3D (the collection of code blocks) usuallyincludes only a few binary files. Unless otherwise noted these files will beone of the CCCC interface files described in Appendices C.I - C I O .

Microscopic cross section libraries are usually maintained as binaryfiles; DIF3D can use two alternative formats, ISOTXS or the code-dependentfile XS.ISO (see Ref. 36).

For restart and in cases where reasonable flux guesses are availablethe binary flux file RTFLUX may be input. The adjoint flux is stored inthe binary file ATFLUX.

Other input binary files may contain macroscopic cross sections (COMPXS)(see Appendix D.I), atom number densities (NDXSRF,ZNATDN), geometry specifica-tions (GEODST), inhomogeneous sources (FIXSRC), criticality search parameters(SEARCH) and code-dependent data (DIF3D) (see Appendix D.2). Files in thisgroup are rarely input to the code; it is usually simpler to supply data incard-image form.

3.1.2 BCD Card-Image Model Input

When input data are not provided in binary files one or more of theinput processors will be evoked t:o read BCD card-image files and to writeappropriate binary files. This Is done automatically; users do not have toprovide any special instructions.

BCD input is divided into . number of blocke of data called "DATASETs".The general BCD input format for DIF3D is described in a later section of thischapter; the card-by-card input descriptions are included in the Appendices \B.1-B.4.

49

Atom number densities, geometry specifications, inhomogeneous sourcesand criticality search parameters can all be input in the A.NIP3 DATASET (seeAppendix B.4).

Microscopic cross sections can be input in BCD form in A.ISO (seeAppendix B.3), a BCD equivalent of ISOTXS.

Finally, at Argonne any of the CCCC files6 ISOTXS, RTFLUX, ATFLUX,NDXSRF.ZNATDN, GEODST, FIXSRC, and SEARCH can be generated directly from theDATASET A.LASIP by the LASIP3 code37. LASIP3 is a Los Alamos NationalLaboratory input processor.

3.1.3 BCD Card-Image Calculation Parameter Input

Two DATASETs, A.DIF3D and A.HMG4C, contain input parameters for the dif-fusion-theor;- calculation and the cross section homogenization, respectively.In practice these DATASETs usually contain only a few cards. Nearly all theparameters have defaults which have been set within the coding to valuesappropriate for a wide range of problems.

Among the more important input job parameters are the sizes of the FCM(fast core) and ECM (extended core) data containers. In several places (e.g.A.NIP3, A.DIF3D, A.HMG4C) the user may override defaults and specify the amountof core individual code blocks are to use for data storage. Even on machineswith only one level of memory (e.g. IBM machines) two containers are required.

3.1.4 Edits

Individual code blocks offer a variety of edits, most of which can becontrolled by the user via input flags. Because most code blocks are indepen-dent programs it frequently happens that particular data can be edited fromseveral different places in the code. For example, macroscopic cross sectionscan be edited in the code block that performs the homogenization (HMG4C) or inthe diffusion-theory solution (DIF3D).

Most edits can be routed to one or both of two output media by means ofthe edit flags. The regular print file (logical unit 6 at Argonne) is normallya printer; the auxiliary print file (logical unit 10 at Argonne) may be anydevice the user chooses (e.g. microfiche or a disk file).

3.2 BCD Input Conventions

In the input convention used in DIF3D and most other Applied Physicscodes, the input BCD card images are grouped into "BLOCKs", and the cardimages within each BLOCK are grouped into "DATASETs". BLOCKs and DATASETsare identified by cards containing one of the following phrases:

BLOCK=blknamDATASET=dsnameUNF0RM=dsnameN0S0RT=dsnameM0DIFY=dsnameREMOVE=dsname

The words to the left of the "=" sign are "keywords"; the words to the rightof the "=" sign are unique BLOCK or DATASET names. Keywords must start incolumn 1 of the card, and there can be no imbedded blanks.

50

Both binary and BCD files are given names and, following the CCCC conven-tions,6 version numbers. Binary files include CCCC standaid interface files,code dependent interface files for passing data between load modules, andscratch files used only within particular load modules. BCD files for AppliedPhysics codes are usually given names starting with "A."; for example A.NIP3is the BCD file which defines the neutronics input geometry and isotopicnumber density data.

The number of versions permitted for a particular file is established byindividual programs. In references in the BCD card input to one of severalversions of a file, the version number must follow the file name and be sepa-rated from it by a comma. Taking examples from the list of keyword phrasesabove:

DATASET=A.SAMPLE,2REMOVE=RTFLUX,1

A version number of unity is implied when no version number is given. Thus,thesecond example above could have been written:

REMOVE=RTFLUX

DIF3D users can normally ignore version numbers; the commonly used files comein only one version. The exceptions are the UDOIT binary files, which areintended for individual applications of DIF3D.

3.2.1 BLOCK=

The BCD input stream is divided into BLOCKs, and each BLOCK starts with acard containing

BLOCK=blknam

In the DIF3D input "blknam" may be either the word "OLD" or the word "STP021".The special case of BLOCK=OLD is discussed in a later section. STPO21, whichstands for "Standard Path 21", is the name given at Argonne to the sequence ofmodules making up a DIF3D calculation. A BLOCK ends at the last card beforethe next BLOCK= card or at the end of the card input file, whichever isencountered first.

As far as the user is concerned, the phrase BL0CK=STP021 causes theexecution of a DIF3D job. If the phrase occurs twice in the input streamDIF3D is executed twice. Only data contained in the first BLOCK are availableto the program during the first execution. Data in the second BLOCK modifyor replace the first BLOCK data for the second execution.

3.2.2 DATASET-, UNFORM=, NOSORT-

The data within each BLOCK are subdivided into DATASETs, and each DATASETstarts with a card containing one of the phrases:

DATASET=dsnameUNFORM-dsnameNOSORT=dsname

51

A DATASET ends at the last card before the next keyword or at the end of thecard input file, whichever comes first. The order of dissimilarly namedDATASETs within a single BLOCK makes no difference to the execution of theprogram.

DATASETs designated DATASET= or UNFORM= are expected to containcards on which the first two columns contain either

1. a positive, 2-digit, nonzero"card type number," or

2. blanks, zeros or ncn-numeric characters.

The type numbers (01, 02, .... 99) are used to identify the type of data oneach card. For example, in the BCD input file named A.NIP3 mesh data aresupplied on "type 09 cards" (card-images that have "09" punched in columns 1-2),

At the beginning of each job the cards with card type numbers are auto-matically rearranged in order of ascending card type number in DATASETs speci-fied by DATASET= or UNFORM=. When more than one card of a particular cardtype is present the relative order of those similarly numbered cards isunchanged.

At the same time as numbered cards are reordered, unnumbered cards (thosewith blanks, zeros or non-numeric characters in cols. 1-2) are collected andplaced after all numbered cards. Some users use unnumbered cards as "commentcards" to annotate their decks of numbered cards ; before the data are read byapplications load modules the unnumbered comment cards are swept to the backof the DATASET where they will not be seen by the load module. A listing ofthe input deck before sorting is printed on the user's output medium so thatthe comments are available for documentation.

DATASETs designated NOSORT= are not reordered in any way. NOSORTDATASETs are normally used for data required by a load module which waswritten at another installation but which was incorporated as a load modulein an Applied Physics production code. In DIF3D A.ISO and A.LASIP are NOSORTDATASETs.

Most DIF3D DATASETs can be input in either formatted or unformattedform. When prefaced by DATASET= the data must all be input in the formatsspecified in the input description for each card type. When prefacedby UNFORM= the data may be in free-format, but subject to the rules outlinedlater in this chapter in the section on free-format syntax. In eithercase cols. 1-2 are still reserved for card type numbers. The format rulesfor NOSORT DATASETs depend on the individual load modules which read them.

When BL0CK=blknain appears twice in the input - specifying two executionsof the same sequence of load modules - DATASETS in the first BLOCK are auto-matically preserved for the second execution unless the user deliberatelyredefines a DATASET in the second BLOCK* For example,

52

BL0CK=STP021DATASET=A.NIP301 data0207

BLOCK=STP021DATASET=A.NIP301 new data0206

The first DATASET is entirely replaced by the second before the second execu-tion. A later section discusses how one can make selective changes to DATASETs.

3.2.3 BLOCK=OLD

The special BLOCK "OLD" permits the user to tell DIF3D which files alreadyexist on disk and are being input to the calculation. Input disk files mustbe listed under BLOCK=OLD in the following manner:

BLOCK=OLDDATASET=dsnameDATASET=dsname

etc.

BLOCK=OLD may be placed anywhere in the BCD card input file.

These BL0CK=0LD files are usually binary library or restart files.Occasionally it may be convenient to create and save a BCD file in one job andthen pass it to a second job on disk rather than in the BCD card input file.In such a situation the DATASET name should appear under BLOCK=OLD in thesecond job and not in any other BLOCK processed by the second job.

3.2.4 M0DIFY=, REMOVE'S nn^DELETE

MODIFY=dsname permits the user to replace cards of a particular card typein an old DATASET without affecting the rest of the data. Type-numbered cardsfollowing M0DIFY=dsname replace the cards of that type (or those types) in apreviously defined DATASET. For example, if a DATASET in one BLOCK containsseven type 09 cards and five new type 09 cards are provided in a second BLOCKunder MODIFY=dsname, then the seven original cards are deleted and the fivenew cards substituted before the second execution.

Some users like to define a reference DATASET with DATASETedsname andthen make changes In the same BLOCK before execution with MODIFY-dsname.

REMOVE-dsname deletes the entire DATASET. This option frequently is usedwith binary files to force applications load modules, for one reason oranother, to rewrite a file.

nn=DELETE, where nn is a card type number, after a MODIFY»dsname willcause all of the type nn cards to be deleted from the DATASET.

53

3.2.5 Sample Input

Figure 3.1 shows a BCD card input file for a fictitious program. Theinput is designed to exercise most of the options described above. Three inputDATASETs are defined; they are two separate versions of a file na.ned A.SAMPLEand one named A.XAMPLE. Below the listing of the input, Figure 3.1 shows thecontents of each file after preprocessing and before the imaginary program isexecuted. There are two BLOCKS (i.e. two executions in the job).

MODIFY= is used in the first BLOCK to modify a DATASET defined in thesame BLOCK (A.SAMPLE,2). It is used in the second BLOCK to modify a DATASETdefined in the first BLOCK (A.SAMPLE,1).

Note that A.SAMPLE,1 and A.SAMPLE,2 are defined with DATASET= and UNFORM=;the cards are reordered according to card type with unnumbered cards placedlast. A.XAMPLE is defined with NOSORT= and is unaffected by the preprocessing.

3.2.6 Output from BCD Input Card Preprocessors

The BCD input preprocessing routines normally produce two kinds of edits.At the beginning of the job the user's input is listed on both the regularand auxiliary output print files by the routine SCAN. In addition, allDATASETs processed under each BLOCK=blknam are edited by the routine STUFF.Users have control over the STUFF edits for each BLOCK through an integersentinel, n, that can be added to the BLOCK= card:

BLOCK=blknam,n

n = 0 , edits given on both regular andauxiliary output files (default).

= 1, edits on regular output file only.= 2, edits on auxiliary output file only.= 3, no edits for the current BLOCK.

3.3 General Philosophy on Input Data

A number of principles have guided the design of BCD card input for DIF3Dand other Applied Physics codes.

1. Data that ara not essential to the problem should not be required inthe BCD card input. In particular, no redundant data should berequired.

2. Card input files should be easy to create and to modify.

3. Whenever possible, labels and names should be used instead of numbersfor descriptive data.

The BCD input conventions defined in the previous section support these prin-ciples.

•• The convention of numbered cards containing very specific types of datahelps to eliminate nonessential and redundant data. The preprocessing routinespass to the applications programs the number of cards of each type contained

54

BLOCK=TESTDATASET=A.SAMPLE

A.SAMPLE,109 09 CARD05 1ST 05 CARD5 2ND 05 CARD To the left is a sample

UNNUMBERED input file illustrating07 07 CARD many of the input processing5 3RD 05 CARD options. There are twoUNF0RM=A.SAMPLE,2 BLOCKS and three DATASETsXX A.SAMPLE referenced.XX VERSION 208 08 CARDM0DIFY=A.SAMPLE,208 REPLACE 08BLOCK=TESi'MODIFY=A.SAMPLE,109=DELETE05 REPLACE 05REM0VE=A.SAMPLE,2NOSORT=A.XAMPLE

A.XAMPLENOSORT

07 TYPE 07 CARDNO NUMBER

07 ANOTHER 07

Contents of each of the three DATASETs after thef'rst BLOCK is processed.

05550709

A.SAMPLEversion 1

1ST 05 CARD2ND 05 CARD3RD 05 CARD07 CARD09 CARDA.SAMPLE,1UNNUMBERED

08XXXX

A.SAMPLEversion 2

REPLACE 08A.SAMPLEVERSION 2

A.XAMPLE

not defined inthe first BLOCK

Contents of each of the three DATASETs after thesecond BLOCK is processed.

0507

REPLACE 0507 CARDA.SAMPLE,1UNNUMBERED

notthe

definedsecond

inBLOCK

07

07

A.XAMPLENOSORTTYPE 07 CARDNO NUMBERANOTHER 07

Fie. 3.1. Illustration of Input Conventions

55

in a particular DATASET. The user never has to tell a code how many data of aparticular type are input; the code determines this fact independently. Defaultvalues can be provided not only when a particular datum is missing, but alsowhen whole card types are missing.

About forty different card types are defined for the geometry and isotopenumber density file A.NTP3. Rarely are more than a dozen used for a particularjob. Instead of user supplied sentinels, the presence or absence of particularcard types signals options. Explicit sentinels would be redundant.

Numbered cards and the free-format option make it relatively easy tocreate and modify DATASETs. Long strings of input data and tables are conven-ient to the programmer but not to the user. Applied Physics input has alwaystended towards requiring only a few pieces of data per card, with the formatof the card designed for the convenience of the user. In some cases cards ofa particular type may be shuffled without affecting the definition of a problem.In other cases the order of cards within a card type has significance; thedata on one card may overlay, in some way, data defined on a previous card.Modifications to input can frequently be made simply by adding or changingthe order of cards; no changes to existing cards are required.

If nothing else, the use of labels instead of numbers for input quantitiesmakes the BCD card input file readable to users. In the A.NIP3 DATASET, forexample, compositions and geometric regions are given labels, and isotopesare referred to by name.

3.4 Free-Format (FFORM) Syntax Rules

Free-format Input is processed by a subroutine named FFORM. The followingset of rules applies to data prepared for UNFORM= DATASETs.

3.4.1 Delimiters

Data (integers, floating point numbers and Hollerith words) must beseparated either by blanks or by combinations cf one or more of the fourspecial delimiters:

, comma( left parenthesis) right parenthesis/ slash

3.4.2 Data Forms

Integer and real numbers must be written according to the usual FORTRANrules and may not have imbedded blanks. Hollerith data can be supplied in anyof the following three ways:

1. A string of letters and numbers, beginning with a letter, with noimbedded blanks.

e.g. U238 PU239

56

2. A string of symbols surrounded by asterisks or apostrophes. In thecurrent version of FFORM for CDC machines only the asterisk can be usedto set off Hollerith data; the apostrophe has not been implemented.

e.g. *NA 23* 'REG1,

3. A string preceded by the Hollerith prefix nH, where n is an integerconstant.

e.g. 3HO16

On IBM machines an asterisk may be part of a Hollerith string only whenthat string is surrounded by apostrohpes (e.g. 'X*Y') or defined by the nHconvention (e.g. 3HX*Y). Similarly an apostrophe may be a part of a Hollerithstring only when that string is surrounded by asterisks (e.g. *ED'S*) ordefined by the nH convention (e.g. 4HED'S). On CDC machines (where FFORMcurrently does not recognize apostrophes) an asterisk may be part of aHollerith string only when that string is defined by the nH convention.

When a single asterisk (or apostrophe) is encountered the remaining dataon the card are treated as Hollerith data. This does not apply, of course, toan asterisk that is clearly a part of a Hollerith string.

When FFORM passes the data it has read to the calling program, it hasstored Hollerith data six characters to the word. If the input descriptioncalls for one or more separate Hollerith words each word, therefore, must besix characters or less.

3.4.3 Implied Blanks and Zeroes

Pairs of commas, slashes, or left and right parentheses in consecutivecolumns of the card image will be interpreted as integer zeroes. Pairs ofasterisks (or apostrophes) in consecutive columns of the card image implyHollerith blanks.

e.g. , , = ( ) = / / = o** = " = 1H

3.4.4 nR, the Repeat Option

nR causes the previous datum to be repeated n-1 times, n is an integerconstant. When several pieces of data are enclosed by slashes or parenthesesand are followed by a repeat instruction, the entire string of data will berepeated. Repeats can be nested by the use of slashes and parentheses, buteach pair of symbols (// or ()) can be used only once per nest. This limitsthe depth of the nest to two levels.

e.g. l.O,3R/2.O,l/2R - 1.0 1.0 1.0 2.0 1 2.0 1/(WORD 2R) 3R/ 4R = WORD 24R

3.4.5 $, End of Card

All data including and following a $ will be ignored. This will permitthe user to include comments on a card. The symbol $ between asterisks (orapostrophes) or somewhere in an nH field is not affected.

57

3.4.6 UNFORM and Card Type Numbers

Card type numbers must continue to appear in columns 1-2, but all subse-quent data can be punched without regard to field definitions.

e.g. UNFORM=A.NIP301 title02 0 1 0 7R .

ef.

3.5 Microscopic Cross Sections - ISOTXS, XS.ISO and A.ISO

The binary CCCC interface file ISOTXS (see Appendix C.I) is the principalmeans for specifying microscopic cross section data for a DIF3D calculation.Users may alternatively supply either A.ISO, the formatted version of ISOTXS,or (at Argonne only) XS.ISO, the predecessor to ISOTXS at Argonne. Data fromthe alternative files are used to create a temporary ISOTXS file, the ultimateform in which data must be specified for use by DIF3D.

At Argonne, ISOTXS (and XS.ISO) files are generated by MC2-2 (Ref. 38),a code which solves the neutron slowing down problem using basic neutron dataderived from ENDF/B data files.39 When XS.ISO is specified, an ISOTXS file iscreated by the module CSE010 early in the DIF3D Standard Path.

The formatted file, A.ISO, provides a machine independent means forexporting ISOTXS data. It also becomes an expedient means for creating smallcross section files for a variety of applications. The sample problem inSection 5.5.1 uses an A.ISO data set.

While creating an A.ISO data set special attention must be given to thefact that certain data records require an extra blank card-image. Thisrequirement arises only when the number of data items is such that the portionof a format statement preceding a slash (/) is exhausted, but the portionfollowing the slash is not used.

3.5.1 Reaction Versus Production Based (n,2n) Cross Sections

Users should be aware of at least two things about ISOTXS. First, in theprincipal cross-section record (also called the 5D record), there are slotsfor both transport and total cross sections. Cross-section sets generated byMC2-2 (Ref. 38) contain both, and they are different. Second, there are slotsfor (n,2n) scattering cross sections in both the principal cross-section recordand in the scattering sub-block record (the 7D record). The principal (n,2n)

cross section, a" n,^, is a vector of length equal to the number of energy

groups. It is the probability, per unit group-g flux and per atom, that aneutron in group g will undergo an (n,2n) scattering reaction; i.e. it is

cr' crreaction-based. The (n,2n) cross section in the 7D record, or 6(n,2n), is a

group-to-group transfer matrix (number of groups by number of groups) whichrepresents the probability that a neutron will be produced in group g, as aresult of a scattering event in group g; it is production-based.

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These definitions are clear in the current, version IV definition ofISOTXS found in Appendix C.I. There are notes at the end of the 4D recordand 5D record that make the distinction and that point out that

n2n,g _ 1

g.

Until about seven years ago, however, the file definition made no distinctionbetween reaction-based and production-based cross sections, and there was adifference of interpretation within the FBR community.

Argonne previously used the XS.ISO format, in which elastic, inelasticand (n,2n) scattering cross sections were carried along in separate records.The (n,2n) reaction data was treated as being reaction-based. The practicewas continued by storing reaction-based elastic, inelastic and (n,2n) scat-tering matrices separately in ISOTXS j our ISOTXS files normally do not con-tain a total scattering matrix. Most of the other FBR laboratories were usedto dealing only with the total scattering cross section, and the factor of2.0 (see Eq. (3.1)) required for the (n,2n) production-based matrix had to befactored into the total when the three partial reaction cross sections weresummed. In other words, they were used to dealing with production-basedcross sections. Due to this confusion it became necessary to tighten thedefinition in favor of the production-based interpretation, because a reaction-based, total scattering cross section is useless once the total has beenformed - it is impossible to insert the factor of 2.0 that is needed inwriting the scattering source terra in the neutron balance equations. As aconsequence of this inconsistency, HMG4C the code block which processes themicroscopic data (ISOTXS) into macroscopic data (COMPXS) performs a check todetermine whether the (n,2n) scattering matrix (if present) is reaction orproduction based. Hence the proper total scattering source is returned undereither definition.

3.6 Number Densities, Cross Section Homogenization and Edits

The code block HMG4C combines microscopic cross sections (from ISOTXS)and atom number densities (from the CCCC files NDXSRF and ZNATDN) to formmacroscopic cross sections. These macroscopic cross sections are output toa binary file called COMPXS (see Appendix D.I) which is read by DIF3D to obtaincomposition and energy group dependent data. HMG4C will optionally edit theCOMPXS file contents.

3.6.1 Compositions, Zones and Subzones - A.NIP3 13 and 14 Cards

The terms composition and zone are used interchangeably in this reportand in associated documentation. The term composition has traditionally beenused at Argonne to mean a mixture of isotopes and a set of macroscopic crosssections. The term zone was introduced by the CCCC file definitions and isfunctionally equivalent to a composition. The definitions are not preciselythe same, however. In the NDXSRF file there are volumes associated withzones - suggesting an addlLijnal, geometrical implication. This impliedrelation is never used by DIF3D. Each composition is simply assigned to oneor more geometric regions of the reactor.

DIF3D provides the user with the means for creating several subcollectionsof isotopes so that the specification of isotopic mixtures may be simplified.This permits a building block approach whereby similar subcollections

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(materials and/or secondary compositions) may be used in several compositions.The example supplied with the A.NIP3 file description (Appendix B.4)illustrates the flexibility provided by the A.NIP3 type 13 and 14 cards.

Materials can be defined on type 13 cards in terms of isotopes and/or interms of other materials. Two types of compositions may be defined on thetype 14 cards. Secondary compositions are mixtures of materials and/orisotopes. Primary compositions are mixtures of secondary compositions,materials and/or isotopes.

Materials do not exist in the CCCC environment, and the identity ofindividual materials is lost when the CCCC files NDXSRF and ZNATDN are created.Secondary compositions are treated as CCCC subzones. Those constituents of aprimary composition which are not themselves subzones (i.e. isotopes andmaterials directly assigned to primary compositions) are combined into CCCCprimary zone assignments.

The full generality of the NDXSRF file (see Appendix C.3) with regard tothe specification of primary zone assignment volume fractions (VFPA(n)) andzone (and subzone) volumes is not, in fact, required by DIF3D. The inputprocessing code block (GNIP4C) always assigns unity to VFPA(n) and the totalvolume occupied by all regions assigned to zone n is assigned to VOLZ(n).Each subzone volume (VLSA(m)) is chosen so that the ratio (VLSA(m)/VOLZ(n))yields the volume fraction of subzone m computed from the type-14-card data.Factors on the type 13 or 14 cards other than subzone volume fractions (i.e.isotope atom densities and material volume fractions) are appropriatelycombined to form the atom density array (ADEN) on the ZNATDN file (seeAppendix C.4). From this discussion we see that nowhere is the magnitude ofVOLZ(n) and VLSA(m) critical; we only require their ratio.

3.6.2 Isotope Sets - ^.NIP3 3? Cards

The concept of isotope sets is used to permit a reducl-'cn in the size ofthe CCCC atom density file (ZNATDN). All isotopes used in a particular zoneor a particular subzone must be assigned to the same nuclide set. The defaulcsituation assigns all isotopes to the same set.

The size reduction occurs because of the nature of the matrix of atomdensities stored on ZNATDN. The matrix is dimensioned NTZSZ x NNS (i.e. numberof zones plus subzones x maximum number of nuclides in a set). Therefore,the introduction of two or more nuclide sets must reduce the dimension NNS.

3.6.3 Homogenization of Principal Cross Sections

The principal microscopic cross sections on the ISOTXS file arehomogenized by the general formula

where

2 X , S - 7, o-?'gn, vf (3.2)m Z_rf i im im x '

2 *° is the macroscopic cross section of type x for energy group g andcomposition m;

denotes the set of isotopes assigned to composition m (via primaryzone assignments and/or subzone assignments);

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<T ' denotes the linear combination of principal microscopic cross sec-tions that define the type x macroscopic cross section (seeTable 3.1);

n is the atom number density (ADEN on the ZNATDN file) assigned toisotope i in composition m;

V is the (primary zone assignment or subzone) volume fraction (on theNDXSRF file) associated with isotope i in composition m.

Table 3.1 summarizes the a,*^assignments for all but the fission spectrum

vector which is treated in Section 3.6.6. The scattering cross section homo-genization also included in Table 3.1 is discussed in the next section.Several points regarding the removal cross section are noted in Section 3.6.5.

3.6.4 Homogenization of the Scattering Cross Section

stot ff' sr

The group g to g' scattering cross section a can also be homogen-

ized by Eq. (3.2) if we generalize the definition of o\'g and Z x , g (i.e. let

x = stot,g'). As shown in Table 3.1, the scattering cross section may beeither in component form or in total form. The total scattering is defined bythe linear combination of scattering components tabulated in Table 3.1. Thefactor f accounts for either reaction-based or production-based (n,2n) crosssections (see Section 3.5.1). If the macroscopic scattering matrix obeys thecurrent ISOTXS rule and is production-based, this factor is unity. When thatrule was imposed, however, Argonne had (and still has) cross section sets inwhich the scattering matrix was reaction-based. A factor of 2.0 was requiredfor the homogenization of these cross sections. The solution of the problemwas to code into the HMG4C module a test to see which form the cross sectiontook. The following ratio is formed for each group that has (n,2n) scattering:

^ f (3.3)g'

where the principal (n,2n) macroscopic cross section Is defined in footnote aof Table 3.1 (see also Eq. 3.1). If, for any group, this ratio is greater than

.75, then f n 2 n = 2.0. If this ratio Is less than .75, f n 2 n = 1.0 (Clearly, rshould be .5 for production based data and 1.0 for reaction-based data). Inthis way HMG4C can detect whether the (n,2n) scattering matrix is reaction-based or production-based. At Argonne we continue to violate the production-based rule in ISOTXS files generated by MC2-2, but HMG4C is able to handle bothlegal and illegal microscopic cross section sets.

In order to minimize storage on COMPXS, composition dependent maximum up-and down-scattering bandwidths (NUP and NDN ) are calculated based on the

gm gmmaximum bandwidths of the isotopic constituents of the corresponding composi-tion.

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TABLE 3.1. Microscopic Cross Section Assignmentsto Macroscopic Cross Sections

Name o. ' 6 assignments

Capturem

o|(n,d) a|(n,t)

Transport Zm

tr,g

Totalm

Fission

Removal

m

mf,gi

ostot,g'g _

Scatteringm

aelas,g'g + ainel,g'g

stot,g'g

components0

total0

Power p cgConversion m

Ecapt,gac,g+Efiss,gaf,g

Neutronsper Fission "m

Fission gSpectrum m

See Eq. (3.4) in text.

a0n2n,g _ 1 fn2n a?'g(n,2n). If ofn'g is absent from ISOTXS and thei 2 gf i ' i

scattering matrices are in total-form, it is the user's responsibility toappropriately reduce (say) the capture cross sections.

bfn2n1 production-based a^ S(n,2n)

2 reaction-based of g(n,2n).

"ISOTXS scattering data may be stored component-wise or in total form.

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If higher order scattering cross sections are present in ISOTXS they willbe ignored by HMG4C. The COMPXS file currently does not permit higher orderscattering.

3.6.5 Discussion of the Removal Cross Section

The removal cross section accounts for two effects:

1. the loss of neutrons from the group due to absorption and outscatter;

2. the addition of neutrons to the group due to within-group (n,2n)scattering events.

The first two terms in the removal cross section definition in Table 3.1 re-

present losses of neutrons from absorption (i.e. from capture and fission).

The last two terms represent the sum of the outscatter losses anH the within

group (n,2n) gain. Recall from Eq. (3.1) that the factor of .5 arises in the

definition of a? n ,® because the (n,2n) scattering matrix is production-based, and

removal is reaction-based.

The presence of the principal cross section a , s in ISOTXS is optional.

As noted in section 3.5.1 and Table 3.1 (footnote a ) , if data are expressed intotal form with reaction-based (n,2n) cross sections, then it is impossiblefor HMG4C to determine the correct removal cross section. Consequently, it is

up to the user to supply an ISOTXS file which accounts for the a. , S effect

in some other way. For example, one could reduce the capture cross section bythe appropriate amount (a practice followed by at least one other laboratory).

3.6.6 Homogenization Options for the Fission Spectrum - A.HMG4C 02 Card

Any of three Lumogenization options are available by means of the prompt*fission spectrum flag. Denoting the fission fraction for group g of composi-

tion m by x » then the options available for computing it are:

,8 - " g(3.4a)

Xg ng Vf*im im im

1 ... x! = ^ ^ . V ^ ~ (3.4b)

vf of (n,f)

<m = x-^s 1 * _ , (3.4c)

*The issue of whether to compute a prompt or a total fission spectrum dependson the ISOTXS file supplied by the user. HMG4C simply uses the fissionspectrum data as they exist on ISOTXS.

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—•CT

where the summation is over all isotopes i contained in composition m. x is

the set fission fraction for group g while x« is the fission fraction forisotope i. The option 1 is termed total fission source weighting and may bederived from the expression for the fission source by assuming the flux isgroup independent. The option 2 is not recommended. In this option there is

no assurance the xz summed over all groups will be unity for a given composi-tion m.

Although the ISOTXS format permits the treatment of isotopic fissionspectrum data which are incident energy dependent (xf/ )» neither the HMG4Cnor the DIF3D code blocks can use such matrices. The weak energy dependenceof the fission spectrum data in' the LMFBR spectrum make it possible to use thevector derived at the average fission energy without any significant error.^^The mixing of the different isotopic data to give a vector introduces a smallerror since the flux distribution is unknown, and assumed constant in therecommended algorithm. The algorithm does, however, account for the pre-dominant isotopic effects so that the more rigorous matrix treatment is notwarranted in view of the considerable data management costs which would resultas a consequence of its use.

The presence on COMPXS of £ and xf data for composition m is indicatedby the sentinel ICHIm. ICHIm

= 0, indicates composition m is nonfissionable(i.e. composition m contains no isotopes with non-zero atom density that havea non-zero (n,f) cross section sentinel (IFIS) on the ISOTOPE-AND-GROUP-INDEPENDENT-DATA record of ISOTXS).

3.6.7 Edit Options and Container Storage - A.HMG4C 02 Card

Edit sentinels enable the user to direct edit output to either the printfile (FT06F001) and/or an auxiliary file (FT10F001). HMG4C error messages,however, will appear only on the print file. Both the COMPXS (including auser supplied COMPXS) and the ISOTXS files may be edited. The ISOTXS edit isa running edit of those isotopes referenced in the homogenization.

The computer resource requirements (both container storage and CPU time)of the HMG4C code block are insignificant compared to the typical requirementsof the DIF3D (neutronics solution) code block. Therefore, the user need onlysupply a main (FCM) memory size on the A.HMG4C type 02 card that is less thanor equal to the sum of the FCM and ECM sizes on the A.DIF3D type 02 card. Ontwo-level machines, of which the CDC 7600 is the only pertinent example, theFCM size from DIP3D is a reasonable estimate. It should be noted that theHMG4C FCM container size may also be specified on the A.NIP3 type 02 card. Ifboth specifications are present, the A.HMG4C specification takes precedence.

In computing the homogenized cross sections, the code attempts to hold asmuch of the macroscopic cross section data in memory as the container spacewill permit. If all the macroscopic data will not fit in the available memory,the code determines the maximum number (m) of compositions which can beaccomodated in a single pass. As many passes are then made as required tohomogenize all the compositions. Taking this multipass mode of operation tothe extreme, just one composition may be computed in each pass. Since there

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are a total of NZONE compositions to be formed (one for each ZONE in theproblem), the expression for the main (FCM) storage requirement is of the form,

FCM = A + mB, l<m<NZONE,

where A is the amount of storage required to hold the microscopic data and Bis the amount needed to hold the macroscopic arrays for a single composition.

HMG4C always prints the actual number of words used and, if in multipassmode, the number of words required for a single composition and the number ofpasses to be used. These data may then be used as a guide for subsequent runs.

3.6.8 Directional Diffusion Coefficient Factors - A.NIP3 35 and 36 Cards

DIF3D will generate directional diffusion coeffficients of the form

D A Dg + Bn,g n = 1 2 3 (3.5)m m m m

using factors A n , g and B n , g specified on the A.NIP3 35 and 36 cards. The codem m v

block MODCXS writes these factors into COMPXS after HMG4C has completed thehomogenizations.

The calculation of transverse leakage by DIF3D always uses the third dimen-3 Ksion diffusion coefficient D for the pseudo absorption

(DB2)g = D 3 , g * (B 2) g (3.6)m m m

used on option regardless of the problem dimension. The composition-dependentbuckling (B ) g is discussed in Section 3.75 and defined in Eq. (3.26) ofSection 3.14.7.

3.6.9 Fission and Capture Energy Conversion Factor Data - A.NIP3 37 and 38Cards

Fission and capture energy conversion factors (E and E ) in the/ m m

ISOTXS file may be overridden for particular compositions by supplying theappropriate data on the A.NIP3 type 37 and 38 cards - units are fissions perwatt-second and captures per watt-second, respectively.3.7 Geometry Input and Edits - A.NIP3 and GEODST

The primary /means of specifying the model geometry for a DIF3D calcula-tion is the A.NJP3 DATASET. The card-by-card input description is given inAppendix B.4. As of the date of this report there are 43 card types in A.NIP3,16 of which (02-12, 15, 29-34 and 43) can be used to define and edit the geo-metry. Of these 16 fewer than half are usually required to define a model.

The alternative to the geometry description cards in A.NIP3 is the CCCCStandard Interface File GEODST. Its file description is included in AppendixC.2.

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The code block GNIP4C reads A.NIP3 (if it is input) and writes a GEODSTfile. GNIP4C also produces an edit of the geometry.

3.7.1 Geometry Types - A.NIP3 03 Card

The only datum on the A.NIP3 03 card is the geometry type sentinel.Geometry types currently implemented in the DIF3D finite-difference solutionalgorithms are:

Slab (10)Cylinder (20)X-Y (40) and X-Y-Z (44)R-Z (50)Theta-R (64) and Theta-R-Z (66)Triangular (70) and Triangular-Z (90), rhombic

region of solution, core center at 60 degreeangle (sixth-core symmetry).

Triangular (72) and Triangular-Z (92), rectangularregion of solution (half-core symmetry).

Triangular (74) and Triangular-Z (94), rhombicregion of solution, core center at 120 degreeangle (third-core symmetry).

Triangular (78) and Triangular-Z (98), rectangularregion of solution (quarter-core symmetry).

Triangular (80) and Triangular-Z (100), rectangularregion of solution (full core).

The numbers in parentheses are the A.NIP3 type 03 card geometry sentinels. Theinput processor GNIP4C will actually accept and correctly process the additionalgeometry sencinels:

Spherical (39)R-9 (60) and R-9-Z (62)Hexagonal with full (110), sixth (114) and third (116) core symetries

Hexagonal-Z with full (120), sixth (124) and third (126) core symetries.

The DIF3D nodal option5 solves the hexagonal geometry options.

3.7.2 Boundary Conditions - A.NIP3 04, 05, 10, 11 and 31 Cards

External boundary conditions types are defined on the type 04 card.Boundary conditions permitted by the DIF3D finite-difference solution optionare:

Zero flux (2)Zero gradient (3)Extrapolated (4) (D • (j>, + A • <(> = 0)Periodic (6), with opposite face (X-direction only)Periodic (7), along the adjacent boundaries meeting at the origin.

GNIP4C will process additional, periodic and transport-theory boundary condi-tions, but the DIF3D code block will not accept them.

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The constants required by the extrapolated condition are input on the 05card. Internal, blackness-theory boundary conditions and constants aredefined on the type 10 and 11 cards. Type 05, 10 and 11 cards may be omittedwhen they are not required.

For triangular mesh geometries it is possible to reduce the region ofsolution b}, not defining a background region (the type 31 card). This yieldsa region of solution outer boundary which can follow the irregular shape ofan outer ring of hexagons. Whenever DIF3D detects an irregular boundarysituation, it determines a single boundary condition from the user-specifiedboundary conditions and applies it Co all external mesh surfaces that do notcoincide with the parallelogram or rectangular envelope of the region ofsolution. If more than one type of boundary condition is specified, the zeroflux condition takes precedence; the extrapolated condition is next in rank,and the zero-current condition is least in rank.

Physical considerations strongly reinforce the recommendation thatboundary condition specifications along the irregular outer boundary shouldbe uniformly specified. Therefores it is recommended that the boundary condi-tion specifications for all X- and Y-direction surfaces which are not symmetric(zero-current) or periodic in nature, be identically specified (e.g. zero-fluxor extrapolated, but not both)!

3.7.3 Regions and Areas - A.NIP3 06, 07, 15, 30 and 31 Cards

Regions are geometrical shapes, bounded by mesh lines, that contain ahomogeneous composition. For orthogonal geometries (e.g. X-Y-Z, R-Z) regionsare defined on the 06 cards. For triangular and hexagonal geometry modelsregions are defined in terms of concentric rings of hexagons on the type 30cards. A region name for the background region, all the mesh cells outsidethe hexagons defined on type 30 cards, is defined on the 31 card.

Areas are collections of possibly non-contiguous regions. They are aconvenience provided for input and editing and are defined on the type 07card.

The correspondence between regions (or areas) and the compositions theycontain is made on the type 15 cards.

3.7.4 Mesh-Spacing - A.NIP3 06, 09 and 29 Cards

The 1st dimension and 2nd dimension mesh for orthogonal geometry modelscan be defined on either the 06 or 09 cards. The 3rd dimension (Z) mesh isalways defined on 09 cards. The mesh size for triangular mesh geometries isdetermined from the hexagon flat-to-flat distance input on the 29 card.

3.7.5 Bucklings - A.NIP3 12 and 34 Cards

Bucklings can be specified by composition and group on the type 34 cards.

Alternatively, the user can input a transverse half height on the type 12card which is used to calculate a group-independent buckling and which is alsoused as a transverse finite dimension for flux and power integrals. Usersshould read the 12 and 34 card input descriptions for a discussion of whathappens when both 12 and 34 cards are input. Section 3.14.2 discusses theimpact of the type 12 and 34 cards on the edits of che flux integrals.

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3.7.6 Geometry Edits - A.NIP3 02 and 43, A.DIF3D 04 Cards

Printer edits of the geometry may be turned on by means of sentinels onthe type 02 card of A.NIP3 and the 04 card of A.DIF3D. These two edits includesubstantially the same data, but in different formats.

Graphics (e.g. CALCOMP) maps of the geometry for two- and three-dimensionalmodels can be produced by setting a flag on the type 43 card. At Argonre theuser must invoke the POSTPLOT procedure to direct the graphics output to thedesired device. The graphics output may not be available in all exportversions of the code (see Section 4.1.5).

3.8 Distributed, Inhomogeneous Sources - A.NIP3, FIXSRC and A.DIF3D

DIF3D will accept any kind of distributed, inhomogeneous source if it isinput in the CCCC Standard Interface File FIXSRC (see Appendix C.5). DIF3D willnot accept inhomogeneous boundary sources. On short-word machines the FIXSRCfile DIF3D expects (and which the GNIP4C code block optionally provides) vio-lates the CCCC standards in one respect; the source distribution must be givenin REAL*8 words, rather than REAL*4 words. FIXSRC sources for adjoint problemsmust be stored in reverse group order, as in the ATFLUX file.

Inhomogeneous source problems are indicated to DIF3D via a sentinelspecified on the type 03 card of A.DIF3D. The type 08 card of A.DIF3D evokesthe alternate outer-iteration acceleration strategy discussed in Section2.2.8; a single asymptotic extrapolation precedes the application of theconventional, Chebyshev semi-iterative acceleration strategy.

The BCD input processor GNIP4C will generate three special types of fixedsources from data on one or more of four A.NIP3 cards (19 and 40-42).

3.8.1 By Group, By Region or Mesh - A.NIP3 19 Cards

Fixed source densities can be input on A.NIP3 type 19 cards by combina-tions of group, region and mesh. This is an efficient way of doing it when afew regions or mesh cells are to contain a constant source density, but itbecomes tedious if the source density extends over a large number of mesh andis mesh and group dependent.

3.8.2 Synthesis Trial Function Source - A.NIP3 40 Card

In flux-synthesis calculations it is sometimes helpful to have trialfunctions which represent axial blanket or reflector zones and which comefrom fixed source calculations. The fixed source is the pointwise product ofa group flux from some other calculation and the local diffusion coefficient.GNIP4C will prepare such a source given an input RTFLUX file and the properflag on the A.NIP3 type 40 card. The user should be aware that DIF3D willoverwrite the input RTFLUX with the flux solution from the fixed sourceproblem.

3.8.3 Natural Decay Source - A.NIP3 41 and 42 Cards

GNIP4C will generate a distributed source which is the product of anisotope decay constant, the isotope number density and an isotope spectrum (orsums of such products) by mesh and group. Isotope names and decay constantsare specified on type 41 cards, the number densities from other input (thetype 13 and 14 cards or the ZNATDN file) and the spectra from type 42 cards.

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3-8.4 Source Edits - A.NIP3 40 Card

An edit of the fixed source file (either generated from A.NIP3 input orinput via FIXSRC directly) may be obtained by turning on the edit sentinel onthe type 40 card. The source edits may be sent to either or both of the editfiles.

3.9 Code Dependent Input - A.DIF3D

DIF3D calculational parameters, storage containers and edit sentinels arespecified via the A.DIF3D DATASET. The card-by-card description of A.DIF3D isfound in APPENDIX B.I.

The alternative to data specification via A.DIF3D is the binary interfacefile named DIF3D (not to be confused with the module DIF3D). Its filedescription is provided in Appendix D.2.

The code block BCDINP reads 4.DIF3D and writes the interface file DIF3D.If A.DIF3D does not exist, BCDINP Writes the DIF3D file using default data.If both A.DIF3D and DIF3D exist BCDINP reads both files. Data existing in theDIF3D file will be overwritten only by its non-zero and non-blank counterpartsin the A.DIF3D data set (i.e. defaulted datum fields cannot overwrite theircounterparts on the DIF3D file). Consequently, it is a good habit to avoidexplicit specification of default data so that recently updated parameters onthe DIF3D file are not reset to the default values in subsequent restart jobs.

3.9.1 Data Management Options and Container Sizes - \.DIF3D 02 Card

The DIF3D data management strategy accomodates a wide variety of problemson computers with differing architectures. The key feature of diis strategyis that it employs a fast core memory (FCM) container and an extended corememory (ECM) container to optimize the storage utilization on both one-leveland two-level storage hierarchy machines in a unified manner (See Section4.3). The two containers reside in separate memory levels on two-leve.",

machines (e.g. SCM and LCM on the CDC 76C0). Both containers reside inmain storage on single hierarchy machines (e.g. IBM 370/195).

Major scratch file buffers (also called ECM files) for the flux, finite-difference coefficients and cross section files reside in the ECM container.Files that cannot be contained in ECM require random access I/O transfersbetween ECM and their peripheral storage devices.

The FCM container contains miscellaneous arrays required for input pro-cessing and several arrays (with lengths on the order of the number of meshintervals in a mesh line) required during the steady state flux calculation.

On two-level machines additional FCM container space is required forbuffering one group of cross sections and blocks of mesh lines in a planebetween ECM and FCM for efficient computation in FCM (see Section 4.3.2.3).

DIF3D invokes one of several storage strategies based on the userspecified FCM and ECM container sizes. On two-level machines the FCM blocksizes range from full plane blocking to partial plane blocking with aminimum of one. inesh line per block.

Except for three-dimensional problems, one group of fluxes, finite-difference coefficients and composition cross sections along with threegroup-independent source arrays and a mesh-interval-to-composition map array

69

are the minimum data that must be contained in ECM. If the available ECMexceeds this minimum, DIF3D first attempts to ECM-contain a scattering band offluxes and then any of the remaining files.

Large three-dimensional problems may require the concurrent inner itera-tion strategy (CIIS). It requires that data for only a subset of the totalnumber of mesh planes be contained in ECM during the inner iterations for anenergy group. In this mode an unlimited number of mesh planes is permittedwith limitations only on the number of mesh cells in the plane.

The strategies just summarized permit the user to vary the computerresource requirements to suit specific needs for a particular job. Threeresources are primarily affected by the choice of container size. Theyinclude core storage, disk storage and I/O processing units (called EXCP's onIBM systems or Peripheral Processor (PP) time on CDC systems). It is usuallypreferable to ECM-contain the maximum amount of data to avoid excessive I/Ocharges. On systems where I/O charges are negligible or when excessively highcore storage requirements inhibit job turnaround time users may choose toincur the additional I/O activity so that earlier job scheduling is obtained.

Users who wish to devote little time to data management considerationsare urged to supply as large an ECM container size as possible since it isusually cheaper to overestimate the required ECM storage size than it is tounderestimate ECM and incur the resulting excessive I/O charges.

Formulas for calculating the minimum FCM and ECM container sizes forone- or two-level machines are displayed in Table 3.2. The minimum ECM sizeestimate for the CIIS is provided primarily to indicate the relative storagerequirements of the problem. Every effort should be made to avoid runningproblems at this minimum ECM size to avoid an enormous I/O overhead. Inextreme cases job costs can be more than tripled!

A summary of the DIF3D storage allocation parameters is edited with everyDIF3D problem. Figure 3.2 illustrates a data management summary page that maybe obtained for Sample Problem 4. Edits of the minimum number of words requir-ed to run the problem in each data management mode provide the user with thenecessary information to determine the feasibility of running a problem witha more efficient strategy. Also included is a tabulation of the location,size and associated record lenths of the principal randum access (DOPC) files.In the two-level implementation an edit of the number of lines per planecontained in FCM is also indicated.

In three-dimensional problems the data management page includes an edit ofthe minimum data required for the CIIS. If the CIIS strategy is invoked, thenumber of planes in a record (or block), the number of records to be simul-taneously contained in ECM and the number of container words in a block ofplanes is edited. The latter data are sufficient to determine the ECM con-tainer size adjustments needed to achieve a given inner iteration bandwidth.

It iu possible to obtain just the data management edit page, so as tooptimize the container size estimates prior to performing the desired neutronicscalculation. This may be accomplished by supplying a ridiculously small ECMcontainer size (say two words) which causes DIF3D to terminate abnormally afterprinting the data management page.

70

TABLE 3.2. A.DIF3D FCM and ECM MinimumContainer Size Estimation

Parameters

I,J,K = Number of 1-, 2-, and 3-D mesh intervalsNRING = Number of hex rings in triangular geometryNDIM = Number of problem dimensions (1,2 or 3)NCELLS - Number of spatial mesh cells (I*J*K)NGROUP = Number of energy groupsMAXSCT = Maximum scattering bandwidthNCMP = Number of compositions (zones)NCXS1G = Storage for 1 group of cross section data

= (9+MAXSCT)*NCMPLDW = Word length parameter

- (1 on longword, 2 on shortword machines)

Triangular Geometry i and J Estimates

I

6*NRING-16*NRING-1

2*J3*NRING2*J

Minimum Storage

J

4*NRING-22*NRING-12*NRING-12*NRING-1

(3*NRING-l)/2

Size Estimates

Symmetry Option

Full CoreHalf CoreThird CoreQuarter CoreSixth Core

Application

FCM = NCXS1G + 12*I*JFCM = NCXS1G + 19*1FCM = MAX(1500, 15*MAX(I,J),

(15+MAXSCT)*NGR0UP)ECM = NCXS1G + (8+1./LDW )*NCELLS

+ I*JECM = NCXS1G + (23+l./LDW)*I*J

2-level full planea

2-level partial planea

l-levelb

1 group in core

Concurrent InnerIteration Strategy

a2-level storage hierarchy machines such as CDC 7600.

b storage hierarchy machines such as IBM 370 systems

*** DIF3D STORAGE ALLOCATION ***

NUMBER OF WORDS IN DATA STORAGE CONTAINER

MINIMUM NUMBER OF WORDS REQUIRED TO RUN THIS PROBLEM

WITH 3 PLANES FOR 1 GROUP IN CORE

WITH ALL DATA FOR 1 GROUP IN CORE

WITH SCATTERING BAND OF FLUXES IN CORE

WITH ALL FILES IN CORE

P'CM

600

508

508

508

508

ECM

75000

12225

152345

205913

438257

LOCATION OF SCRATCH FILES DURING STEADY STATE CALCULATION

FILE CONTENTS

NEW FISSION SOURCE

OLD FISSION SRC. 1

OLD FISSION SRC. 2

TOTAL SOURCE

COMPOSITION MAP

FLUX ITERATE

CROSS SECTIONS

FINITEDIFF. COEFS.

NO. OFRECORDS

8

8

8

8

8

32

4

32

RECORDLENGTH

2480

2480

2480

2480

1240

2480

72

9920

FILELENGTH

17856

17856

17856

17856

8928

71424

288

285696

LOCATION

DISK

DISK

DISK

DISK

DISK

DISK

CORE

DISK

RECORDSIN CORE

1

1

1

4

1

6

4

4

PROBLEM WILL BE RUN WITH AN EFFECTIVE BANDWIDTH OF 2 RECORDS WITH 5 PLANES/RECORDYIELDING 10 INNER ITERATIONS/CONCURRENT ITERATION PASS. THE NUMBER OF ECM CONTAINERWORDS REQUIRED TO INCREMENT OR DECREMENT THE INNER ITERATION BANDWIDTH BY 5 INNERITERATIONS IS 14880 WORDS PROVIDED THE CURRENT BLOCK LENGTH IS MAINTAINED.(I.E. ENTER THE BLOCK LENGTH 2480 IN COLS. 25-30 OF THE A.DIF3D TYPE 03 CARD).

TOTAL NUMBER OF WORDS USED FOR THIS PROBLEM = 508

Fig. 3.2. A Data Management Page Edit for Sample Problem 4

73945

72

3.9.2 Solution Options and Control Parameters - A.DIF3D 03 Card

Parameters supplied on the type 03 card of A.DIF3D select the problemtype (criticality or distributed inhomogeneous source) and the solution type(real or adjoint). Outer iteration control parameters which limit the maximumnumber of outer iterations, and optionally override the Chebyshev accelerationof the outers are also present. The outer iteration limit can be used tobypass the outers entirely and simply obtain selected integral edits. Inlarge problems requiring one or more restarts it is economical to requestthe integral edits only after convergence is achieved.

. Two parameters on this card are related to the concurrent inner iterationstrategy (CIIS) which is invoked in large three-dimensional problems wheneverthe ECM container storage is insufficient for the one-group-in-core strategy(see Section 3.9.1). The first parameter is the minimum record size (MINBSZ)in long words for the I/O transfer of blocks of planes in the CIIS. The defaultvalues were chosen in an attempt to balance I/O overhead with the ECM storageoverhead incurred as the size of the blocks of planes increases (see Section3.10). The other parameter, the CIIS efficiency factor, avoids the last passof inner iterations in those groups for which the number of inner iterationsfalls below a code-dependent threshold. The following simple example illus-trates the point: suppose a bandwidth of 12 inner iterations can be performedin a single concurrent iteration I/O pass across the group-dependent data. Ifin a particular group the required number of inners/outer (mg) is 13, thenthe second I/O pass reo aired to perform the single remaining inner iterationis scarcely cost effective.

Problems with thermal scattering frequently require upscatter iterationsto ensure convergence. The number of such upscatter iterations performedin every outer is specified on the type 03 card if the default value of 5upscatter iterations per outer iteration is inappropriate.

The job time limit entry on the type 03 card of A.DIF3D is intended toforce graceful termination (i.e. to ensure that restart files - RTFLUX andDIF3D - are saved) on those systems in which the amount of CPU time remainingis not an available quantity to subroutine TIMER. To prevent job failures dueto time limit, the user must specify a time limit on the type 03 card which issufficiently less than the job time limit to permit DIF3D to trigger a gracefultermination based on the elapsed time clock.

3.9.3 Convergence Criteria - A.DIF3D 05 and 06 Cards

Three outer iteration convergence criteria (Eqs. 2.89 - 2.91) are suppliedon the type 05 card of A.DIF3D:

1. Absolute eigenvalue change, e^;

2. Pointwise fission source error, e^j

3. Average relative fission source error, £«*•

All criteria must be satisfied before the outer iterations are converged.When the default convergence criteria are used, the pointwise fission sourceconvergence is typically the last criterion satisfied.

73

Only one parameter related to the inner Iteration convergence can bespecified by the user and it is on the type 06 card of A.DIF3D. This parameterspecifies the error reduction factor to be achieved by each series of Inneriterations for each group during each outer iteration of the calculation.Prior to the start of the outer iterations this factor is used along with theprecalculated optimum overrelaxation factors to compute the number of inneriterations required in each group. Experience has shown that this parameterprovides an effective means for ensuring uniform convergence behavior.

Included in the edits of every DIF3D problem will be the precalculatedoptimum overrelaxation factors and an iteration history in which the fissionsource and k-effective convergence are tabulated. Figure 3.3 illustrates theouter iteration history page from Sample Problem 1.

3.9.4 Edit Options and Interface File Output - A.DIF3D 04 Card

The first four of the eleven edit options on the type 04 card of A.DIF3Dsimply provide edits of various input quantifies and all but the first havealready been discussed in their respective applications. Key dimensions forgeometry and cross section data are edited along with boundary conditions,zone bucklings, mesh interval data and region to zone assignments.

Certain data are always edited. Included in this category are the dataspecified on the A.DIF3D file, the DIF3D data management page (a summary ofstorage allocation options), lists of interface files read or written, theouter iteration history, the optimum overrelaxation factors by group, and acomputing time summary which tabulates computation times by each logical com-putation section in DIF3D.

Edit options five through nine provide integrals by region, region andgroup, and by group for neutron balance, power distribution and flux distribu-tion. Except for the neutron balance these items are also available by meshcell. All but power distribution data are available also for adjoint problems.

The mesh cell and energy dependent flux interface, file RTFLUX (ATFLUXin adjoint problems) is always written upon termination of the outer iterations.The power-density-distribution-by-mesh-cell interface file PWDINT and thezone-averaged flux file RZFLUX can be optionally written in real problems byspecifying edit option ten.

DIF3D provides edits of commonly expected integral quantities. Allrequested edits that are not also written to one of the CCCC interface filesare written to the code-dependent interface file D3EDIT. Section 3.14 definesthese edit quantities.

Some users find it useful to obtain additional edits appropriate to theirapplications by writing programs which manipulate data available on the var-ious interface files described in this document. The UD0IT1 - UD0IT4 modulesdiscussed in Section 4.1.11 are appropriate for this application.

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 ****

OUTER ITERATION SUMMARY REAL

OPTIMIZED INNER ITERATION STRATEGY

2D SNR BENCHMARK - RODS IN - FD06

SOLUTION K-EFF. PROBLEM

1/05/84 2222.100 PAGE 28

GROUPNO.

1

OUTERIT. NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

OPTIMUM NO. OFOMEGA INNERS

1.42092D+00 7

REL. POINTERROR

6.O55469D-01

4.704232D-C!

1.767146D-01

8.690130D-02

3.722962D-02

1.064050D-02

3.829818D-03

1.806451D-03

4.606560D-04

1.203257D-04

2.823481D-05

1.556538D-05

4.066891D-06

9.684399D-07

2.049522D-07

GROUP OPTIMUM NO. OFNO. OMEGA INNERS

2 1.57656D+00 11

REL. SUMERROR

1.686693D-01

1.306399D-01

7.337978D-02

4.552007D-02

2.073863D-02

6.314254D-03

2.197660D-03

1.012883D-03

2.320342D-04

7.173725D-05

1.472779D-05

1.031790D-05

1.710762D-06

7.739674P-07

1.272518D-07

EIGENVALUE

CHANGE

5.676263D-02

3.391310D-02

1.908419D-02

8.680460D-03

5.1O7754D-03

2.468417D-03

8.781398D-04

2.399321D-04

9.278793D-05

3.893697D-05

1.O5O2O5D-O5

2.427902D-06

7.286502D-O7

3.097159D-07

8.601389D-08

I

POLY.ORDER

0

0

0

1

2

3

1

2

3

4

1

3

4

1

GROUP OPTIMUMNO. OMEGA

NO. OFINNERS

3 1.27169D+00 5

DOM. RATIO

USED

0.0

0.0

0.0

5.957153D-01

5.957153D-01

5.957153D-01

6.280142D-01

6.28O142D-01

6.28O142D-O1

6.280142D-01

6.331385D-01

6.331385D-01

6.331385D-01

6.331385D-01

6.577679D-01

DOM. RATIO

ESTIMATED

0.0

8.269922D-01

5.957153D-01

5.957153D-01

6.254009D-01

6.280142D-01

6.280142D-01

6.305913D-01

6.2O3958D-O,

6.331385D-O1

6.331385D-0!

7.953652D-O1

6.3O4855D-O1

6.577679D-O1

6.5r/679D-01


4 1.26615D+00 5

K-EFFECTIVE

1.05676263D+00

1.O9O67574D+OO

1.10975993D+00

1.11844039D+O0

1.12354814D+O0

1.12601656D+00

1.12689470D+00

1.12713463D+O0

/22742D+00

1.12726635D+00

1.12727686D+OO

1.12727928D+00

1.12728001D+00

1.12728032D+O0

1.12728041D+O0

OUTER ITERATIONS COMPLETED AT ITERATION 15, ITERATIONS HAVE CONVERGED

K-EFFECTIVE - 1.12728040833

TO RESTART THIS CALCULATION, INPUT FOLLOWING VALUES

DOMINANCE RATIO (SIGBAR) - 6.577679231397D-O1

OPTIMIZED OVER-RELAXATION FACTORS

GROUP OPTIMUM GROUP OPTIMUM GROUP OPTIMUMNO. OMEGA NO. OMEGA NO. OMEGA

1 1.42092D+00 2 1.57656D+O0 3 1.27169D+00

MAXIMUM POWER DENSITY 2.68379D-04 OCCURS AT MESH CELL (I,J,K) - ( 1, 1, 1)

PEAK POWER DENSITY IS CALCULATED BY SAMPLING THE AVERAGE FLUX VALUES ON THE CELL SURFACES AND WITHIN THE CELL.

GROUPNO.4 1

OPTIMUMOMEGA

.26615D+00

GKOUPNO.

OPTIMUMOMEGA

Fig. 3.3. Iteration History Page Edit for Sample Problem 1.

75

3.9.5 Restart Option - A.DIF3D 03, 06 and 07 Cards

Restart jobs generally differ from the original job in two ways. Theappropriate flux DATASET (RTFLUX or ATFLUX) must be provided and specifiedunder "BL0CK=0LD" in the BCD input data. Appropriate JCL designations arerequired to ensure that the system accesses the appropriate restart flux file.Optimum overrelaxation factors and the latest eigenvalue and dominance ratioestimates should also be provided. The most convenient means for specifyingthe last three items is to supply the restart file DIF3D and specify it under"BL0CK=0LD". Note that the restart sentinel will already be set on the DIF3Dfile if the file was written by a job in which outer iteration convergence wasnot achieved. An alternative is to revise the original A.DIF3D file byspecifying the above data on card types 06 and 07 and by specifying therestart sentinel on the type 03 card.

The precalculation cf optimuir overrelaxation factors generally requiresCPU time equivalent to two or three outer iterations, so that it is well worththe effort in problem restarts to supply these factors. The remaining factorssupplied during restarts facilitate resumption of the Chebyshev fission sourceacceleration with minimal loss of efficiency. In applications in which aseries of related problems are to be solved the optimum overrelaxation factorsfrequently are quite similar. Consequently the optimum overrelaxation factorsfor a common set of problems may be calculated once in the first problem ofthe set and used throughout.

3.9.6 Acceleration of Near-Critical Source Problems - A.DIF3D 08 Card

An optional strategy which accelerates the outer iteration convergence innear-critical systems with an inhomogeneous source (see Section 2.2.8) can beinvoked, by specifying the appropriate data on the type 08 card of A.DIF3D.Thr. strategy provides more rapid convergence for this class of problems thanthe Chebyshev acceleration techniques generally applied to most DIF3D problems.

3.9.7 Neutron Transport Option - A.DIF3D 09 Card

At Argonne there exists a version of DIF3D in which the diffusion theoryinner iteration routines have been replaced by a transport theory (Sn) calcu-lation. As of the date of this report there were no plans to make a formalrelease of DIF3D/transport to any code centers.

One invokes DIF3D/transport in the Argonne system by including

PRELIB='CI16.B99983.MODLIB'

on the EXEC card for STP021. The type 09 card of A.DIF3D specifies the trans-port option. It contains the S n order as well as the control parameters forthe innermost line-sweep iteration.

3.10 Guidelines for the Efficient Use of the CIIS

Typical problems invoking the Concurrent Inner Iteration Strategy (CIIS)(see Section 4.3.2.2) make heavy demands on computing system resourcesincluding:

76

1. CPU Time,. -

2. I/O Processor Time (EXCP's on IBM systems),

3. Central Memory Storage (FCM and ECM),

4. Disk Storage.

Items (1) and (4) are essentiall> invariant for a given problem, while items(2) and (3) are dependent on the ECM storage container size. Item (2) is alsodependent on MINBSZ, the desired I/O record size (see Section 3.9.2). Withinpractical limits, resources (2) and (3) are roughly inversely proportional, sothat as the ECM size increases, the inner iteration bandwidth B increases,yielding a corresponding decrease in the number of inner iteration I/O passesand vice versa. This flexibility in resource allocation afforded by the rangeof permissible ECM values enables the user to tailor the resource utilizationfor an arbitrary problem to an arbitrary host installation.

3.10.1 Optimal ECM Size Estimation - A.DIF3D 02 Card

If a reasonable estimate exists for M, the aver-ge number of inner itera-tions per outer iteration required for the problem at hand, then the procedurebelow determines the least storage needed to minimize the number of inneriteration I/O passes having block size MINBSZ. For example, if M=24 in a givenproblem but the maximum ECM-containable inner iteration bandwidth B is B=18,then the algorithm will choose U, the number of ECM-contained I/O blocks, andL, the number of planes in an I/O block, such that B=U*L > 12. A bandwidthof 12 iterations requires the least ECM storage to perform the inner iterationsin two I/O passes.

The four-step procedure detailed below, provides simple guidelines forusers to obtain a quick estimation of the appropriate ECM container size for aproblem that may need the CIIS option. Formulas and parameter definitionsare tabulated in Table 3.3 for short-word and long-word machines and formachines with one- or two-level storage hierarchies. Figure 3.4 graphicallydepicts ECM storage requirements W(U,L) as a function of the number of ECM-contained blocks U for blocks ranging in size from L=l to L=15 planes.Constant bandwidth (dashed) curves, B=U*L, B=5,10,...,50 are also plottedto clearly indicate the relative storage overhead incurred as the block size Lis increased.

The ECM estimation procedure is given by the following four steps:

Step 1: Determine the maximum container space available for the variablesize plane-block arrays,

WMAX = ( min (ECMMAX, ECM1G) - ECMISC ) / (IM*JM) .

WMAX is limited by either the machine dependent maximum ECM size(ECMMAX) or by the minimum container size (ECM1G) for the one-groupcontained data management option.

77

TABLE 3.3. ECM Size Estimation for the CIIS

Parameter Defz.nitionsa

M = Maximum number of inner iterations (ffig) per outer in any group.BLMAX = Maximum ECM system buffer length (usually 32768).b

INDEXR = ECM space required for dynamic random access I/O index in XCM.MACHUPEC = 3000K bytes or the IBM 370/195 at ANL.

= 800CK bytes on the IBM 3033's at ANL.= 393216 LCM words on the CDC 7600 at LBL.= 294912 words of LCM on the CDC 7600 at BNL.

MACHUPFC = 61440 words of SCM on the CDC 7600.PROGSIZE = Memoi/ required to contain longest overlay in DIF3D.ECMISC = (9+MAXSCT)*NCMP+I*J

= I MACHUPE-FCM-PROGSIZE on the IBM 370/195.IMACHUPE-FCM-PROGSIZE-BLMAX-INDEXR(L) on the CDC 7600.

ECM1G = ECMISC+(8+l/LDW)*NCELLSINDEXR(L) = Q(L)*(5*NGROUP+9) + NGROUP

Q(L) = (K-D/L+lW(U,L) = (min(U+2, Q(L))*5 + min(U+3, Q(L)) + 4.5)*L

ECM Estimation Algorithm Summary

1) WMAX = ( min (ECMMAX, ECM1G) - ECMISC) / (IM*JM)2) L = min ( MINBSZ/(I*J)+.5, K, WMAX/W(1,1) )3a) U = max U subject to W(U,L)<WMAX (graphical estimate Fig. 3.4.)3b) P = (M-1)/(L*U) + 13c) U = (M-l)/P + 14)ECMCC = ECMISC + W(U,L)*I*J

aSee Table 3.2 for additional parameter definitions.ty)n the LBL system default system buffer sizes are overridden by the FBSIZEand GBSIZE control cards.

cMACHUPn is the estimated maximum storage available to the user for the ECMcontainer (n=E) or FCM container (n=F).

78

500

O (U, L) PARAMETER DOMAINL= NUMBER OF MESH PLANES PER I /O BLOCK

' — B = U-L, THE CDS BANDWIDTH (IN MESH PLANES)

400

v>

J5a.

v>o>

I 300

CO

<_>

UJ

CO

o

200

100

B=IO

0 5 10: NUMBER OF ECM-CONTAINED 1/0 BLOCKS

15

Fig. 3.4. CIIS ECM Storage Requirements Guide

79

Step 2: Determine L, the near-optimal number of planes in a block

L = min( MINBSZ/(I*J)+.5, K, WMAX/W(1,1) ) .

L cannot exceed the number of planes (K) in the problem or the maxi-mum number of ECM-containable blocks in the problem.

Step 3: Having chosen L, determine the number of blocks (U) to be ECM-contained:

(a) Determine the upper bound for U satisfying W(U,L) < WMAX.Graphical determination using the domain in Fig. 3.4 bounded bythe lines WMAX and L and by the bandwidth curves B<M providesthe quickest solution.

(b) Determine the minimum number of I/O passes (P)

P = ( M-l ) / (L*U) + 1

required to perform the inner iterations for each group duringeach outer iteration.

(c) Minimize U subject to P (just as in the example at the start ofthis section), i.e. calculate

U = ( M-l ) / (L*P) + 1 .

Step 4: Calculate ECMCC, the ECM container size for the CIIS

ECMCC = ECMISC + W(U,L)*I*J.

The above procedure minimizes I/O operations and memory requirements sub-ject to the fixed values of parameters MINBSZ, M and ECMMAX. In analyzing aparticular job, one should be cognizant of the fact that there is a certainlevel of performance uncertainty largely attributed to the presence of over-lapped I/O and CPU operations and to the subjectiveness of the optimal valuefor the MINBSZ parameter. The degree of overlap (concurrency) achieved rela-tive to the potential overlap attainable is influenced by the resident job mixat execution time as well as the parameters U and L. Depending on the chargingalgorithm employed, it may be cheaper at certain host installations to arbi-trarily reduce region size at the expense of I/O or vice versa to obtainreduced overall job cost or improved turnaround time.

3.11 Criticality Search Input and Edits

The primary means for specifying criticality search data is via theA.NIP3 type 21-26 cards. The card-by-card description of A.NIP3 is found inAPPENDIX B.4.

The general form of the search equations is

P(x) = P(0) + x • M

80

where P is the quantity being varied. The user must specify the followingdata:

1. the parametric modifiers M of the search quantity P

2. bounds for and two initial estimates of the search parameter x

3. the desired search k-effective, k^;

4. the search k-effective convergence criterion (EPSRCH) ;

j. the maximum number of search passes permitted.

The alternative to criticality search data specification via A.NIP3 is tosupply the CCCC standard interface file SEARCH. The SEARCH file descriptionprovided in APPENDIX C indicates the subset of SEARCH options implemented atANL and the corresponding ANL modifications to SEARCH.

The code block GNT.P4C reads A.NIP3 and writes a SEARCH file when theappropriate type 21-26 cards are present.

3.11.1 Parametric Modifiers M - A.NIP3 23-26 Cards

The desired search option is indicated by the presence of one of the fourmutually exclusive A.NIP3 type 23-26 cards. DIF3D currently permits only anuclide concentration search via the type 23 card of A.NIP3.

The nuclide concentration search operates on subzone volume fractions,modifying the net atom densities in each zone (composition) to which the modi-fier subzone is assigned. Modifier subzones and the zones they modify areboth specified on the type 23 card of A.NIP3.

3.11.2 Search Parameter Estimates x - A.NIP3 22 Card

Two initial estimates for the criticality search parameter and upper andlower bounds for the search parameter during the course of the search arespecified on the type 22 card of A.NIP3. The search problem should be formu-lated such that the magnitude of the search parameter estimate satisfies(.Kx<1.0) for best performance of the parabolic interpolation option of thesearch procedure. The A.NIP3 type 22 card is optional.

3.11.3 Search Pass Control Parameters - A.NIP3 21 Card

Search passes are normally terminated by one of four conditions:

1. search convergence; ^

2. the maximum number of search passes reached;

3. computing time limit detected;

4. the search parameter out of range.

81

The user specifies the dssired k-effective, the relative k-effective errorbound (EPSRCH) and the maximum number of search passes on the type 21 card ofA.NIP3. Specification of the search parameter range restrictions is discussedin the previous section.

From an efficiency standpoint it is recommended that the neutronics cal-culation k-effective convergence criterion (ek) be no more than an order ofmagnitude tighter than EPSRCH during the search passes. Upon search convergencethe flux can be more tightly converged via an appropriate restart of theneutronics problem.

3.11.4 Search Restarts - A.HIP3 21 and 22 Cards

In the event of abnormal termination, or if tighter k-effectiveconvergence is desired, the search pass loop may be efficiently restarted bysupplying the appropriately saved SEARCH, RTFLUX and DIF3D files and byspecifying them under "BLOCK=OLD" in the BCD input data. Data supplied on thetype 21 and 22 cards of A.NIP3 will override corresponding data items on theexisting SEARCH file.

3.11.5 Search Edits - A.NIP3 21 Card

An edit of a newly created or a previously existing SEARCH file may beobtained from GNIP4C via a sentinel on the type 21 card of A.NIP3. Sentinelsfor editing the search parameter data and the search quantity at each searchpass are also provided on the type 21 card of A.NIP3.

A sentinel provided on the type 04 card of A.DIF3D permits user controlof the frequency of the DIF3D neutronics edits. The latter edits are usuallydeferred until search convergence.

3.12 Running DIF3D

3.12.1 Input and Output Interface Datasets

The BCD and binary input and output files potentially encountered duringthe execution of DIF3D are tabulated in Table 3.4. User input and outputoptions are such that only a problem dependent subset of these files arerequired. The next several subsections address details pertinent to theexecution of DIF3D on specific classes of host system environments. Much ofthis discussion is based on DIF3D implementation experience gained on computerswhich are representative of each environment class.

3.12.2 Sample Input

Figure 3.5 illustrates a job input deck for Sample Problem 1 in theNational Energy Software Center (NESC) package (see Section 5.3). The microscopiccross section file ISOTXS is supplied in BCD card image form via the A.ISOfile. In typical production applications the ISOTXS binary interface file isusually specified under BLOCK=OLD since it is generated by appropriate crosssection processing codes. The remaining interface file data is specifiedusing free format input.

82

TABLE 3.4. DIF3D Interface Files (COCC and code-dependent)

BCD

A.NIP3

A.ISO

Bznary

GEODSTb

NDXSRFZNATDNFIXSRCSEARCH

ISOTXSXS.ISO

Modea

I/SI/SIII/R

II

A.HMG4C ICOMPXSb I/S

A.DIF3D DIF3Db I/R

A.LASIP3

RTFLUX*1

ATFLUX"NHFLUX6

NAFLUX6

RZFLUXPWDINTPKEDITD3EDIT

I

O/RO/RO/RO/R0000

Contents

Model GeometryComposition definition(Sub) Zone atom densitiesDistributed inhomogeneous sourceCriticality search specifications

Microscopic cross sectionsConverted to ISOTXS by CSEO1O

HMG4C control parametersMacroscopic cross sections0

DIF3D control parameters

LASIP3 input processor data

Real flux

Adjoint fluxNodal real solution vectorsNodal adjoint solution vectorsReal zone averaged fluxPower densityPeak power and flux by mesh cellDIF3D integral edits

aFile usage (I=Input, O=Output, R=Restart, S=Modified by SRCH4C)

^Binary input files ultimately required by DIF3D.cCan be created from ISOTXS, NDXSRF and ZNATDN by FMG4C.dBinary output files required by BIF3D (RTFLUX and/or ATFLUX).eBinary output files required by DIF3D nodal option (NHFLUX and/or NAFLUX).

//SAMPLE1 JOB REGION=1200K,TIME=3,CLASS=W//*MAIN ORG=PR0,LINE8=10// EXEC ARCSP021,RTFLUX='C116.B20245.SAMPLE.RTFLUX,,// RTCYL=1,RTDSP=(NEW,CATLG)//SYSIN DD *BLOCK=STP021

NOSORT=A.ISO

<A.ISO dataset is listed in Fig. 5.l>

UNFORM=A.NIP3

<A.NIP3 dataset is listed in Fig. 5.l>

UNFORM=A.DIF3D<A.DIF3D dataset is listed in Fig. 5.l>

Fig. 3.5. ANL DIF3D Input Skeleton for Sample Problem 1

83

When the inquired binary files already exist (possibly created via analternative CCCC interface file input processor), the minimal input dataillustrated in Fig. 3.6 is sufficient to run DIF3D. At Argonne it is occasion-ally convenient to employ LASIP3,37 a generalized BCD input processor codeblock for CCCC standard interface files. Figure 3.7 illustrates a skeletonof the input data required to execute LASIP3. The optional FPRINT data setsupplied in the A.LASIP3 input specifies selective edits of the CCCC inter-face file data.

3.12.3 IBM Considerations - ARCSP021 Symbolic Parameters

Several key Job Control parameters including Job REGION size and JobTIME limit must be specified by the user. Table 3.5 contains the formula forcomputing the Job REGION size which must include space for the FCM and ECMcontainers in addition to the space required for the DIF3D program and its I/Obuffers. CPU time requirements depend upon the problem size and type, andthe data management option employed. At Argonne no limit is placed on theI/O activity in a job; the EXCP's component of the current charging algorithmassesses the use of I/O resources. Therefore, the EXCP charge is influenceddirectly by the active DIF3D management option and typically accounts for 30to 40% of the job cost in large problems.

CPU times for the finite-difference option in DIF3D are roughly linearwith the number of flux work units (MFWU) defined by:

MFWU = 10 6*NCELLS*N*W

where NCELLS is the number of space mesh cells, N is the number of outeriterations and mg is the number of inner iterations in group g. The m^ areconstant throughout the problem and typically range between 8 to 25 inners perouter, nig increases monotonically as the spectral radius increases. The upperend of tnis range is typically achieved in problems having very fine mesh widthspecifications. Typical ranges for the number of outer iterations vary between15 to 25 iterations to achieve the default convergence criteria. The highervalues in this range are achieved as the dominance ratio (the ratio of thefundamental eigenvalue to the first harmonic) increases towards its limitingvalue of unity.

Based upon statistics gathered from a variety of DIF3D jobs run on theIBM 370/195 computers, typical computation rates between 6 and 12 MFWU perminute are standard. Problems with large numbers of mesh cells in the firstcoordinate ("X") dimension achieve even higher values. For example, the 1 cmmesh (170 x 170) 2U IAEA benchmark problem (see general description in Section5.3.2) achieves 17 MFWTi. This corresponds to 3.9 megaflops (millions offloating point operations per second) when the 13 floating point operations(add or multiplies) per FWU in two-dimensional problems are considered. Lowercomputation rates are encountered in triangular geometry problems due toadditional computational overhead. The ratio of EXCP to CPU charges intriangular geometry problems is also increased due to the extra backgroundmesh cells which are carried along for coding convenience but are not withinthe solution domain.

84

BLOCK=OLDDATASET=GEODSTDATASET=ISOTXSDATASET=NDXSRFDATASET=ZNATDNBL0CK=STP021UNF0RM=A.DIF3D

/*

Fig. 3.6. Minimal Input Data Example

BLOCK=OLDDATASET=NDXSRFDATASET=ZNATDNBL0CK=STP021UNF0RM=A.DIF3D

N0S0RT=A.LASIP35000

OV FPRINTID 40002D GEODST 00002D ISOTXS 00323D 1 4 54D 1: 42D NDXSRF 00002D ZNATDN 0000

OV GEODST

/ (6X,4I6) BPOINTER container size (see Section 3.13)

/ Process four files with the print/ Print all GEODST record types/ Print three record types and two isotopes/ ISOTXS record types to be printed/ ISOTXS isotopes to be printed/ Print all NDXSRF record types/ Print all ZNATDN record types

0V ISOTXS

STOP/*

Fig. 3.7. LASIP-3 Input Skeleton

85

TABLE 3.5. Job Region S . ze and Dataset SpaceEstimation for ARCSP021

Parameters

NCELLS = Number of mesh cells in the problemNDIM = Number of problem dimensions (1, 2 or 3)NGROUP = Number of energy groupsNGUP = First group with nonzero upscatter sourceS = 2*NDIM-0, number of orthogonal geometry surfaces

= 2*NDIM-1, number of triangular geometry surfacesECM = ECM or FCM container sizea

PROGSIZE = 325K bytes, the storage required for DIF3D programand 1/0 buffers

REGION = (ECM+FCM)/128 + PROGSIZE = JOB CARD Region Size

Data Set Space Allocation Estimation

ARCSP021SymbolicParameters^

DatasetName FTXXF001

StorageEstimateCylinders

FLXCYL(l) group inde- 46-49,51,1= NCELLS*8/CYLSIZC

pendent data 55,56 'ZONCYL(l) ZONMAP 52 = FLXCYL/2

RTCYL(5)ATCYL(5)PSICYL(5)PSICYLPSICYL

PSUCYL(3)

FDCCYL(20)DMY1CYL(21)

DMY2CYLDMY2CYL(7)DMY2CYL

DMY5CYL(5)SRFCYL(12)

RTFLUXATFLUXPSINEWPSIOLDFSRC

NGUP

FDCOEF&&DUMMY1

&&DUMMY2&&DUMMY3&&DUMMY4

&&DUMMY5SCR001SCR002

3031414254

43

45DUMMY1

DUMMY2DUMMY3DUMMY4

DUMMY566,67

, = FLXCYL*NGROUP

= FLXCYL*(NGROUP+1-NGUP)

= PSICYL*(NDIM+1)= FDCCYL+ZONCYL

> = PSICYL+FLXCYL*2

= PSUCYL+FLHSYL= 2*NCELLS*(S+1)/CYLSIZ

aRefer to Table 3.2.

^Symbolic parameter defaults are enclosed in parenthesis.CCYLSIZ is dependent on device type and block size.When the BLKSIZE=6136, CYLSIZ=12280*19 on a 3330 disk(CYLSIZ=18416*30 on a 3350 disk).

86

Many files are accessed during the course of a DIF3D calculation and eachof them requires a Data Definition (DD) card to describe the file characteris-tics including sise allocations, disposition, volume identification, DCBinformation and the dataset name. To simplify the input deck for users of theANL IBM computers a cataloged procedure (ARCSP021) was written (see listing inAppendix A ) . Symbolic procedure parameters in ARCSP021 permit convenient userspecification of key parameters for various DD cards without recoding theenti a. DD statement. Comments within the ARCSP021 procedure tabulate thedefailt values and usage of the symbolic parameters and the logical unit num-bers (FTnnFOOl) to which they apply. Several symbolic parameters deserve spe-cial attention and are described in the following paragraphs.

The default value (RECFM=U) of the symbolic parameter MODEDCB designatesthirteen files as random access I/O files to the I/O package (SIO) employed byDIF3D. An attempt to minimize disk head contention is made by suballocatingthese files in a particular ordering among the five available scratch diskvolumes at ANL. The user must override the default space allocations forthese files when the space estimation formulas in Table 3.5 indicate thedefault values are insufficient. The formulas provide allocation estimatesfor the thirteen individual files, for RTFLUX and ATFLUX files, and for thefive dummy datasets on which the thirteen scratch files are suballocated.Whan estimating the cylinder sizes for the dummy datasets all fractions mustbe rounded to the next highest integral number of cylinders. Appropriatecylinder sizes are edited for all ARCSPO21 parameters immediately before thedata management summary page.

The parameters UNITSCR=SASCR and UNITS=BATCRDSK denote the system scratchdisk volumes and the pool of disk volumes on which datasets can be cataloged,respectively. The latter designation is given to files which are deemedlikely to be cataloged by a user.

All files but the thirteen random access files are given block sizeparameters appropriate to their anticipated I/O activity. When explicitlyoverriding JCL for any file care must be exercised to specify block sizesappropriate to the output device type so as to avoid inefficient use ofstorage space.

Insufficient disk storage for extremely large jobs require users to assignthe largest scratch file FT45F001 to a 6250 BPI scratch tape. In this eventthe entire DD card is overridden with the following alternate specification:

//FT45F001 DD UNIT=READ625O,SUBALLOC=,// DCB=(RECFM=VBS,LRECL=X,BLKSIZE=12280,DEN=4)

If the job using a scratch tape "has the possibility of running on OS/MVT(i.e. the IBM/195), then some additional JCL is needed to prevent the operatorfrom issuing a tape save request which assigns the tape to the user's account.The following two steps are recommended:

1. Add the following JCL as the first step of the job

//STEP1 EXEC PGM=IEFBR14//$$N0SAVE DD VOL=SER»,UNIT-READ6250,DISP=(NEW,PASS),// DCB-(RECFM-VBS,LRECL«X,BLKSIZE«12280,DEN«4)

87

2. then override the FT45F001 card:

//FT45F001 DD UNIT=READ6250,SUBALLOC=,// VOL=REF=*.STEP1.$$NOSAVE,DISP«(NEW,DELETE),// DCB=(RECFM=VBS,LRECL=X,BLKSIZE=12280,DEN=4)

3.12.4 CDC 7600 Considerations

Figures 3.8 and 3.9 illustrate the structure of a typical job to beexecuted on the CDC 7600 at Lawrence Berkeley Laboratory (LBL) and at BrookhavenNational Laboratory (BNL), respectively, the problem to be solved is identicalto that shown in Figure 3.5. As in the latter example for IBM systems, theassumption is made that an absolute overlay module already exists and in thisexample is merely "STAGEd in" from a magnetic tape library.

When the DIF3D absolute overlay module is created, minimum field lengthrequirements for all subsequent executions of this module can be easilyobtained by scanning the loader map for the maximum SCM and LCM field lengths.These field lengths are dynamically requested prior to invoking DIF3D usingeither the SFL card at LBL or the RFL card on "off the shelf" CDC systemssuch as the system at BNL. A nominal field length sufficient to perform thestaging is specified on the JOB card in these examples.

Additional SCM or LCM field length required for BPOINTER containers sub-sequently used in DIF3D is dynamically allocated and deallocated appropriatelyduring the execution. In fact, the user must not preallocate space forthe BPOINTER containers since DIF3D only uses space dynamically allocatedby DIF3D. Error messages result when insufficient field length is availablefor dynamic allocation. Consequently, the user never needs to compute theSCM and LCM field lengths associated with the BPOINTER container sizes.

On standard CDC installations such as the one at Brookhaven NationalLaboratory, less SCM space is demanded by the I/O buffers. About 70,000 octalSCM words are required, thereby permitting a substantial increase in the FCMcontainer size.

Upper bounds for computing units (CU's) at LBL or Central Processor (CP)seconds at BNL are also required on the JOB card. Estimates of CP seconds forthe CDC 7600 are from 10 to 25% less than the corresponding estimates for theIBM 370/195 (see Section 3.12.3). The CU's quantity at LBL is defined as

CU=3*CP+.5*BLD+IT0.

The BLD quantity is discussed below. The interference to others (IT0) quantitymeasures the efficiency of the utilization of system resources acquired by ajob. Figuring heavily in the IT0 computation is the LCM size and the frequencyof 1/0 requests.

The relatively simple Job Control Language on CDC systems simplifies theuser's dealings with the many binary files required by DIF3D. Two I/O relatedconsiderations, however, are pertinent to execution at LBL.

A significant fraction of the cost of executing jobs requiring largeamounts of disk to ECM data transfers is based on the number of buffer loads(BLD). Therefore it is desirable to reduce the number of BLD's by increasingthe size of LCM system buffers for the large files when they are not core-contained. This is accomplished via the control card

FBSIZE,filename=m.

88

LBLJOB,7,600,10000.xxxxxx.username jGBSIZE.20.GETTAPE,DIF3D/*,nnnnn.GBSIZE,5.FBSIZE,DIF3D=100.SFL,120000,1.DIF3D,LC=77777.FILES.7-8-9 END-OF-RECORD CARDBL0CK=STP021NOSORT=A.ISO

<See A.ISO DATASET specified in Fig. 5.l>

UNFORM=A.NIP3

<See A.NIP3 DATASET specified in Fig. 5.l>

UNF0RM=A.DIF3D

<See A.DIF3D DATASET specified in Fig. 5.l>

6-7-8-9 END-OF-INFORMATION CARD

Fig. 3.8. Structure of Job Deck for CDC 7600 at LBL

BNLJOB,T400,CM20000.STAGE,DIF3DUB,E,PE,VSN=KXXXX.REWIND,DIF3DUB.COPYBF.DIF3DUB,DIF3D.RETURN,DIF3DUB.RFL,70000,L=l.DIF3D.7-8-9 END OF RECORD CARD

BLOCK=STP021

<See identiral input data record in Fig. 3.8.>

6-7-8-9 END-OF-INFORMATION CARD

Fig. 3.9. Structure of Job Deck for CDC 7600 at BNL

89

where filename is the appropriate file name and m is the buffer size in unitsof 1000 words, m=100 is recommended for large files. In all problems it isrecommended that a global buffer size value be changed to 20 by the controlcard

GBSIZE=20.

as in the example in Figure 3.8, thereby attempting to reduce the BLD costsfor all files.

The control card, FILES, provides detailed information concerning theBLD's and sectors required by each file in a job, and is useful for determiningthe distribution of I/O costs by file name. If used it should be inserted atthe end of the control card record.

The control card

DISKHOG.n.

is required to override the default limit of 4000 sectors when problems whichuse more than 4000 disk sectors must be executed. The DISKHOG card should beinserted after the JOB card.

An estimate of the number of sectors, n, required by a given job can beobtained from the following formula

n = 1.1 * NCELLS * 2 + NGR0UP * (5+NDIM)

where the variab.'es are defined in Table 3.2. The estimate for n is made withthe assumption that the major scratch files on logical units (41, 42, 45, 48,49 and 53) are on disk.

3.12.5 Multiple Problems and Resta.-S - RTFLUX and DIF3D

Practical economic reasons necessitate the inclusion of a restart capa-bility in DIF3D. This feature primarily permits the resumption of the outeriteration process from the point of termination by employing the RTFLUX(ATFLUX) file saved when the previous job terminated (gracefully). It is alsoadvantageous to supply the optimum overrelaxation factors during restartsbecause they account for 5 to 10% of the cost in most calculations withoutrestarts. The simplest way to supply these factors is to save the DIF3Drestart: dataset named DIF3D. It contains the DIF3D control parameters, themost recently updated k-effective and dominance ratio estimates, and theoptimum overrelaxation factors.

For certain classes of problems it is economical to retain a fixed set ofoptimum overrelaxation factors for the entire set of similar jobs. These fac-tors are always identical for real and adjoint calculations of a given problemconfiguration. Control rod worth studies as well as many criticality searchproblems frequently yield practically identical convergence rates with theinitially computed set of optimum overrelaxation factors.

From time to time users attempt to reduce computing times by starting offwith an initial flux guess which is the converged solution of a related

90

problem configuration. This is probably most effective in near-critical fixedsource problems where the magnitude of the flux is an important factor. Prob-lems requiring thermal iterations are likely to benefit from this practice also.However, situations have been encountered where the use >f initial flux guessesrequire additional outer iterations to satisfy the same convergence criteriaas that attained by a similar calculation with an initial flat flux guess.

It is sometimes convenient to stack similar model cases in a single jobstep by employing successive sets of BLOCK=STP021 data blocks. Unless expli-citly REMOVEd by an appropriately placed REMOVE=filename input command, previ-ously created, binary and BCD files remain in existence. Consequently, thebinary interface file ultimately to be changed must be explicitly removed sothat the modified file can be created. Typical candidates here are the CCCCinterface files GEODST, COMPXS, NDXSRF and/or ZNATDN.

3.13 LASIP3 CCCC Standard Interface File Processor

LASIP337 will permit the specification and editting of all CCCC interfacefiles. In the Argonne implementation of LASIP3, two additional card-imagesmust immediately precede the normal LASIP3 input data specified in Ref. 37.The first of these card-images must be the NOSORT=A.LASIP3 card which signalsthe start of LASIP3 input. The second contains BPOINTER control informationand a data item LASTCL that indicates the number of columns (default=72) to beprocessed by the LASIP3 free-field input processor. The card has the format(6X, 416) and contains the four data items: MAXSIZ, MAXBLK, IPRINT andLASTCL. MAXSIZ is the FCM container size in long (REAL*8) words. MAXBLK isunused. IPRINT is the BPOINTER debugging sentinel and has input options iden-tical to those described on the A.DIF3D type 02 card. A MAXSIZ value of 5000to 10000 is usually quite adequate for most applications. However, aconservative approach is simply to supply a container size bounded by the sumof the FCM and ECK sizes on specified in A.DIF3D. Figure 3.7 contains anexample of data set A.LASIP3.

3.14 Definitions of Output Integral Quantities

As noted in Section 3.9.4, DIF3D provides optional edits of commonlyexpected flux integral quantities. Five sentinels (items 5-9) on the type 04card of dataset A.DIF3D provide the user with the ability to select thedesired subset of edits. The sentinels for items 5, 6 and 7 are multidigitnumbers which permit edits by region and/or group, and by mesh cell and/orgroup (see Appendix B.I).

The' definition of the various integrals for each of the five major editoptions are tabulated separately and in the order of their appearance in theindividual edits. A preliminary subsection is devoted to establishing thedefinitions and notation for the integral forms used in the tabulation. Anexplanation of the iteration history page is also included.

3.14.1 Iteration History Quantities

In multidimensional geometries the iteration history page begins with atabulation of the group-dependent inner iteration optimum overrelaxation fac-tors w g together with m g the corresponding fixed number of inner iterationsper outer iteration. These factors are absent in the one-dimensional casebecause the resulting tridiagonal inner iteration matrix is solved directly.

91

Following the optimum factor edit, a one-line summary of key parametersfor ecich outer iteration is printed. The first three items are outer itera-tion convergence criteria:

1) the relative pointwise fission source error,

r(n) ,(n)

4 • —r^—- <3-7>

monitors the pointwise eigenvector convergence ;

2) the relative fission source sum error,

(

monitors the average eigenvector convergence ;

3) the eigenvalue change,

(n) (n)_ (n-1)£k eff eff ' U , y ;

is a measure of the eigenvalue convergence.

Next in appearance are three items pertinent to the Chebyshev acceleration ofthe outer (power) iterations:

1) the order p of the Chebyshev polynomi?1 in the current extrapolationcycle ;

2) o, the dominance ratio estimate for a to be used in Eq. (2.61);

3) a, is the most recent update for the dominance ratio estimate (seeEq. 2.84).

When the Chebyshev acceleration is not applied, p and a will be zero.

The last item on each history line is keff which is computed duringouter iteration n (see Eq. 2.92), except during external source problems in

which case kgff E p is constant and is followed by the (unnormalized) totalfission source integral for the reactor. In fixed source problems thedominance ratio estimates are replaced by the spectral radius estimates of theouter iteration matrix.

92

Upon termination of the outer iterations one of three messages appear:

1) ou^er iterations converged ;

2) maximum number of outer iteration achieved ;

3) time limit exceeded.

This message is followed by the most recent eigenvalue estimate and a summaryedit of the parameters needed for a subsequent restart of the terminatingDIF3D job.

In most problems the relative pointwise fission source error in Eq. (3.6)is the quantity most frequently monitored by users to indicate satisfactoryconvergence. The eigenvalue change (Eq. (3.8)), an integral parameter,usually is several orders of magnitude less than the pointwise monitor.

3.14.2 Preliminary Definition of Integral Forms

The output tabulations include flux distributions by aesh cell andintegrals of the flux including power distribution and neutron balances byregion and/or group. Note, that throughout this section we frequently usethe full subscript ijk when only ij or i are required. In such cases theredundant subscripts may be assumed to be unity. Note also that the * super-script is left off adjoint fluxes.

All tabulations are based on weighted integrals of the flux as a functionof three spatial variables and one energy variable with the integralsextending over the domain of the reactor.

Region-dependent extrapolated half heights H r n, n=1,N may be optionallyspecified for the N(=l or 2) transverse directions in one- or two-dimensionalproblems. The H r n generate the cosine flux shape W r n(£ n).

cos -=2- n = 1 or 2 (3.10)2Hrn

1 n = 0

in transverse direction £n. The notation is generalized to include n=0, thecase when H r n is unspecified, so that the following two equations summarize theflux shapes that may be assumed in DIF3D:

1. X, XY,XYZ or triangular (T or TZ) geometries:

N

n=0 <|)(x,y,z)

N = 0N = ON = O

, 1or

or1

2 ;:•

XXYXYZ

or Tor TZ

(3.11)

93

2. R, RZ, 0R, 8RZ geometries:

<b(9,r,z)n=0

W m ( 5 n > ' • (4><<f>(

rr99

),z), r )> r , z )

N = 0N = ON = ON = O

or

or

1

1

:• R: RZ: 9R: 9RZ

where the product symbol is defined by

(3.12)

N

n=0t = t «t.«t '...'t .n o 1 2 n

Consider any macroscopic cross section E r, 5 in region r (having unextrapolated

half-height H r n ) . Using XY geometry as an example a typical integral editmight involve the numerical approximation to the following integral

I* = W r / / dxdy E*><x,yer

'" ij(3.13)

where the V^J are defined in Table 2.2 and the flux integration weight factoris defined by

Wr N /"rn

II / d^ W (?\L J ^n rn nn—J. —tl

rn

for N = 0

) for N = 1 or 2

(3.14)

In this case

4Hrl / i r Hri\w = ' '" sin i nT1 i*

\ 2 Hrl/(3.15)

94

A second weighting factor, the volume integration weight factor

1 N = 0

Wr (3.16)NII 2H N = 1 or 2II T rn

n=1

is required to compute region volumes

'r " V (3'17)ijker J

and the total reactor volume

VT = 2^Vr. (3.18)

In real homogeneous problems the flux is normalized to the user-specifiedpower level, Po, i.e.

(3.19)

The normalization factor N is calculated the following way

N = J P /P for real homogeneous problems (3.20)

\1 for adjoint homogeneous and fixed source problems

where

G RP = ^ ;• W ij>g (3.21)u / * f J r r

g=1 r=1

r ijker r 13IC 1 J K

PCg is the power conversion factor, see the COMPXS description in

Appendix D.I.

95

DIF3D permits the user to specify arbitrary collections of regions (calledareas) over which the various output integrals are to be performed. A typicalintegral over area a is defined in terms of region integrals, i.e.

*a = 21?* (3*23)

If areas exist, they will be editted whenever region edits are requested. Theregion to area assignments are recorded in the 2D record of the LABELS file(see Appendix D.3).

Improved accuracy may be obtained for peak flux and power edits based onpointwise flux or power distributions if the average flux distribution <j>|>m

on the m = 1,2 M surfaces of each mesh cell are computed in addition to thecell-averaged flux. (The surface index assignments follow the conventions ofSection 2.1.2 where m = 1 for -x, m = 2 for +x,..., m = 6 for +z.) M = 2N inorthogonal geometry where N = 1,2 or 3 denotes the number of coordinatedirections in the problem. In triangular geometry M = 2N-1 because only asingle second-dimension surface assignment is required to index the alternatingpattern of upper and lo^er triangle surfaces.

Equation (2.18) in the finite-difference coefficients derivation providesan interpolation formula that yields surface-averaged fluxes with an 0(h2)accuracy consistent with that of the cell-averaged fluxes, i.e. for m = 2

•i+ljk ( 3' 2 4 )• 5 . • Df.kAx. ' Axi+1

• *?jk +

Dg

i+ljkAxi+1

.LJ X\. ( JL 1 J- J tv

Ax Ax

Consistent with this notation the cell-averaged flux is assigned to index M+I,i.e.,

gM+1 _ g ._

We can now display the calculations made in the five edit categories

3.14.3 Region and Mesh Cell Flux Integrals

1. Neutron flux by mesh cell and group (RTFLUX or ATFLUX)

96

2. Group-integrated neutron flux by mesh cell

•ijk pijk

3. Region and/or group and area flux integrals

a. Total flux (neutron-cm/sec)

G

r / * T* T .

S*.rea

where *g is defined using Eq. (3.13) with Z x , g = 1.

b» Peak group-integrated mesh cell flux (neutron/cm2-sec)

m a x (J)mijk

(j>T = max <f..r,

maxrea

c. Total fast flux (neutron-cm/sec)

g.

g - a*g'*g - a*r

g

a X J rrea

where

1 -J t n ( E100 / Emax )

£n(Eg. /Eg )min max

100 keV, the fast flux energy threshold

energy group in which V?1n < E 1 0 Q <

"100

g.

cr aYr and Ee. are the maximum and minimum energy bounds for group gmax min

97

d. Peak mesh cell fast flux (neutrons/cm2-sec)

•r = maxKm<M+l

= max *rea r

f ,m » <t>T = max •Jr

where

»m2-4 *ijkg=1

e. Total flux by region and group (neutron-cm/sec)

= W

ijker

3> = > $ijk' T / /

a x ^ rrea

3.14.4 Region-Averaged Flux Integrals

Average total ,flux by region (neutron/cm2-sec)

G

r ~ / j r r' T T T

3.14.5 Zone-Averaged Flux Integrals (RZFLUX)

Average total flux by zone (neutron/cm2-sec)

rec g=1

g /V . *g

r ' c' T/VV T

5/V 3c Z^l r/Vc' T

recVVT

98

where

rec

3.14.6 Region and Mesh Cell Power Density Integrals (PWDINT)

1. Power density by mesh cell (PWDINT interface file):

G.

PCijk*ijk

2. Region, region-integrated and area tabulation:

a. Flux integration weight factor Wr (see Eq. (3.14))

b. Total power (watts)

G

PCg$g

r r

- y?/ j r

rea

c. Average power density (watts/cc)

P = P /Vr r r

d. Peak

P

rea rea

power density

= maxijker

Km<M+l

99

PT = max Pr

P = max Pa I rrea

e. Peak-to-average power density:

P A = P /Pr r r"

PA = P /P

A •* .~P = P /Pa a a

f. Mesh cell indices (i,j,k)p associated with peak power density of

type p where p = P , P or P .r I 3.

g. Power density (three-dimensional problems only) in the axialcolumn of mesii cells in area a that includes the mesh cell location

h. Peak-to-average power density in the axial column described forthe preceding item

K • h<3.14.7 Region and Group Balance Integral Components

1. Principal Balance Integral Components

For each of the three balance options (e.g. by region, by group or byregion and group) the principal balance components

Bg - Lg + Ia'g + I°>g - Ii,g - ,-i- If *g - Sg (3.26)r r r r r kgff r r

100

are edited first and are defined below. The variety of integral forms

available will only be listed for the balance term. The corresponding forms

for each principal component is obvious:

Be = Γ B?rea

W B/ j V

Ba

g

a. Net Leakage

r Z ^ rn=1

rea-E

The LS , n

are defined later in this section.

b. Absorption (Capture + Fission)

r r r

c. Gutscatter (Removal - Absorption)

See Table 3.1 for a definition of the removal cross section.

co,g

= ( zr,g _

r

d. Inscatter Source

i,

rs,g

g g

r r

e. Fission Source

r r

g'-l

(Real)

rf»g = '*f' (Adjoint)

g'-l

101

f. External Source (Inhomogeneous problems only)

C o _ T7

ijk ijkijker

2. i akage and Buckling Components

In any problem the net leakage (item la. above) is defined by upto three directed leakage components corresponding to the problem coordinate

& h 2directions. L ' denotes an optional DB leakage term applicable to one-

or two-dimensional problems. The L g , n, n=1,2,3 are defined by

g>n _ ijker

where the mesh cell leakage components L?'. = Ljf' are defined by

gn _ 2n 2n , _2n-l 2n-l , o ,

see the definitions of j " and A^ in Eq. (2.15) and Table 2.2, respectively.

a 1In triangular geometry the L term includes leakage components from both

g 1"X" and "Y" directions. L is therefore replaced by the more useful planar

leakage given by L g , + L g , . The quantity Lg' is also editted, but probably

has limited use since it does not represent the entire "Y" leakage component.

2 j 3By convention the DB leakage term always uses D (see Section 3.6.8) so

that r

The leakage components L may be used to define effective region buckllngs

Lg,n

(B2)g'n = r

n , n = 1,2,3. (3.26)

r r

102

3. Miscellaneous Edits

a. Capture Rate

b. Fission Rate

Fg =

r r

The following components are found on the group-integratededits only.

c. (N,2N) Source

TN2N To Tir r r

d* Net production

The next three median energy edits use the following definitions:

S £TI ' = the type s reaction rate or flux integral

E = the maximum energy bound (ev) for group g

Z = In (E-/E ) = lethargy for group g

The median energy of the type s integral is defined by

E° = E1/e B B x 6 (3.27)

where

1 Is -

g<g'\ K E Z (3-28)

g' = { min g

103

The following three median energy integrals may then be definedusing Eqs. (3.27)-(3.29).

e. Median Energy of Fission Source

E f, let IS'g = If'g

r, r r

f. Median Energy Absorption Rate

E a, let I S' g = Ia'g

r, r r

g. Median Energy of Total Flux

E*, let IS'g = *g.r, r r

3.15 Signs of Trouble

3.15.1 Error Messages

During the processing of input data an effort is made to detect as manyuser errors as possible in a single job. To this end, fatal errors arerecorded and printed as they occur, but in many situations processing isresumed until the currently executing module completes its tasks. Non-fatalwarning messages may occur from time to time indicating situations that may besuspect, and therefore warrant the users attention.

A typical case in point occurs when DIF3D iterations are prematurelyterminated because the outer iteration limit has been exceeded. Here themessage is intended to simply remind the user that the specified convergencehas not been achieved.

The warning message advising that the iteration threshold has been reachedduring the optimum overrelaxation factor calculation frequently occurs inapplications for which the spectral radii of the inner iteration matrices areclose to unity, as is frequently the case in thermal reactor problems. Inpractice this message is no cause for alarm, but simply reflects the fact thatthe convergence test in Eq. (2.94) is too stringent.

Reactor models with steep flux gradients near reactor boundaries (researchreactors are a good example here) frequently trigger underflow error messagesduring the calculation of optimum overrelaxation factors. The error messagesimply reflects the fact that some of the mesh cell fluxes that are involvedin a squaring operation are extremely small. The message may be ignored,since the offending fluxes have a negligible contribution to the norms beingcalculated. However, it should be clear that such pathological situationsare the cause of the messages and not some more basic difficulty in problemspecification.

3.15.2 Non-monotonic Convergence

Other than convergence criteria, the only parameter the user has at hisdisposal to influence the DIF3D outer iteration process is the inner iterationerror reduction factor which may be supplied on the Type 06 card of A.DIF3D.

104

When the user has specified a factor that is too "loose", the pointwise fis-sion source monitor on the outer iteration history page undergoes erraticbehavior. In extreme cases iterations may reach a point after which nofurther progress is made. When such behavior is observed it is useful totake note of the dominance ratio estimates which also appear in the iterationhistory edit. If these are erratic or exceed unity, it is a "ign that theinner iteration error reduction factor must be "tightened" (i.e. reduced inmagnitude).

The effects of increasing and decreasing (by powers of 4) the error re-duction factor (ein) *-s illustrated in Tables 3.6-3.8 for three reactor models.In a given model, the container storage remained fixed for all e. Consequently,EXCP charges and job cost are not optimized in cases involving the concurrentinner iteration strategy (i.e. the optimal CIIS bandwidth changes as the numberof inner iterations change). The results indicate that 0.04 is at best conserva-tive (i.e. in these problems there is no incentive to tighten the error reduction),On the other hand if the user plans to run a series of similar models, it willlikely be to his advantage to attempt further cost reduction by first looseningthe error reduction (increasing e^ n), then adjusting the DIF3D ECM containersize to a value which yields the optimum inner iteration bandwidth for thisproblem.

TABLE 3.6. Inner Iteration Error Reduction Effectsfor the SNR Benchmark Problem8

g k.

1 1.45386

2 1.60581

3 1.32388

4 1.40978

NO. INNERS/OUTERS

TOTAL OUTERS

TOTAL INNERS

CPU SEC. (195)

EXCP

COST

a4 group 31 x 16 x

m (.64)bg

3

5

3

3

14

39

546

40

2745

$8.11

m (.16)bg

6

9

4

5

24

20

480

32

2745

$7.00

18 sixth-core model of

m (.04)bg

8

12

6

7

33

17

561

34

2713

$7.21

m (.01)bg

10

15

7

9

41

15

615

34

2710

$7.25

• m (.0025)bg

12

18

9

11

50

15

750

40

2737

$8.06

the original triangular-geometrySNRbenchmark problem (see Section 5.3.1).

bmg(ein) is the number of inner iterations in group g required to achievean error reduction factor of £ < n l

105

TABLE 3.7. Inner Iteration Error ReductionEffects for the LCCEWG BenchmarkProblema

m (g

m (.04)g m (

1

2

3

4

1.59915

1.66320

1.60623

1.65964

8

10

8

10

NO. INNERS/OUTER 36

TOTAL OUTERS 27

TOTAL INNERS 972

CPU SEC. (3033) 273

EXCP 38339

COST $44.68

11

14

12

13

50

23

1150

315

40443

$49.62

14

17

15

17

63

22

1386

349

42261

$53.59

a4-group 49 x 25 x 28, sixth-core model of theLCCEWG benchmark BOL problem.28

^ g ^ i n ) -*-s t n e number of inner iterations ingroup g required to achieve an errorreduction factor of

106

TABLE 3.8.

g

1

2

3

4

5

6

7

8

9

NO.

(0

g

1.71197

1.73051

1.75589

1.76420

1.76339

1.74382

1.74804

1.76436

1.74110

Inner Iteration Error ReductionEffects for a ZPPR 11(B) Modela

m (.16)g

12

13

15

15

15

14

14

15

14

INNERS/OUTER 127

TOTAL OUTERS(eA-10-5)

TOTAL INNERS

CPU

EXCP

COST

SEC. (195)

25

3175

115

15650

$23.02

m (.04)b

g

17

18

21

21

21

20

20

21

19

178

23

4094

130

14787

$24.14

m (.01)b

g

22

24

26

27

27

25

25

27

25

228

23

5244

153

14795

$26.22

a9 group 60 v 120 half-core ZPPR 11(B) model.

bmg(£in) is the number of inner iterations ingroup g required to achieve an error reductionfactor of e±n.

107

3.16 Special DIF3D Applications

The following sections are brief outlines of some of the special applica-tions of DIF3D available at Mgonne. These are not available in the exportversion of the code ; they are included in this report primarily to stimulateusers to use the code in unique and creative ways. Some of the special appli-cations make use of one or more of the four user modules UD0IT1 - UD0IT4 whichare discussed in Section 4.1.11, (see also Fig. 1.1).

3.16.1 Perturbation Theory - VARI3D

VARI3D is a set of code blocks curicntly under development in theApplied Physics Division for doing ordinary and generalized perturbationtheory calculations. Many of the code blocks and files described in thisreport are also used in VARI3D. Additional code blocks have been written toset up direct and adjoint DIF3D calculations, to calculate inner products andto edit the perturbation results.

3.16.2 Fuel Cycle Analysis - REBUS-3

REBUS-3 is a set of code blocks currently under development in theApplied Physics Division for doing fuel cycle analysis for one-, two- andthree-dimensional diffusion theory models. Many of the code blocks and filesdescribed in this report are also used in REBUS-3. Additional code blocks arebeing written to set up DIF3D calculations and to calculate the burn-up.

3.16.3 Calculating Higher Harmonics

DIF3D has been used a number of times to calculate higher harmonics of theone-, two- and three-dimensional neutron-diffusion finite-difference equation.

The UD0IT2 dummy code block, which is executed just prior to the DIF3Dsolution code block, is replaced by a program which generates and saves a fluxguess which contains all harmonics ; this is currently done using a randomnumber generator.

Next, fundamental mode direct and adjoint flux solutions are run withtighter than USL 1 convergence criteria. The UD0IT3 position, just after theDIF3D solution code block, is used for a program which strips the fundamentalmode from the original flux guess using the orthogonality condition for eigen-functions.

The path of the calculation then loops back to the DIF3D solution codeblock for a few outer iterations, after which the latest flux iterate is againpurged of the fundamental by the UDOIT3 coding. This loop continues until thesecond and higher harmonics have been iterated out of the fl t. If the firstharmonic flux and adjoint are calculated in this way the UD0^J3 coding can bemade to drive second harmonic calculations.

DIF3D can calculate harmonics because it uses a linear acceleration schemethat cannot reintroduce large components of the fundamental into the fluxiterate. The fundamental does grow back into the flux iterate (therefore thesuccession of purges), Lut it does so starting from the level of the conver-gence of the original flux and adjoint problems. Periodic purging easilykeeps it in check.

108

In this application of DIF3D the only programming involved is in theUDOIT2 and UD0IT3 positions. The remainder of the code is used withoutinternal changes.

3.16.4 Calculating Electrostatic Potential Distributions

DIF3D has been used on one occasion to solve for the electrostatic poten-tial distribution in a relatively complicated system of conducting electrodesaad dielectric material. DIF3D does not permit internal, inhomogeneous(fixed-potential) boundary conditions of the sort needed for electrostatics,but this difficulty was overcome by a Green's function approach and the UDOITfeature of the code.

The electrodes, on which fixed potentials are to be applied, are dividedinto regions small enough that the internal charge distributions can beapproximated by a constant. A "multigroup" cross section set (A.ISO) of oneisotope is set up with no group-to-group transfer, no removal or fission andunit transport cross section. The dielectric constant for various regions canthen be jet by adjusting the number density input for each region of themodel. A fixad source (FIJSRC file) is generated, each group of which has aunit source in a different, individual electrode region and a zero sourceelsewhere. One solution of this "multigroup" fixed source problem yields thesimultaneous solution for the complete set of Green's functions, one for eachelectrode region.

The overall potential distribution in the model is the sum of products ofeach Green's function distribution times a charge-density multiplier for thecorresponding electrode region. An additional program was written for theUD0IT3 position in the code to calculate the multipliers for each Green'sfunction (i.e. each electrode region). A least-squares criterion was appliedto minimize the difference between the Green's function solution and theapplied voltages in the electrode regions.

In this application of DIF3D the only programming involved was in theUDOIT3 position. The remainder of the code was used without internal changes.

3.16.5 Neutron Transport with Isotropic Scattering

A version of the DIF3D code block has been modified at Argonne to performS n transport calculations for isotropic scattering. The diffusion-theoryequation coefficient and solution routines were replaced by transport theorycounterparts for two-dimensional X-Y, R-Z and triangular geometries. Althoughthis still must be considered an experimental code, DIF3D/transport is usedquite regularly in the analysis of critical experiments and in core designapplications. Its main advantage over other available transport codes isthat its input is identical to the standard, diffusion-thaory version of thecode, which is a considerable convenience to analysts at Argonne.

109

4. PROGRAMMING INFORMATION

This chapter contains detailed programming information concerning theoverall structure and function of the major code blocks in the DIF3D system.The information is primarily intended for the programmer concerned with DIF3Dsource code modifications and for users who wish to understand particulardetails of the calculational flow. Additional details are provided byinternal code documentation included in the DIF3D source code.

4.1 Role and Function of Subprograms

The DIF3D system consists of a collection of large independent codeblocks logically connected by a small "driver" subroutine D3DRIV (standardpath STP021 in ARC System terminology)". D3DRIV dynamically invokes the codeblocks according to data-dependent logic. The code blocks communicate witheach other, and with D3DRIV, by means of interface files ; with the exceptionof the three utility routine COMMON blocks mentioned in Section 4.1.1, nodata are passed in-core from one code block to another.

DIF3D is carefully designed to run in one of two different environments:modular and standalone. In the modular format each code block, includingSTP021, is organized as a separate load module. Each load module containsversions of all the utility subroutines called from the module and is, infact, an executable program. At Argonne, and at other IBM installationsat which Argonne staff maintain codes, DIF3D is set up in modular style.

In the standalone format the entire production code is a single loadmodule. D3DRIV and the utility subroutines are contained in the root overlay;the code blocks executed by D3DRIV are separate overlays. The National EnergySoftware Center versions of DIF3D are set up in standalone style (see Chapter 5),

4.1.1 Module and Overlay Driver - STP021 (D3DRIV)

D3DRIV (STP021) is a small driver subroutine that controls the loadmodule (overlay) calculational sequence ("path") in all DIF3D problems.Figure 1.1 illustrates the sequence of module calls in D3DRIV and the input andoutput datasets employed by each module. (See Table 4.2 for a detailed list ofinput and output data sets for each module). Module execution is initiatedvia the LINKERO or LINKER1 subroutines described below.

The path has a simple loop structure which permits multiple case problemsets ; modules in the path are conditionally executed based on the existenceof interface files. Within the case loop there exists a search loop whichis only triggered by the existence of the SEARCH interface file. Terminationof the search loop is triggered by a sentinel on the SEARCH file.

The file "existence" attribute is obtained via calls to the CCCC utilitysubroutine SEEK (see the discussion in section 4.3.4.1). These dynamicattributes are maintained by SEEK and changed by modules in the course ofproblem execution. Prior to invoking the first module, D3DRIV initializessubroutine SEEK by passing to it a list of file names (DSNAME array) and acorresponding list of logical unit number assignments (NREF array). It mustalso initialize the COMMON blocks IOPUT, PTITLE and STFARC, which are requiredby certain of the utility subroutines.

110

The logical unit numbers (NIN, NOUT and NOUT2) for the card-input andthe two printer-output files are defined and stored In COMMON block /IOPUT/.They are also stored in COMMON block /PTITLE/. The page heading informationand timing information in /PTITLE/ are frequently reinitialized upon entry toa new module. Initialization of COMMON block /STFARC/ is described in thediscussion of the SCAN module in the next section.

Subroutines LINKERO and LINKER1 were written to simplify the readibilityand programming of D3DRIV. The subroutines are identical in coding; separatenames are required to prevent recursion. Their function is to provide themodule calling sequence appropriate to the modular or stand-alone environments.In a modular environment on IBM/370 systems execution is transferred to loadmodules via the LINK^^l macro. In a stand-alone system the appropriateoverlay call is generated. Auxiliary functions including elapsed time ofmodule execution and (in the ANL modular system) the detection and listing oflogical unit numbers left open upon module exit, are also provided.

4.1.2 Input Preprocessors - SCAN and STUFF

The two code blocks which preprocess the BCD card input file are SCAN andSTUFF. This section discusses their use in a program (see also Ref. 41).

SCAN must be called before any BCD input is read and before che firstcall to STUFF; it is called only once in a job. The initialization call toSEEK must precede the call to SCAN. SCAN reads the entire BCD card input filefrom logical unit NIN (NIN is the first variable in the labeled common block/IOPUT/) and copies it to another file which is either the file named ARCor, if ARC is not in the SEEK tables, logical unit 9. In the process it setsup a table of pointers to the beginning of each BLOCK. The call to SCAN alsoprocesses the data in BLOCK=OLD if that block is present in the input file.

All BLOCKs other than BL0CK=0LD are processed by calls to STUFF. Beforeeach call to STUFF the variable STFNAM (the first variable in the labeledcommon block /STFARC/) must be set equal to the name of the BLOCK to beprocessed. For the DIF3D code that name is "STP021". STUFF returns a flag(NRET in /STFARC/) which permits the program to test for end of input.STUFF vrrites, or rewrites, each BCD disk file referenced under the particularBLOCK=STFNAM according to the instructions in the input (DATASET=, MODIFY=,etc.). It is STUFF that reorders, replaces and deletes numbered cards.Since the STUFF processing follows the processing of BL0CK=0LD by SCAN, anew DATASET input on cards would destroy the data already on an existing fileof the same name referenced under BLOCK=OLD.

Figure 4.1 shows a simple driver that uses SCAN and STUFF to preprocessBCD card input. In fact, this driver could be used with the input shown inFigure 3.1 since the BLOCK and DATASET names are consistent. The driver startsby setting card and printer file numbers and by initializing SEEK, TIMER andLINES. Following the single call to SCAN it goes into a loop containing a callto STUFF and an execution of a program (PROG). Execution terminates when thelast BLOCK=TEST has been processed. Figure 4.1 is a simplified, but otherwisetypical, driver; a calculation is performed for each BLOCK in the input.

As it writes or rewrites a BCD card image file STUFF inserts a fewformatted records at the beginning which contain information about thestructure of the file. These lead records may be read:

Ill

cswIMPLICIT REAL*8(A-H,0-Z)

CSWCOMMON /PTITLE /TITLE(66), TIME(IO), HNAME(4), KOUT, KOUT2, NTITLECOMMON / IOPUT / NIN, NOUT, NOUT2COMMON / STFARC / STFNAM, BLKNAM(50), IBLTAB(3,5O), NBLOCK, NRETDIMENSION DSNAME(6)DATA DSNAME / 8HA.SAMPLE, 8HA.SAMPLE, 8HA.XAMPLE, 6HRTFLUX,

1 6HISOTXS, 1H$ /DATA BLOCK/4HTEST/, BLANK/6H /DATA IM1/-1/, 10/0/, 11/1/, 13/3/, 14/4/, 111/11/

CNIN=5NOUT=6KOUT=NOUTNOUT2=IOKOUT2=NOUT2NTITLE=0

CC INITIALIZE TITLE AND HNAME TO BLANKSC

CALL FLTSET(TITLE,BLANK,111)CALL FLTSET(HNAME,BLANK,14)

CN=OCALL SEEK(DSNAME,I1,N,I3)CALL TIMER(IO,TIME)CALL TIMER(IMl.TIME)CALL LINES(10,I)CALL SCAN

CSTFNAM=BLOCK

10 CONTINUECALL STUFFIF( NRET.LE.O ) GO TO 20CALL PROGGO TO 10

C20 CONTINUE

RETURNEND

Fig. 4.1. An Example of the Use of SCAN and STUFF

-\

112

READ(M,99)ANAME,MAXTYP,NONUM,NOFORM,(N(I),l=1,MAXTYP)99 F0RMAT(A8,315/(1615))

M file logical unit numberANAME file nameMAXTYP highest card type number in fileNONUM number of unnumbered cardsNOFORM 0/1, cards are to be read

formatted/free-formatN(I) number of cards of type I

The logical unit number, M, should be obtained through calls to SEEK andSEKPHL:

CALL SEEK(ANAME,IVER,1,0)CALL SEKPHL(I,M,0)

IVER file version numberI file reference number

There are always at least two of these lead records in a BCD file written bySTUFF; FORTRAN I/O expects a second record even if MAXTYPO. Indeed, forNOSORT DATASETs MAXTYP is zero.

The NOFORM sentinel is 0 for files designated DATASET= or SUBLOCK=; it is1 for files designated UNFORM=.

These lead records permit applications modules reading BCD files to makedecisions based on the presence or absence of particular card types. Theuser's input card images follow the lead records and can be read as if theywere cards - one 80-column card per record.

4.1.3 CSE010 (ANL only)

CSE010 converts cross section data from the ARC System (XS.ISO) file36format to the CCCC isotope ordered file format (ISOTXS). The code will alsomerge two ISOTXS files into a single output file. CSE010 is made up of fivesubprograms and is not overlayed. The entry routine CSE010 allocates theBPOINTER container array and calls the various subroutines to perform theirspecific tasks. The input files used by CSE010 are XS.ISO, the input ARCSystem double precision cross section file, IS0TX1 and ISOTX2, the input CCCCfiles which may be merged into the final output ISOTXS file. There is no BCDinput to the routine. Following problem setup the subroutine CTAD is calledto load isotope independent data from the XS.ISO file into appropriate arrays.PRINXD is then called in a loop over isotopes to process the isotope crosssections from the XS.ISO file. Since the ARC System file contains deriveddata rather than the specific cross sections required in the ISOTXS file, anapproximation is required in deriving the CCCC data. In particular, it isassumed that the flux and current weighted total cross sections are equal.This approximation allows a unique conversion of the XS.ISO data to' an ISOTXSformat. If input ISOTXS files ISOTX1 and/or IS0TX2 are available, the sub-routines ISOCTL and PRINO are called to add these data to the data generatedfrom the XS.ISO conversion.

4.1.4 LASIP3 (ANL only)

The LASIP3 module37 was developed at Los Alamos for processing Version-3standard CCCC interface data files. It performs two distinct tasks; namely

113

transforming free-field format, BCD data into well-defined binary files andproviding for printing and punching data in the binary files.

LASIP3 is implemented in the modular environment on the IBM 370/195at Argonne to provide auxiliary input processing capabilities of interest toa limited number of DIF3D users. It it; not implemented in the NESC versionsof DIF3D detailed in Chapter 5.

LASIP3 was modified to incorporate the dynamic storage allocationcapability provided by the BPOINTER package discussed elsewhere in thisdocument, thereby eliminating a fixed length working storage array previouslyrequired in LASIP3 (see sample input in Fig. 3.7).

4.1.5 The General Input Processor - GNIP4C

GNIP4C is an input processor that generates a number of CCCC StandardInterface Files from BCD card-image input. Figure 4.2 shows the structure ofthe code. The main driver (GNIP4C) calls on one or more of nine subprograms.

The combination of subprograms RANIPl and FGEODS reads geometry data fromA.NIP3 cards and generates a GEODST file. For the most part RANIPl reads andchecks the data, and FGEODS composes the GEODST and LABELS files. Allsubroutines in GNIP4C whose names start with "ANIP" (e.g. any of the routinesin RANIPl) read one (and occasionally two) card types. If a GEODST fileis input RANIPl and FGEODS are skipped.

The third subprogram, EGEODS, edits the GEODST file at the user's request.EGEODS contains graphics and printer output routines that generate maps ofarrays of hexagons (TRIPLT) or orthogonal geometries (ORTMAP). TRIPLT usesdata from the A.NIP3 type 15 and 30 cards, and so GNIP4C is not able togenerate hexagonal array maps when the geometry is input via a GEODST file.ORTMAP generates its maps from data in the GEODST file. There is coding inthe subroutines associated with TRIPLT and ORTMAP to generate computergraphics maps via standard CA^COMP or DISPLA calls. This coding is commentedout in the NESC versions of the code, but it is not difficult to reactivate.

RANIP2 and FADENS read A.NIP3 data and write the number density files(ND'-IRF and ZNATDN). Number density edits are produced as the input data areprocessed from A.NIP3 into GEODST, and so it is not possible for GNIP4C toedit atom densities when they are input to the code in the ZNATDN file.RANIP2 and FADENS are skipped entirely if NDXSRF and ZNATDN already exist.

BCDXTT reads the formatted version of the ISOTXS file from a NOSORTDATASET named A.ISO. This is the only direct means by which the user caninput cross sections to the code on cards. BCDXST converts the formatted, BCDform into the binary file ISOTXS. Coding exists in the subprogram to convertin a similar way a formatted version of the delayed neutron data file DLAYXS6

to a binary form, however, the delayed neutron file names have not beenincluded in the DIF3D SEEK tables. There are internal flags in BCDXST whichtrigger edits of ISOTXS and DLAYXS; however, these flags cannot be manipulatedfrom outside the code.

The seventh subprogram, WRSORC, reads inhomogeneous source specificationsfrom A.NIP3 cards and generates and edits a FIXSRC file. WRSORC is skippedwhen none of the fixed source card types (A.NIP3 19 and 40-42) appear in theinput.

114

GNIP4CANIPO1ANIP02ANIP14GETZONGETSZNCPYLBG

UTILITY ROUTINES

IEQUATERRORFLTSETSQUEZELINESTIMERFFORMCKED

COMMON

ARRAYIOPUTPTITLE

REEDBPOINTERINTSETSRLABSEEKFEQUATSPACE

BLOCKS

BCDFLTISIZESBCDINT

1

I—RANI PI

I--FGEODSI LOCHEX

I--EGEODS

1 ANIP031 ANIP041 ANIP051 ANIP061 ANIPO71 ANIP09 CHEK091 ANIP101 ANIP111 ANIP121 ANIP151 ANIPHX1 ANIP34

1 GETHCT1 GETMSH-1 GETREG1 GETBUC1 GETBC

1 —CMESH1—FMESH

1 GETMR 1 --RCMESH1 VOLREG I--TRIGOM1 REDMSH

1 MAKMSH1 PRCEOD—! MPGEOD—1 ANIP431 TRIPLT—

PRNTIXMSHMAP

1—HEXPC1HEXPIC |—HEXPC4HEXPC2HEXPC3

ORTMAP ORTPC1

—RANIP2

——CAnPNQ———

--BCDXST

--WRSORC

--WRSRCH 1

--WRRODS 1

ANIP13GETMATGETISOANIP39GETSET

SORT 13—— cnoTlA

WNDXSR

RWISOTRWDELY—

ANIP19ANIP40ANIP41ANIP42S OR DAT—

ADS

WRSEDSORC

ANIP21ANIP22SRCH4DANIP24SRCH3DANIP25SRCH6DANIP26EDSRCH

ANIP44SORROD

1 MAKROD1 WRTROD

ORTPC2ORTPC6

—1—VALU2D1— SET2DI TMT1FY

—EDTMAT

—RWDY1—RWDY2

—

--SORLAB--SORMSH—SORNZN—SORDIF

—ADS1--ADS2--ADS3

—WRSO—WRS11—WRS 2

EDTROD

1—HEXPC51—HEXPC6I—HEXPC7

-1—ORTPC3I—ORTPC4I—ORTPC5

Fig. 4.2. Subroutine Map for the GNIP4C Code Block

115

WRSRCH reads specifications for the criticality search option and writesand edits the SEARCH file. WRSRCH is skipped when none of the search cardtypes (A.NIP3 21-26) appear in the input.

WRRODS processes the input for the control rod model and it is skippedwhen the A.NIP3 type 44 cards are absent.

4.1.6 Cross Section Homogenization - HMG4C

HMG4C is a cross section processor which generates the macroscopiccross section file COMPXS based on the data contained in the CCCC filesISOTXS, NDXSRF, ZNATDN, and DLAYXS. In generating the macroscopic data, it isassumed that there is a one-to-one correspondence between compositions andzones. Thus, for example, the fifth composition on the completed COMPXS filecorresponds to the data fcr zone number five on the two CCCC files NDXSRFand ZNATDN. The code accepts the CCCC files in their full generality withthe single exception that an isotope or file-wide CHI matrix is not permitted.

The data management strategy used by the codo is rather straightforward.After reading and storing the data obtained from the ZNATDN and NDXSRF files,and the isotope independent data of ISOTXS and DLAYXS, the code attemptsto hold all of the fourteen different types of macroscopic array data inthe remaining container space. If this is possible then a single pass ismade through the ISOTXS file and the contribution of each relevant isotope isadded to each macroscopic cross section of each composition. If all themacroscopic arrays wil1. not fit in the available core, the code determines themaximum number of compositions which can be homogenized in a single pass. Asmany passes are then made as required to completely process the data. Theresults of each pass are written on a scratch file (SCR001) for temporarystorage before being rewritten to the COMPXS file.

The three CCCC files ISOTXS, NDXSRF, and ZNATDN are always requiredinput to HMG4C and hence must be declared under a BLOCK=OLD statement in theinput data or generated from input BCD data by the code block GNIP4C. Thefile DLAYXS is optional but must be included under BLOCK=OLD if delayedneutron data are required. Additionally, the user may specify the BPOINTERcontainer size, the method by which the composition fission spectra are to becomputed, and various edit options on the BCD dataset A.HMG4C.

" Figure 4.3 shows the structure of the code. The subroutines of HMG4Cmay be divided into four separate functional units of code each of which maybe linked to form a separate overlay. The first overlay, OVL1, reads all ofthe input data except for the microscopic cross sections. The second overlay,OVL2, computes the homogenized cross sections in the form of fourteen macro-scopic arrays which are the working storage units of the code block. Inthe third overlay, 0VL3, the COMPXS data set is written from the data containedin the fourteen working arrays. The fourth overlay, OVL4, is essentiallyindependent of the preceding three and is used to edit a COMPXS file. HMG4Cmay be used for the express purpose of editing a user input COMPXS file, inwhich case only the fourth overlay is executed.

4.1.7 MODCXS

MODCXS is an input processor that modifies an input macroscopic crosssection file, COMPXS, to account for user specified directional diffusioncoefficients and/or energy conversion factors. A COMPXS file generated by the

116

I-

HMG4C

UTILITY ROUTINES

FFORM REEDERROR B-CINTERTIMER LINESSQUEZE SEEK

•RDNDXRDATDN ATDN3

—OVL1 1 ISOR14I EDTISO

IDLR13I 1

-0VL2CLEAR

ISOR58

—OVL3

—OVL4

-WREC1-WREC2-WREC3-WREC4

-EDTXS1-SVXS-EDTXS2

-EDTR5-EDTR6-SVSCAT--EDTR8-UPDATE-MAXBND-FISPEC

I-—FARSET—ZROSET

COMMON BLOCKS

ARRAY REFIOPUT HMGPTRPTITLE SCAT

Fig. 4.3. Subroutine Map for the HMG4C Code Block

117

code block HMG4C does not include any directional diffusion coefficientcapability. Furthermore, the fission and capture energy conversion factors arederived directly from the data available on the input ISOTXS cross sectionfile. User input to override these data may be specified and the code blockMODCXS processes these data.

The code block MODCXS is made up of five subroutines. The main driverMODCXS allocates the BPOINTER container for the code block and controls theprogram flow. The first program routine called by MODCXS is ANIP35 whichreads and validates the directional diffusion coefficient data input by theuser on the Type 35 and Type 36 cards of the A.NIP3 dataset. The subroutineANIP37 is then called to read and validate the energy conversion factordata from the Type 37 and/or Type 38 cards of A.NIP3. The subroutine DOMODSis then called to process the user input data. DOMODS reads version 1 ofthe file COMPXS and writes the file SCR001 in the same format as the COMPXSfile after modifying the power conversion and directional diffusion coefficientfactors according to the user specifications. Finally the subroutine COPIERis called to copy the dara from the file SCR001 onto the file COMPXS. Thestandard utility routines ire used throughout the code block to ensure codestandards.

4.1.8 BCDINP

BCDINP creates and modifies the DIF3D control file (also called DIF3D)from default values and/or from the BCD dataset A.DIF3D. BCDINP is comprisedof three subroutines and is not overlayed. The driver subroutine BCDINP setsthe A.DIF3D default parameters for the DIF3D file. If an old DIF3D fileexists the default data is overridden by data read from the existing DIF3Dfile. If an A.DIF3D file exists, subroutine RADF3D reads A.DIF3D and updatesthe DIF3D file arrays with non-default data from A.DIF3D. Upon successfulvalidati of the DIF3D file arrays by subroutine PP^-^n. BCDINP writes theinterface file DIF3D.

4.1.9 SRCH4C

The SRCH4C module controls the criticality search iterative process byadjusting certain parametric vectors in order to achieve a desired value ofk-effective. Search control information including the three most relevantsearch pass parameter estimates are maintained by SRCH4C on the CCCC interfacefile SEARCH (Appendix C.7). The interface files containing the parameter vec-tors appropriate for the selected search option are also modified by SRCH4C.

At the start of each search pass SRCH4C reads the SEARCH file to establishthe search control parameters. Next the header records of interface datasetsrequired for the selected search option are read and checked for data consis-tency. Subroutine GETCON performs this function in the concentration searchoption. Data management requirements for performing the interface file modi-fications in core-contained mode or with auxiliary disk storage are determinedat this time. If the DIF3D file is present the BPOINTER ECM container sizeestimate is obtained to determine the feasibility of the core-containedoption.

( The most recent eigenvalue estimate will be read from the DIF3D file,if present, otherwise it will be taken from the RTFLUX file. Then subroutineSRCHX is invoked to calculate the new search parameter estimate based upon

118

the previous estimates. A parabolic extrapolation method with root-brackettinguses three recent estimates to accelerate the parameter search process. Uponcompletion of the two initial search passes with initial parameter estimates,one linearly extrapolated estimate is employed before the parabolic procedureis invoked. The search parameter is permitted to exceed its user specifiedrange only once during the estimation algorithm. Subsequent occurences leadto problem termination.

Upon return from SRCHX the search history array is updated and theSEARCH file is rewritten. If the search parameter has not yet convergedthe subroutine which modifies the search quantity interface files'is called.Subroutine DMDCON modifies the subzone volume fractions on the NDXSRF filefor the concentration search option. Upon successful modification of NDXSRF,DMDCON turns off the COMPXS existence sentinel so that upon return fromSRCH4C, subroutine D3DRIV will invoke HMG4C and MODCXS to obtain updatedmacroscopic cross sections.

SRCH4C has several features which exploit the time remaining feature ofsome systems and which exploit the DIF3D file if it is present. Consequently,the search is gracefully terminated if time limit is imminent. Abnormaltermination of the DIF3D neutronics module is detected from the restart fileDIF3D thereby causing SRCH4C to end gracefully and permitting a subsequentrestart at: the current search extrapolation cycle and/or at the next DIF3Douter iteration.

4.1.10 DIF3D

The DIF3D module performs the neutron flux and criticality calculations.Figure 4.4 illustrates the structure of the DIF3D module. Names preceded byasterisks in Fig. 4.4 are relevant only to the nodal solution option describedin Ref. 5. They will not be discussed here. The four primary overlays calledby DIF3D (BIN1NP, SSINIT, SSTATE and DSSTOU) share COMMON blocks and BPOINTERFCM and ECM container arrays. Logic sentinels and problem specifications datareside in the /CONTRL/ and /SPECS/ COMMON blocks, respectively. Definitionsfor the elements of the COMMON blocks are located in subroutine BLOCKS whichis included with the DIF3D source listing.

In stand-alone mode, the three-level overlay structure permitted by theCDC Overlay feature is retained by adding the DIF3D subroutine (and requiredutility subprograms) to the driver module D3DRIV. The different callingsequences required for the execution of DIF3D in a variety of computer systemsin modular or standalone mode are unified via the subroutines LINKRO, LINKR1and LINKR2. The suffixes 0,1 or 2 denote the (0,0)-, primary- and secondary-level overlay calls, respectively.

The module driver subroutine DIF3D initializes TIMER and then callssubroutine START which performs the following initialization functions:

1. Zeroes COMMON blocks ;

2. Sets the machine dependent word length parameter LDW («1 or *2) ;

3. Sets I/O mode parameters

4. Initializes units for BCD input and output files ;

119

DIF3DLINKR1LINKR2AREASVOLUMEGETBNDREVRSEWDIF3D

UTILITIES=========

DEFICFPURGCFOPENCFCLOSCFSTATCFFEQUATFLTSETIN2LITLINKERROKSEEKCREDPCREDBPOINTER

BLKGETBLKPUTOPEIvDFCLOSDFDO PCIEQUATINTSETLINESTIMEROPENDSREEDDREDPNTGET

COMMON BLOCKS

ARRAYCONTRLIOCOMVERNUMDEBUGBALBUF

*NHCNTL*NHIOPC*NHIOPD

SPECSIOPUTIOCOMCIOCOMDEDITDMPTITLE

*NHSFCM*NHIOCM

--START

-BININP--

-SSINITEDITOR

--RDIF3D--RLABEL--RSEARC--RCMPXS- -ADSCTM

—RGEODS I — FORMSH|-*FORMCM

—RRTFLX-*RNHFLX—RFIXSR

--FDINIT-

--ZMINIT

• I — SSCORE!— SSDISK

—INEDIT--FORMMZ-

-*NHINIT

I—XSINIT-

— S STATE

—DXSREV-

—DFDCAL

--DORPES

OSWEEPPSWEEPTSWEEPROWSRCTRISRCSORINVSCTSRCTOTSRCFISSRCZEROBAOUTEDOOUTEDTCHEBEDACOSH

FILCPYRBOSOR (CRAY-l only)RBOSRC (CRAY-l only)

-REGMAP

-*NHGEOM-*HEXMAP *GETIJ-*NHZMAP-*NHPNT-*NHCCPT-*NHINED-*NHCORE-*NHDISK

--XSGET1-—XSGET2

-XSEDIT

—XSREV-*NHSIGA

—ORTFDC—TRIFDC

—ORPES1-—ORPES2-—RFLXIN—FSRCIN

—DOUTR1 0 UT ER1

— D O UTR 2 0 UT ER 2

—ORPIN1—ORPIN2

—INNER1--CHEBY1

—SCTSD2—TOTSD2—INN^ki—FISSD2—CHEBY2

Fig. 4.4. Subroutine Map for the DIF3D Code ~lock

121

5. Reads BPOINTER container size data from the binary interface fileDIF3D and allocates the container space.

TJpon return from START, and prior to Invoking the primary modules, DIF3Dinitializes the random access dataset utility routine DOPC.

The binary file input processor overlay driver, BININP, reads the speci-fication records from the DIF3D input interface files listed in Table 4.2(Section 4.2). The data is checked for consistency and entered into thepertinent COMMON block variables.

Using the data obtained in the BININP overlay, the SSINIT overlay callsSSCORE to determine the storage requirements for the DIF3D data manangementoptions. From these options SSCORE chooses the option that maximizes theusage of the available BPOINTER container space.

Upon completion of the data management edits in SSCORE, SSDISK is calledto establish (via DOPC) the random access disk file group assignments requiredin the multilevel data management strategy. On CDC systems an auxiliary ECMcontainer (see XCM discussion in Section 4.3.5.2) is allocated for storing thetable of pointers that index the random access file records.

The problem input data and geometry description are edited by subroutineINEDIT. During the process of forming the zone map array, FORMMZ optionallycalls subroutine REGMAP to edit the region and/or zone to mesh intervalmaps. If the zone map array cannot be ECM-contained in concurrent inneriteration problems, it is written to the random access scratch file ZONMAP.

XSGET1 reorders the group within composition (or zone) cross sectiondata from the COMPXS interface file so that data is ordered by zone withincross section type for a given energy group. During this reordering process,XSGET1 computes directional diffusion coefficients and calls XSEDIT to editthe macroscopic cross sections. If the reordering process cannot be core-contained, cross sections are written by composition to the auxiliary fileSCR001 by subroutine XSGET1. Subroutine XSGET2 performs the necessary numberof read passes across SCR001 to complete the reordering process. In eachpass a core-containable bandwidth of groups is processed.

The primary overlay SSTATE has five secondary overlays (DXSREV, DFDCAL,DORPES, D0UTR1 and D0UTR2). In adjoint problems, DXSREV calls XSREV whichreverses the cross section group ordering and forms the adjoint scatteringmatrix. In the event that the available container storage is insufficientto core-contain all groups, the real problem cross sections are copied toauxiliary file SCR001. The cross section reversal process is then performedin multi-pass mode with the maximum permissible bandwidth of groups core-contained in each pass.

Overlay DFDCAL calls FDCAL which controls the finite difference coefficientcalculation by calling the appropriate subroutines ORTFDC or TRIFDC fororthogonal or triangular geometries, respectively. For data managementpurposes, mesh cells for both orthogonal and triangular geometries are mappedby mesh plane onto a rectangular array. In certain triangular geometryproblems and in problems with black absorber composition assignments some of

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the mesh cells are excluded from the problem solution domain. In triangulargeometry two arrays IS(j) and IE(j),j=l,2 J define the lower and upperindex limits of the active mesh cells on line j . Mesh positions outside theselimits are logically excluded from all calculations. Mesh cells which must beexcluded from the problem domain, but which lie within the limits of theactive mesh cells are effectively excluded from the problem domain by assigningthe value zero to transverse direction coupling coefficients. Thus, computa-tions proceed in an identical fashion for both active and excluded mesh cellswith no additional logic overhead.

The DORPES overlay calls ORPES1 or ORPE32 to compute the optima successiveline overrelaxation factors for the inner (within group flux) iteration.Because of significant differences in data management strategy, dual sets ofsubroutines, differentiated by the suffixes 1 or 2, are employed. The firstset applies to strategies in which at least one energy groups worth of data isECM-contained : the second set applies to the concurrent inner iterationstrategy which requires a minimum of three planes worth of data to be ECM-contained. Subroutines 0RPIN1 and 0RPIN2 control the Gauss-Seidel inneriterations employed to estimate the optimum factors u>g. These routineswere cloned from the routines INNER1 and INNER2 which perform the inner itera-tion sweeps during the outer iteration.

DORPES also calls RFLXIN and FSRCIN to read the real (adjoint) fluxfile RTFLUX (ATFLUX) and the fixed distributed inhomogeneous source fileFIXSRC. If the the flux file does not exist, RFLXIN creates a flat flux guessof unity. In near-critical inhomogeneous source problems, an initial* fluxguess of zero is optionally generated. Mesh cells are initialized to zerowhen they are within the active portion of the rectangular data structure ofthe mesh plane arrays, but they are not part of the problem domain.

Overlay D0UTR1 calls subroutine 0UTER1 which controls the outer (fissionsource) iterations and in thermal problems the upscatter iterations which jare required to solve the multidimensional neutron diffusion equation whenat least one energy group of flux, finite difference coefficients and crosssection files can be ECM-contained. OUTER1 calls subroutines FISSRC, SCTSRCand TOTSRC which compute the fission, scattering and leakage sources and addthem to the fixed source, if present. It also calls subroutines INNER1 andCHEBY1 which perform the inner iterations (within group flux calculations) andextrapolate the resulting fission source, respectively.

One of two data management strategies for calculating the scatteringsource are chosen based on whether or not the rcattering band of fluxes canbe ECM-contained. When the latter is true, the scattering source calculationis performed by double buffering the scatter band of fluxes through memoryfrom disk one group at a time. When the former is true, the buffer for thescatter band of fluxes is treated in a circular manner. Upon filling thecircular buffer, unneeded flux values are displaced, if necessary, byappropriate fluxes as the group index advances during each outer iteration.

Following each completed outer iteration pass, the average time requiredper outer iteration is computed to determine the feasibility of performingthe next outer iteration and completing the editting wrapup in the remainingtime indicated by the TIMER subroutine.

123

Overlay DOUTR2 calls subroutine OUTER2 which controls the outer iterationsfor the concurrent inner iteration option. The source computation routines(FISSRC, SCTSRC and TOTSRC) are called from the intermediate driver routinesFISSD2, SCTSD2, and TOTSD2, respectively. The initial fission source iscomputed by IFISD2. Subroutines INNER2 and CHEBY2 perform the inner iterationsand extrapolate the resulting fission source, respectively.

The scattering source calculation accesses blocks of flux planes from theenergy groups in the scattering band of fluxes pertinent to the current energygroup. The I/O requirements of such calculations are appropriately treated bythe random access I/O features available on the IBM and CDC versions of DIF3D.

The DSSTOU overlay calls three secondary overlays (DSSTO1, DSSTO2 andDSSTO3) that perform the optional region, area and mesh cell flux integraledits. Two general purpose subroutines (TWODPR and TWODTB) are employed toperform mesh cell tabulations and region (and area) tabulations, respectively.TWODTB also writes a copy of the editted tables to the D3EDIT interface file.

The DSSTO1 overlay initializes the editting overlays by establishingthe edit sentinels in COMMON block EDITDM and then calls FORMMR to generatethe region-to-mesh-interval map array and BKLWGT to compute region-dependenttransverse-direction weight factors for the volume and flux integrals.Subroutine SSTOU1 performs the following tasks:

1. Obtains the power normalization factor in real criticality(homogeneous) problems ;

2. Edits and/or writes the PWDINT power density interface file;

3. Edits total power in real fixed source problems;

4. Controls the surface power and flux calculations in the ORTSRF andTRISRF subroutines ;

5. Writes via WPKEDT the peak (surface) power interface file, PKEDIT,for the post processing edit module SUMMARY;

6. Edits maximum power density and corresponding mesh cell indices;

7. Creates the mesh cell power densities for subsequent use by thePOWINT, RPWADD and APWADD subroutines which compute and edit theregion and area dependent power density integrals.

The DSSTO2 overlay establishes via subroutine EDCORE the block sizesfor the requested region and area integrals. Then subroutine SSTOU2 is calledto write the appropriate flux interface files RTFLUX or ATFLUX. In realhomogeneous problems the flux is power-normalized prior to editing or writing.The group-integrated fluxes by mesh cell are optionally edited here,also.If region or zone integral edits are requested, RPSADD is called to computethe region flux integrals. ORTBAL and TRIBAL are called to compute regionleakage components in orthogonal or triangular geometries. Overhead isminimized by requiring only one I/O pass over the unnormalized flux data.Depending opon the requested edit options one or more sweeps across theresident block of fluxes may be required. In the first sweep, fluxes are

124

power-normalized, written and optionally editted. The group-integrated fluxesby mesh cell are accumulated also. In adjoint problems an additional I/O passis required to reverse the flux group ordering for integral edits. An addi-tional NBLKR sweeps (NBLKR is the number of region blocks) over the residentblock of flux planes are made to compute the region flux integrals and theleakage component integrals for the neutron balance edits. Prior to exitingSSTOU2 the region-to-mesh-interval map is converted back to a zone-to-mesh-interval map.

The DSSTO3 overlay optionally calls three subroutines (BALINT, FLXINTand FLXRZ) which edit the region and area balance integrals, the region andarea flux integral totals and/or the region averaged fluxes, and the zone-averaged fluxes (e.g. the RZFLUX file), respectively.

4.1.11 SUMMARY (ANL only)

The SUMMARY module is used with DIF3D at. ANL to edit summary reactionrates and isotopic masses. It is evoked whenever the A.SUMMAR data set issupplied with the input data (the single card-image "DATASET=A.SUMMAR" issufficient data to trigger a SUMMARY edit). The interface files RTFLUX,GEODST, ISOTXS, NDXSRF, ZNATDN and COMPXS must also be present (these normal-ly exist following a typical DIF3D calculation). If present, SUMMARY willalso use the LABELS, PKEDIT, and NHFLUX files.

4.1.12 UD0IT1-UD0IT4

The four UDOIT modules, UD0IT1 - UD0IT4 are user modules placed at stra-tegic points in D3DRIV to provide the user with additional processing capabi-lity during the calculational sequence (see Fig. 1.1). This feature of DIF3Dis particularly useful in modular systems where the dummy UDOIT modules maybe easily pre-empted by user UDOIT modules located in an automatic-call li-brary that may be processed via the ARCSP021 procedure parameter PRELIB=,name'.The user merely creates a self-contained load module which communicates withthe DIF3D system via the appropriate interface files and thereby tailorsDIF3D processing capabilities to suit his needs. This feature may beexploited in stand-alone implementations by relinking DIF3D with dummy useroverlays appropriately replaced. Four interface file names (three binaryfiles UDOIT versions 1, 2 and 3 and one BCD file A.UDOIT) are reserved in theSEEK file table for UDOIT applications.

4.2 Data Set Classification and Use by Code Block

Table 4.1 lists all of the data sets used by the code blocks in DIF3D andclassifies them into one of five different categories:

BCD: Formatted, sequential access input and output, includingstandard system data sets (see definitions in Appendix B) ;

CDB: Code-dependent (including ARC system) binary (unformattedsequential access) interface data sets (see definitions inAppendix D) ;

CCCC: CCCC binary interface data sets (see definitions in Appendix C)j

DOPC: Unformatted random access scratch data sets;

SCR: Sequential access scratch data sets.

125

TABLE A.I. Data Set Classification and Description

FileReferenceNumber

FileName

FileType

FileDescription

456891011121314151617181920222324252627282930313233343536373839

41-5661,6266-7576-7880

DSPLASC1

DSPLAFNT

A.DIF3DA.NIP3A.HMG4C

A.LASIP3A. ISOBCDSOB

A.SUMMARDIF3DCOMPXSLABELSD3EDITNHFLUXNAFLUXPKEDITGEODSTISOTXSNDXSRFZNATDNRTFLUXATFLUXFIXSRCRZFLUXPWDINTISNTXSISOTX1ISOTX2SNCONSSEARCHRNDMnnXSISO

SCROOl-10UDOITAUDOIT

SCRBCDBCDCDBBCDBCDBCDBCDBCDBCDBCDBCDBCDCDBCDBCDBCDBCDBCDBCDB

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDOPCCDBSCRCDBBCD

graphics scratch fileinput data for SCAN moduleoutput data all modulesgraphics font datainput data spool from SCANauxiliary output all modulesDIF3D controlGNIP4C controlHMG4C controlLASIP3 controlBCD ISOTXSBCD LASIP3 outputSUMMARY controlDIF3D controlmacroscopic cross sectionslabels, half-heightstabular edits spoolnodal restart (real)nodal restart (adjoint)peak power/flux interfacegeometry descriptionmicroscopic cross sectionsnuclide/zone referencezone nuclide atom densitiesreal fluxadjoint fluxfixed sourcezone flux averagespower densityaux. ISOTXS slotaux. ISOTXS slotaux. ISOTXS slotSn constants (transport)SRCH4C controlrandom access scratch files (Table 4.3)micro, cross section files 1 and 2scratch filesUDOIT versions 1-3UDOIT module input

126

The file reference numbers are assigned in the SEEK initialization call. Inthe Argonne implementation of the CCCC routines REED/RITE and SEEK, theFortran logical unit numbers are identical to the file reference number. Theabsence of a file name in Table 4.1 indicates a system data set; these do notappear in the SEEK table. Files of type DOPC are listed in Table 4.3 (Section4.3). The Argonne implementation of DOPC (see Sections 4.3.4.3 and 4.3.4.1)assigns Fortran logical unit numbers to DOPC files RNDM01 - RNDM14 via a callto SEEK. This, of course, has no effect on other DOPC implementations (i.e.,the data set names RNDM01-RNDM14 will never be referenced). The data setsaccessed by a given module are summarized in Table 4.2.

TABLE 4.2. Interface File Usage by Module

Module Input Files Output Files

SCAN

STUFF

UDOITl.2,3,4

CSE010

LASIP3

GNIP4C

HMG4C

MODCXS

BCDINP

SRCH4C

DIF3D

SUMMARY

BLOCK=OLD and BLOCK=dsname(BCD card image input)BLOCK=STP021

See footnote a

XS.ISO or ISOTX1, ISOTX2

A.LASIP3 andCCCC interface files

A.ISO, A.NIP3, GEODST,NDXSRF, ZNATDN, ISOTXS,FIXSRC, SEARCH

A.HMG4C, A.NIP3, LABELS,ISOTXS, NDXSRF, ZNATDN

A.NIP3, COMPXS, LABELS

A.DIF3D, DIF3D

SEARCH, RTFLUX or DIF3D,NDXSRF,ZNATDN, GEODST,LABELS

DIF3D, GEODST, COMPXS,FIXSRC, LABELS, RTFLUX,ATFLUX, SEARCH, SNCONS,UHFLUX, NAFLUX

A.SUMMAR, GEODST, COMPXS,ISOTXS, NDXSRF, ZNATDN,RTFLUX, NHFLUX, PKEDIT,LABELS

ARCBCD (BCD input data spool

BCD input files from BLOCK=STP02i

See footnote a

ISOTXS (on ISNTXS unit)

CCCC interface files

ISOTXS from A.ISO,GEODST, NDXSRF, ZNATDN, FIXSRC,LABELS, SEARCH from A.NIP3

COMPXS

COMPXS

DIF3D

SEARCH, NDXSRF, GEODST,LABELS

DIF3D, RTFLUX, ATFLUX,RZFLUX, PWDINT, D3EDIT,PKEDIT, NHFLUX, NAFLUX

aFiles A.UDOIT and UDOIT (versions 1, 2 and 3) are available in the SEEK tableand intended for UDOIT module applications.

127

» 4.3 Data Management Considerations

A multilevel transfer approach that unifies the treatment of one- ortwo-level storage hierarchy machines is adopted in DIF3D. The implementationemploys a set of high level subroutines to perform the data management tasks.These subroutines in turn exclusively employ the standardized utility sub-routine calling sequences defined by the CCCC6, thereby providing a highlyexportable code system that has been tailored to utilize machine-dependentmultilevel and random access I/O methods.

4.3.1 Data Management Concepts

The following terminology will be used in the ensuing discussion (seeRef. 6 for more detailed definitions):

1. Extended Core Memory (ECM): That (physically separate or logicallydesignated) portion of a computing system containing storage locationswhich serve as a buffer for random access data.

2. ECM File: A named array allocated within the BPOINTER ECM container.This array provides a buffer area for one or more blocks of randomaccess file data. Associated with an ECM file is a block structureidentical to the random access files it services.

3. Fast Core Memory (FCM): That portion of a computing system whichcontains storage for both data and instructions, which is directlycoupled to the computations portion of the system, and which isdirectly coupled to ECM. FCM may be the entire central memory or itmay be that portion of central memory remaining after an ECM portionis designated.

4. Random Access Data: Data which can be transferred between FCM andECM in out-of-sequence strings.

5. String: A subportion of a random access file block. Data transfersbeween FCM and ECM are string transfers.

6. Random Access File: (Also called Direct Access File). A namedcollection of data which is stored on a peripheral storage device.The file data are arranged in blocks which can be transferred betweenECM and peripheral storage randomly, i.e. out of sequence.

7. Logical File: A random access file. The identity of a logical filein DIF3D is established by an integer variable, the (logical) filereference (or unit) number.

8. Logical Record: A basic unit of information used in the definitionof a logical file ; all records in a Logical file are the same length.

9. Logical Record Group: A logical collection of records. Each recordgroup in a file has the same number of records (e.g. a group andspace-dependent flux file has each flux plane of each group as arecord and all flux planes (records) in a particular energy group asa logical record group).

128

10. Block: A collection of logical records in a record group of arandom access file. Each block consists of an equal number ofrecords (N) except for the last block in a record group which mayhave M<N records. The block length is always less than or equal tothe record group length. Data transfers between disk and ECM areblock transfers.

11. Disk: A generic name for a peripheral storage device used forstoring random access files.

12. Physical Unit: An identifiable subpait of a disk. One of morephysical units comprise a disk.

13. File-Group: A collection of one or more random access files. Thefile-group collection is assigned to a single physical unit.

4.3.2 Multilevel Data Management Strategy

The standardized method5 of multilevel data management employs thedata transfer paths illustrated in Fig. 4.5. Each random access file iscomposed of one or more record groups and resides on a physical unit. Whenneeded, data is transferred (via DRED and DRIT) in blocks of records betweendisk and ECM, and then strings of data are transferred (via CRED and CRIT)between ECM and FCM. When the ECM and FCM BPOINTER containers both reside inthe same memory level, data from ECM is used directly, thereby avoidingredundant memory allocation and data transfer. Most of the bookkeepingassociated with this data management approach is consolidated and eliminatedby the high level data management routines described in Section 4.3.4.

The principal goal of the DIF3D data management strategy is to minimizethe use of costly random access 1/0 transfers by optimizing the use of theavailable ECM container (ECM size is specified on the type 02 card of A.DIF3D).As mentioned in Section 3.9.1 two principal strategy options, the one-group-contained option and the concurrent inner iteration option, are availableto achieve this goal. The latter option performs one or more I/O sweepsacross the data required in the within-group (inner) iteration for a givenouter iteration because the data for all planes in the current group are notsimultaneously contained in ECM. The former option requires exactly one I/Opass across the data. As ECM size is increased beyond the one-group-containedthreshold an attempt is made to contain additional data, namely, a scatteringband of fluxes or the entire flux file, and/or cross sections, finite-differ-ence coefficients and fission sources. Ultimately, a third option, all filesECM-contained, is possible at which point no DOPC files are required except forthe DOPC file FSRC in inhomogeneous source problem.

The principal data structures in the strategy options are the ECM filesthrough which all data are buffered for the (up to 14) random access disk fileslisted in Table 4.3. The block structure of an ECM file is identical to thestructure of the random access disk files that it will service. However,only a subset of the total number of blocks in a DOPC file is typicallyallocated to an ECM file in most strategy options.

Data is transferred between the random access scratch files in Table 4.3and the corresponding ECM files listed in Table 4.4 using the DIF3D datamanagement routines BLKGET and BLKPUT which in turn call the standardized CCCC6

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DISK

ONE

LEVEL

MACHINE

FAST CORE MEMORY I FCM)

DRED

DRIT

ECM

BUFFERS

CRED

CRIT

FCM

ARRAYS,

BUFFERS

EXTENDED COREMEMORY (ECM)

FCM

TWO

LEVEL

MACHINE

Fig. 4.5. Multilevel Data Transfer Paths

130

TABLL 4.3. Random Access File Descriptions

DO PCReferenceNumber

1234567891011121314

FileGroupNumber

23512345416423

SEEKReferenceNumber

4142434546474849515253545556

SEEKTableFile Name

RNDM01RNDM02RNDM03RNDM04RNDM05RNDM06RNDM07RNDM08RNDM09RNDM10RNDM11RNDM12RNDM13RNDM14

ARCSP021FileName

PSIOLDPSINEWPSIUPFDCOEFFRNOLDFRNNEWFRNM1FRNM2SRCNEWZONMAPCXSECTFSRCPSIGOPSIGN

TABLE 4.4. Correspondence Between ECM and Disk Files

ECMFile Name

DiskFile Name File Contents

ZONMAPCXSECTZONMPC*PSINEW \BPSI* JFDCOEFSRCNEWFRBUFS IFRNM1**,2**JCXSADJVOLUMEAREATC*AREAFC*AREALC*

ZONMAPCXSECT

,•1 TOLD,PSINEW(PSIGO**,PSIGN**FDCOEFSRCNEW**

j FRNM1.FRNM.2\FRNOLD** sFRNNEW**CXSECT

Zone to fine mesh mapMacroscopic cross section?Zone to coarse mesh cell mapFlux iterate (all groups)Flux iterate (current group)Finite difference coefficientsGroup total sourceFission source iterates

Adjoint ordered cross sectionsUnit height mesh cell volumes in X-Y planeCross sectional area for any X-Y planeCross sectional area for any X-Z planeCross sectional area for any Y-Z plane

REGMPCPOWERF PSIGO**,PSIGN**PEAKFL FRNNEW**PEAKFF FRFOLD**PEAKPW SRCNEW**SRFBUF SCR001.2RPWINT SCR001APWINT SCR002TOTPSI PSIGO**,PSIGN**RPSINT SCR001APSINTRBLBUF SCR006.3.4RBLINT SCR003,l,2RBLTNT SCROO3.1.2ABLINT SCR004.5ABLTNT SCR004.5ZPSINT SCR005

Region to coarse mesh cell mapPower density by mesh cellPeak total flux by mesh cellPeak fast flux by mesh cellPeak power density by mesh cellSurface fluxes by mesh cellRegion power integralsArea power integralsTotal flux by mesh cellRegion flux integralsArea flux integralsRegion balance (leakage) integralsRegion balance integralsRegion balance integral totalsArea balance integralsArea balance integral totalsZone-averaged flux integrals

* Temporary ECM files** CIIS option only

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rojtines DRED and DRIT. ECM files are opened (via calls to OPENCF) with thenumber of blocks required by the current data management option.

Except for ZONMAP and CXSECT which are defined in SSINIT, all ECM filesin the upper half of Table 4.4 are defined (via DEFICF) in subroutine SSTATE.ECM files in the lower half of Table 4.4 are defined in one of the three editoverlay drivers (DSST01, DSST02 or DSST03). The ECM files are not opened(i.e. ECM container space is not suballocated to a particular ECM file)until an OPENCF call is issued. When an ECM file is no longer needed its ECMspace may be via a call to CLOSCF. The definitions of the DOPC files are made(via DOPC and DEFIDF) in subroutine SSDISK. The characteristics of the ECMand DOPC files are provided in the subroutine calls to DEFICF and DEFIDF andwill not be repeated here.

Several of the ECM files in Table 4.4 are temporary files needed duringpreliminary stages of the DIF3D calculation (e.g. ZONMPC, CXSADJ, AREATC,AREAFC and AREALC). The temporary files use ECM space that will later bereused by the major ECM files during the outer iteration strategy.

Numerous small arrays are allocated in the FCM container. Documentationof these arrays occurs in the source listings of the subroutines which usethem. Data transfer required for these arrays is performed by the CCCCroutines REED and RITE. An auxiliary group of arrays are allocated inFCM on two-level machines, of which the CDC 7600 is the only machine on whichwe have had operating experience. These FCM arrays provide a computationalbuffer area in which data passed from ECM may be efficiently processed,thereby avoiding the less efficient computations that result when ECM filesare directly addressed (see discussion in Section 4.3.2,3).

The auxiliary edit files in the lower half of Table 4.4 are opened atdifferent stages in the editing overlays. A number of these ECM files areregion and area integral files which have a logical record group structuresimilar to the flux files. Within a record group, however, blocking is simplybased on the available ECM container space; a natural block size (such as amesh plane in files of mesh cell data) does not exist. Because of the specialnature of these region and area files and their relatively limited resourceutilization, the BLKGET and BLKPUT routines are not used to transfer databetween disk and ECM. Instead we use the sequential access routines REED andRITE to transfer data from scratch files SCR001-SCR006 directly to ECM fileson one-level machines. On two-level machines auxiliary FCM sub-blocks areallocated for computational efficiency (as noted in Section 4.3.2.3) and datais transferred between disk and FCM using REED and RITE. After processing asub-block of data pertinent sub-blocks are transferred between FCM and ECM usingCRED and CRIT. Several sub-blocks of data may then be successively saved inand reused from ECM until the next region or area block is required.

4.3.2.1 The One-Group-Contained Strategy

In this strategy each block of an ECM file contains all data for atleast one energy group (i.e. all mesh planes in mesh cell dependent files).Therefore, each ECM file requires one block of appropriate size. During theouter iterations the FDCOEF and BPSI files are alternately opened and closedonce each outer to permit the reuse of ECM space. When a scattering band offluxes is ECM-contained, the ECM file (PSINEW) is opened with MAXSCT+1 blocks

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where MAXSCT is the maximum scattering bandwidth. The BPSI file is not usedin this case. The three most recent iterates of the fission source file arerequired for the Chebyshev acceleration of the outers. The two most recentiterates are held in the ECM file FRBUFS which unlike the other ECM files isnormally assigned two blocks. The oldest iterate is buffered through the ECMfile SRCNEW alternately from DOPC files FRNM1 or FRNM2 on which it had beenpreviously saved. When sufficient ECM space exists, three blocks are allo-cated to FRBUFS thereby permitting the three most recent fissiqfh source esti-mates to ECM contained.

4.3.2.2 Concurrent Inner Iteration Strategy

The concurrent inner iteration strategy (CIIS) requires that data foronly a fraction of the total number of mesh planes be ECM-contained duringthe within-group inner iterations. Consequently, three-dimensional problemswith an unlimited number of mesh planes are permitted with .ie number of meshcells on a plane dictated by the ECM container size.

The K planes in each energy group are partitioned into Q blocks ofplanes with block size L. An upper bound on the block size L is an inputparameter on the type 03 card of A.DIF3D. This bound represents an estimatedoptimal block length for efficient I/O performance on a particular machine.As mentioned in section 3.10.1, an attempt is made to ECM contain as manyblocks of planes of size L as is possible with the given ECM container size.

The CIIS algorithm is sketched in a FORTRAN-like notation in Fig. 4.6.

The inner iterations sweep across the mesh planes in a wave-front fashion,processing all data on a particular plane before proceeding to the next plane.As an inner iteration for one block completes, the next iteration for allpreceding blocks can be performed. U, the effective number of blocks whichcan be simultaneously contained in ECM determines the wavefront or bandwidthof inner iterations (B=UL) which can be performed in a single I/O pass overthe current group data. After the B'-th iteration has completed for all planesin a given block the write operation for the block may be initiated. Althoughthe calculations for the new flux in this block are completed, the block mustremain in ECM for the next I/O cycle because data in the last plane of theblock is required during the next cycle. During this cycle the asynchronouswrite operation is given time to complete. The number of inner iterations,Mg, for each outer iteration determines the number of I/O passes, Pg,

Pg = (Mg + B - 1) / B

required to complete the inner iterations in group g. A diagram of the I/Oand CPU actxvity that occurs in the ECM file PSINEW on two successive I/Ocycles c and c+1 is Illustrated in Fig. 4.7.

In summary, each inner iteration pass, p=1,2,...,Pg, is comprised ofc=1,2,...,C 1/0 cycles. The following events occur in cycle c:

1. The asynchronous reads for block c (c<Q) are completed and reads forblock c+1 (c<Q) are initiated.

2. In the first pass (p=1) the group source for block c is calculatedand saved for for later passes.

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Q = (K+L-l) / LB = U * LC = U+QDO 400 g = 1.NGR0UP

Pg = (Mg-1)/B + 1DO 300 p = l,Pg

B' = min( B, Mg-(p-l)*B )'initiate reads on block (l,g) data,

DO 200 c = 1,CIF (c<0) 'finish reads on block (c,g) data'IF (c<0) 'initiate reads on block (c+l,g) data,

IF (c<Q and p=1) 'calculate block (c,g) group source,

DO 100 b = 1,B'Ks = max( 1, c*L - b - L + 1 )Ke = min( K, c*L - b )IF ( Ks<Ke ) 'perform inner iteration for planes Ks to Ke'

100 CONTINUEIF (c>U+L) 'finish write of flux block (c-U-l,g)'IF (c>U) 'initiate write of flux block (c-U,g)'IF (p=Pg and c>U) 'compute fission source for block (c-U,g)'IF (p=Pg and c>U and g=G) 'perform Chebyshev acceleration on

fission source block (c-U,g)'200 CONTINUE

'finish writes on flux block (Q,g)'300 CONTINUE400 CONTINUE

Fig. 4.6. Concurrent Inner Iteration Algorithm

134

I/O CYCLE c I /O CYCLE c+l

c-U-l

c-U

BLOCK c _,INDICES

INNER ITERATIONSWEEP INDICES

I 2 3 4 5 6

c+l

WRITINGFLUX-BLOCK

c-U-l

/

/ 5

/ 4 5

/ 3 4 5

1 2 3 /

I 2 /PLANE

1 / PLANE

' PLANE

/ 6

6

6 /

/

cL-2

cL-l

cL

READINGFLUX-BLOCK

C+l

INNER ITERATIONSWEEP INDICES

1 2 3 4 5— »

READINGFLUX-BLOCK

c + 2

WRITINGFLUX-BLOCK

c-U

/

/

/ 4 5

/3 4 5/

< 2 3 /

6

6

6

y

c + 2

c-U

c-l

c + l

Fig. 4.7. Concurrent Inner IterationI/O Cycle Description (L=3, U=2)

135

3. The B' inner iterations for blocks c-U to c are performed (SeeFig. 4.7).

4. The write for flux block c-U-1 is completed and the write for blockc-U is initiated.

5. On the last pass Pg the block c-U fission source is calculated andChebyshev acceleration is applied.

The storage requirements (in units of mesh planes) for the variable sizeCIIS blocks are summarized by:

1. U+3 fluxes.,

2. 4(U+2) finite difference coefficients,

3. U+2 total group sources,

4. 4+1/LDW miscellaneous data (3 fission sources, 1 flux and 1/LDW zonemap).

The constant terror in these storage requirements formulas account for auxiliaryblocks required to achieve a high degree of I/O and CPU concurrency. LDW is aword length parameter which accounts for the fact that integer array storagerequirements are half that of long words on short word machines. The procedurefor estimating the optimal ECM size for a given problem and for determiningthe appropriate value for U is presented in Section 3.10.1.

4.3.2.3 Two-Level Machine Data Management Considerations

As mentioned earlier (Section 4.3.2) transfers between ECM files andFCM arrays use the CCCC utility routines, CRED and CRIT. This practice avoidsthe inefficiencies obtained when single data items are directly addressedat random locations in ECM. After allocating required fixed size arrays inFCM including the cross sections array for one group, the remaining plane-oriented mesh cell arrays are blocked with one or more mesh lines per blockbased on the FCM container size (specified on card 02 of A.DIF3D file).

Because of the regular nature of the mesh cell structure in the DIF3Dfinite difference option, the two-level strategy is implemented with noessential change to the solution algorithm. Loops over the J lines in a planeare replaced by an equivalent set of two loops ; a loop over blocks of lines ina plane and a loop over lines within each such block. The one-level implementa-tion simply uses the special case of all J lines contained in a single block.

Prior to processing each block of lines, data from appropriate ECMfiles must be transferred to FCM (via CRED). After processing each block oflines newly calculated data must be transferred to ECM (via CRIT). Thepointers to the FCM arrays used which receive the ECM data are always passedas subroutine arguments t:o the routines in which the CRED and CRIT occur. Onone-level implementations tuese pointers are set to the appropriate locationin the directly addressable ECM file.

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Coding which is pertinent only to the two-level data transfers (e.g.CRED and CRIT calls and associated indexing) is bracketted by C2LV commentcards1,1 which are "activated" by a preprocessor code when generating atwo-level implementation of DTF3D. When partial plane blocking is requiredin FCM, additional coding is required for initialization tasks in the next-adjacent-face periodic boundary condition option. An additional array isneeded to contain the boundary fluxes (along the lower X-boundary on planek) which are required in the transverse leakage calculations for the j=1 lineon plane k. A similar array is needed for the reverse calculation.

4.3.3 DIF3D Data Management Routines

The high level data management routines developed for DIF3D are designedto simplify the bookkeeping associated with managing the disk and ECM files ina variety of machine environments. These routines employ the BPOINTER routinesto manage ECM file allocations in the ECM container and call the CCCC routinesDOPC, DRED and DRIT to perform asynchronous, random access I/O tasks.

The DIF3D routines may be logically divided into two primary groups,those related to ECM files and those related to DOPC files. The first groupincludes DEFICF, OPENCF, CLOSCF, PURGCF, PNTGET and PCRED. They communicatewith each other via the CFTABL COMMON block in which is located data definingthe characteristics and current state of each ECM file. The second groupincludes DEFIDF, OPENDF and CLOSDF which communicate via the RNDMFL COMMONblock in which is located data defining the characteristics and currentstate of each DOPC file. The BLKGET subroutine with entry points (FINGET,BLKPUT and FINPUT) controls data transfer between DOPC files and ECM filesand therefore belongs to both groups.

The PCRED routine with entry points (ICRED, PCRIT and ICRIT) is a recentaddition to these data management routines and is employed only in the nodaloption.

4.3.3.1 DEFICF

The characteristics of each ECM file are specified to the DIF3D datamanagement routines by a call to DEFICF. The calling sequence for DEFICF is:

CALL DEFICF ( CFNAM, NREC, LREC, NRBLK, NRGRP, LCFN)

This call defines the characteristics of ECM file, CFNAM, which has NRECrecords of length LREC (single precision) words. There are NRBLK records ina block and NRGRP records in a record group. LCFN is the ECM file referencenumber by which this file may be addressed and is simply the index of thenext available entry in the ECM file table in COMMON block CFTABL. CallingDEFICF with CFNAM = CLEARC will initialize the CFTABL COMMON block.

Entry point DELECF deletes file CFNAM and zeroes its CFTABL entries.Entry point CHNGCF changes the name of the ECM file having reference numberLCFN to the name CFNAM.

4.3.3.2 OPENCF

After the characteristics of an ECM file have been defined (via DEFICF),ECM container space may be suballocated for it via a call to OPENCF:

137

CALL OPENCF( CFNAM, LCFN, NBUFS, IFTYP )

This call issues a call to the BPOINTER routine PUTB to allocate an arraynamed CFNAM. The call allocates space for NBUFS blocks where the size of ablock was given in the DEFICF call. The sentinel IFTYP signals one of twooperational modes for the ECM file. Files that require I/O transfers aredesignated with IFTYP=1. Random access files that are ECM-contained andrequire no I/O transfers are designated by IFTYP=0. Subsequent calls toBLKGET or BLKPUT will automatically ignore I/O requests for these files.Note below the effect of CLOSCF calls with action sentinel unity on IFTYP=0files.

Calls to OPENCF for files that have already been opened are ignored ifeither the file is already ECM-contained or if the existing file is not ECM-contained but has sufficient space to contain the requested NBUFS blocks. Afile opened with IFTYP=1 can be changed to ECM-contained mode (IFTYP=0) bycalling OPENCF with IFTYP=0 provided NBUFS is identical to the existing numberof blocks already allocated.

4.3.3.3 CLOSCF

When an ECM file is temporarily or permanently no longer needed, theCLOSCF subroutine may be used to release the buffer space. The callingsequence for CLOSCF is:

CALL CLOSCF ( LCFN, NOP )

This call releases the suballocated buffer space for the ECM file with referencenumber LCFN depending on its associated OPENCF sentinel and the action sentinelNOP. If NOP = 0 or 2, the buffer space is unconditionally released (via theBPOINTER WIPOUT command). When NOP = 0 this call also deletes (via an internalDELECF call) the ECM file from the list of files in the CFTABL common block.Calls to CLOSCF with NOP = 1 are ignored when the file is ECM-contained (i.e.opened with IFTYP = 0).

4.3.3.4 PURGCF

Following one or more calls to CLOSCF, the released ECM container storagemay be recycled for subsequent use by calling PURGCF. The calling sequencefor PURGCF is:

CALL PURGCF (LSTBUF)

PURGCF calls the BPOINTER routine PURGEB to clean up a fragmented ECM con-tainer and then refreshes the ECM pointers for all ECM files that remainopen. A pointer to the first unused ECM location is returned in LSTBUF.

4.3.3.5 BLKGET, FINGET, BLKPUT and FINPUT

All I/O requests to random access files are channeled through BLKGETand FINGET or BLKPUT and FINPUT which ultimately invoke the CCCC routines DREDor DRIT. The calling sequence for BLKGET (which calls DRED) is:

CALL BLKGET ( LCFN, NCBLOK, LDFN, NDBLOK )

138

This call requests the NDBLOK-th block from the random access file withDOPC reference number LDFN to be read into the NCBLOK-th block of the ECMfile having reference number LCFN. A corresponding FINGET call is requiredto ensure that the potentially asynchronous I/O operation has completed priorto using the requested data. An identical calling sequence is required forthe BLKPUT and FINPUT routines for writing random access files to disk.

If the designated ECM file is core-contained (IFTYP=O in the OPENCFcall) no data transfer requests are issued by these routines. If NBUFSdenotes the number of blocks allocated to an ECM file, then the block in whichthe data transfer occurs is determined as NCBLOK modulo NBUFS. This enablesthe programmer to use the natural block index of the DOPC file rather than theindex imposed by the size of the ECM file. In most applications NCBLOK andNDBLOK will be identical.

4.3.3.6 DEFIDF

Members of DOPC random access file groups are defined via calls toDEFIDF. The calling sequence of DEFIDF is:

CALL DEFIDF ( DFNAME, LDFN, MXBLOK, MXLEN, LENFIL )

This call defines the characteristics of the random access file having DOPCreference number LDFN. The maximum number of blocks (MXBLOK), the maximumblock length (MXLEN) and the length of the file (LENFIL) are the parameterspassed on to DOPC within DEFIDF. The file name DFNAME is used internally bythe DIF3D data management routines for the programmer's convenience.

The random access file table in the RNDMFL COMMON block must be initializedby calling DEFIDF with file name CLEARD prior to defining the first DOPC file.A DOPC initialization call (action code 0) will also be made by DEFIDF. ADOPC file group is defined by calling DOPC with action code 3 following one ormore DEFIDF calls which define the member files of the corresponding filegroup. Null files are defined when MXBLOK=0 and provide a means for simplify-ing program logic. Such files are not added to DOPC file groups, but areentered into the random file table COMMON block, RNDMFL.

4.3.3.7 OPENDF and CLOSDF \

The calling sequence for OPENDF is:

CALL OPENDF ( DFNAME, LDFN )

This call returns the DOPC reference number (LDFN) associated with a randomaccess file name and does not initiate I/O activity.

The calling sequence for CLOSDF is:

CALL CLOSDF ( LDFN, NOP )

This call closes the random access file with DOPC reference number LDFN bycalling either DRED or DRIT with record number zero. The choice of DRED or \DRIT depends on the most recent file activity. When action flag NOP = 0, the ]associated file is deleted from the random access file table.

139

4.3.3.8 PNTGET and IPTGET

Pointers to particular records within an ECM file are obtained bysubroutine PNTGET. The calling sequence for PNTGET is:

CALL PNTGET ( LCFN, ICREC, LPT )

This call returns the pointer (LPT) to record number ICREC in the ECM filedenoted by the reference number LCFN. LPT is a pointer relative to a longword ECM container array. A long word array is single precision on a longword computer such as the CDC 7600 or the CRAY-1. On short word machines(e.g. IBM 3033) a long word array is a double precision (REAL*8) array. Asimilar calling sequence used with IPTGET returns the pointer (LPT) to arequested record in the LCFN file relative to a short word (single precision)ECM container array.

On two-level implementations the ECM container is never directlyaddressed therefore PNTGET is made equivalent to IPTGET. The pointers arethen appropriate for use in the CRED/CRIT routines which transfer data betweenECM and FCM.

4.3.3.9 PCRED, ICRED, PCRIT and ICRIT

PCRED and ICRED combine the functions of returning ECM pointers to arequested record of an ECM file (a PNTGET cr IPTGET function, respectively) andthen, on two-level machines, transferring data for the requested record fromECM to FCM (a CRED function). The calling sequence for PCRED is:

CALL PCRED ( NCFN, ICREC, MCPNT, LCPNT, NREC, IREAD )

This call returns the pointer (MCPNT) to record number ICREC in ECM file NCFN.In one-level machine implementations the ECM container is directly addres-sable, therefore PCRED also sets the FCM pointer LCPNT to MCPNT prior toreturn. In two-level implementations LCPNT is an input argument to thePCRED call and NREC records are transferred to FCM (starting at FCM pointerLCPNT) from ECM file NCFN (starting at ECM pointer MCPNT) whenever the sentinelIREAD is nonzero.

In two-level implementations PCRIT and ICRIT transfer NRECS records fromFCM (starting from FCM pointer LCPNT) to ECM file NCFN (starting from ECMpointer MCPNT). MCPNT must be already defined before a PCRIT or ICRIT call ismade.

4.3.3.10 STATCF

STATCF is a debugging tool that displays the currently defined ECM filesand their associated characteristics.

4.3.4 CCCC Utility Routines

Reference 6 describes a set of subroutine calls defined by the Committeeon Computer Code Coordination (CCCC) which standardizes data management inorder to facilitate the exchange of programs between different computers andlaboratories. Only the calling sequences and functions are standardized; theactual coding of each routine is left to individual installations.

140

The set of routines*•!• developed at ANL are designed to operate on machineswith either one level of memory (e.g. IBM and Cray computers) or two levels(e.g. the CDC 7600). The machine-dependent coding has been kept to a minumum.Not only does this approach make code export easier, it also permits thetesting of a two-level data-management strategy on a one-level machine.

The calling sequences and functions are defined fully in Ref. 6. Thissection goes into some of the coding details for the versions of the CCCCsubroutines included in the utility subroutine package.

4.3.4.1 SEEK

In the ANL implementation of the CCCC standards all data sets exceptthe output print file and input card image file are given names and versionnumbers. Some file formats (e.g. those containing isotopic neutron crosssections or the neutron flux distributions) are defined by the CCCC, butothers (e.g. the file used by Applied Physics codes to store macroscopic crosssections) are code-dependent. Subroutine SEEK provides the connection betweenfile names and logical unit numbers, even for scratch files. SEEK is verysimilar to the ARC System routine SNIFF36.

SEEK must create and maintain a table (the "SEEK table") that associateseach unique file name and version number pair with a "file reference number".The SEEK table must also tell whether a file "exists" (i.e. has had somethingwritten into it) or not. The method of initializing the SEEK table is entirelyup to the individual installation. The ANL version of SEEK permits twodifferent methods for initialization. Both are described in the writeup ofSEEK in Appendix A of Reference 41. One is the same as the procedure requiredby SNIFF, the other is more flexible. SEEK must be initialized before anyfiles (binary or BCD) are read.

A distinction must be made between the "file reference number" used inthe arguments of CCCC routines and the "logical unit number" that a programmercodes into a Fortran I/O statement. In the Los Alamos implementation ofthe CCCC standards the two are not the same. The programmer need not beconcerned with the difference when dealing with binary files since all I/O isperformed through calls to CCCC routines ; applications programs should containno Fortran statements such as READ or WRITE for binary files. It is a commonANL practice, however, to employ a number of BCD input files and to managethem with SEEK. This means that ANL coding contains calls to SEEK whichreference file reference numbers as well as Fortran I/O READs and WRITES whichreference logical unit numbers for such BCD files. The correspondence betweenthe two numbers is managed by means of a subroutine, SEKPHL, which is describedlater.

Because we employ subroutine SEEK with BCD and random access files inaddition to sequential access files, it is instructive to review the followingguidelines to avoid potential portability problems.

1. A call to SEEK with the proper read/write mode flag must be issuedprior to the first read or write to a data set and prior to the firstread or write to a data set that has been rewound. This practice isnecessary for compatibility with implementations that dynamicallyassign logical unit reference numbers upon each call to SEEK anddynamically release logical unit numbers after a data set rewindcommand is received. A call to the appropriate routine, REED orRITE, with a record number of zero rewinds the data set.

141

2. The logical unit number for BCD data sets must be obtained by callingsubroutine SEKPHL following the call to SEEK. SEKPHL returns thelogical unit number corresponding to the logical unit reference numberreturned by SEEK. SEKPHL must also be used to rewind and close BCDfiles. See the SEKPHL example in Section 4.1.2; also see Ref. 41.

3. A set of fifteen generic file names (RNDMO1-RNDM15) have been reservedfor random access I/O applications. In order to maintain portability,calls to SEEK for random access data sets are embedded within ourversion of DOPC and DRED/DRIT. Consequently, SEEK calls for randomaccess files are not otherwise necessary and should never be coded bythe programmer.

4. Successive calls to SEEK (with different read/write mode flags)without intervening rewinds must be avoided. Such situations mayarise when SEEK is called in a read mode solely to determine fileexistence. If the file exists, but the programmer does not intend toread the file, then REED (for binary files) or SEKPHL (for BCD files)should be called to rewind it. Later, if the file is actually to beread, SEEK must be called again. The compatibility issues raised onpoint 1 (above) apply here as well.

The version of SEEK in the utility package performs no finalizing orwrap-up function (N0P=2). The other operations specified by the CCCC standardare all implemented (NOP = 0, 1, 3, 4, 5).

4.3.4.2 REED/RITE

The CCCC standards require that all binary I/O operations be executedthrough calls to standard subroutines, not through Fortran I/O statementscoded into applications programs. This practice permits individual installa-tions to take advantage of locally available, efficient access methods withoutrecoding programs ; all that is needed is a local set of CCCC standard I/Oroutines.

REED and RITE are the CCCC routines specified for binary sequential datatransfer between fast core (FCM) and external data files (disk). The callingsequence for REED is:

CALL REED(NREF,IREC,ARRAY(I),NWDS,MODE)

This call transfers NWDS single-precision words from record number IREC of thesequential file with logical unit reference number NREF to the FCM locationsstarting at the address of ARRAY(I). A similar call to RITE performs theinverse operation. MODE is a sentinel that permits a programmer to codebuffered I/O. When M0DE=0 I/O operations are completed before the returnfrom REED/RITE. When MODE=1 I/O operations are not necessarily completedbefore the return to the calling program; a subsequent call with M0DE=2 isrequired to complete the outstanding I/O operation.

The ANL version of REED/RITE includes IBM assembler language code thatprovides optional special access methods. In addition to providing thestandard sequential I/O capability of the Fortran language, this version ofREED/RITE provides an asynchronous, random access I/O capability. The SIO

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program (see Section 4.4.3.1) is used to obtain this capability. In short,S10 uses IBM BSAM macro instructions, along with internal tables and absolutetrack addressing, to process the I/O requests. SIO was originally written forthe OS/MVT operating system as a more efficient and more convenient alternativeto IBM Fortran Direct Access. The current version of the routine runs underboth OS/MVT and OS/MVS. The record format for SIO files must have the undefinedattribute (RECFM=U). Since each logical record requires at least one track ofdirect access storage, the use of the SIO access capability for short recordtransfers is not efficient.

Within the REED/RITE subroutine, the RECFM parameter of a file's JCLis interrogated by a call to the subroutine RECFM. If the file has anundefined attribute (RECFM=U) the code will use SIO access methods. Any otherrecord format (e.g. VBS, VS, FB, etc.) is processed by standard Fortransequential I/O. To perform the SIO data transfers, a subroutine SIO isinvoked. This routine in turn invokes the subtask SIOSUB which actuallyperforms the I/O operations. The MODE parameter which is passed to REED/RITEis used to determine whether transfer is returned to the calling routinebefore the I/O operation is complete. This facility, therefore, provides theuser with the ability to overlap I/O and CPU operations or I/O operations onone file with those on another.

4.3.4.3 DOPC and DRED/DRIT

The CCCC standards require that all random access I/O operations bechanneled through calls to standard subroutines, not through Fortran I/Ostatements coded into applications programs. Also specified is the fact thatsuch data should be transferred between external data files (disk) and extendedcore memory (ECM).

The calling sequence for DRED is:

CALL DRED( NREF, IREC, LOCBFU, NWDS, MODE )

This call transfers NWDS single-precision words from record number IREC ofthe random access file with logical unit reference number NREF to the ECMlocations starting LOCBFU words from the (user) ECM reference address (seeIOP=0, below). A similar call to DRIT performs the inverse operations. MODEis a sentinel that permits the programmer to code asynchronous I/O. WhenMODE=0 operations are completed before return from DRED/DRIT. When MODE=1 I/Ooperations are not necessarily completed before return from DRED/DRIT; asubsequent call with MODE=2 completes the outstanding I/O operation.

Prior to calling DRED/DRIT the random access I/O implementation must beinitialized by several DOPC calls. The five DOPC calling options aresummarized below:

1. (I0P=0) Initialize DOPC and, in one-level implementations, supply apseudo ECM reference location.

2. (IOP=1) Supply f^le characteristics for reference number NREF.

3. (I0P=2) Conclude the definition of the file group, NGREF. NGREFincludes all files defined with IOP=1 calls since either the lastI0P=2 call or the original IOP-0 call.

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4. (I0P=3) Delete file group NGREF and its constituent files.

5. (I0E'=4) Finalize DOPC at the conclusion of the program module. Allfile groups are deleted.

The connection between a random access file reference number NREF andits corresponding logical unit number is established in the ANL implementationby calling subroutine SEEK during the processing of each DOPC (IOP=1) call.The call to SEEK uses the generic random access file name RNDMnn which byconvention corresponds to the random access file reference number NREF=nn.Currently NREF must satisfy 0<NREF<16. Codes which use this version ofDOPC and DRED/DRIT need only supply in the SEEK initialization call thosegeneric file names used by the applications code.

The DOPC initialization call establishes the pseudo ECM reference pointfor DRED and DRIT calls on one level machines. Although never explicitlyspecified in the CCCC standards, this pseudo ECM reference point initializationmust also apply to CRED and CR1T usage. Consequently, all calls to DRED,DRIT, CRED and CRIT on one-level machines must be preceded by a DOPC initiali-zation call. By definition in the CCCC standard, the ECM reference locationon two-level machines is the first word of ECM (e.g. LCM on the CDC 7600).It should be erphasized that the ECM reference point does not necessarilyspecify the starting location of ECM.

Except for the implementations on the CDC and CRAY computers (see sections4.4.3.2 and 4.4.3.3), DRED/DRIT call REED/RITE to perform the random access I/Ooperations. Consequently, the implementation of DRED/DRIT on IBM 370 systemsis simply the REED/RITE implementation discussed earlier in this section.

4.3.4.4 CRED/CRIT

CRED and CRIT are the CCCC routines specified for data string transferbetween ECM and FCM. The calling sequence for CRED is:

CALL CRED ( FCM(I), LECM, NWDS, IER )

This call transfers NWDS single precision words starting from ECM locationLECM to the FCM locations starting at the address of FCM(I). IER it anerror sentinel. A similar call to CRIT performs the inverse operation.

The implementation of CRED/CRIT on the CDC 7600 employs the COMPASSassembly language routines WRITEC and READEC to perform the actual datatransfers between ECM and FCM. The three arguments in the calling sequencefor WRITEC are identical in type to the first three arguments in the CRITcalling sequence (e.g. CALL WRITEC ( FCM, LECM-1, NWDS ) ).

The second parameter LECM in CRIT denotes an ECM location relative tothe ECM reference array, while the second parameter supplied in the WRITECcall denotes the corresponding ECM address (e.g. LECM-1). On one-levelimplementations CRED and CRIT simply transfer data between FCM and pseudo ECMlocations both of which reside in the same memory level. The transfers areperformed via standaid Fortran assignment statements.

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As noted in the DOPC and DRED/DRIT section, CRED/CRIT are interlockedwith DOPC to ensure that the ECM container reference address pointers havebeen initialized by DOPC.

4.3.4.5 ECMV

ECMV is the CCCC routine specified for transfering data strings betweenlocations in ECM on two-level machines (e.g. CDC 7600). Transfers are per-formed using CRED and CRIT which route data through a 64-word FCM bufferarray local to ECMV. This approach circumvents the compiler restrictionlimiting array sizes to 131071 words on the CDC 7600. The calling sequencefor ECMV is:

CALL ECMV ( LECM1, LECM2, NWDS )

This call transfers NWDS single precision words starting from ECM locationLECM2 to the ECM location starting at LECMi.

4.3.5 BPOINTER, a Dynamic Storage Allocation Program

The problem size limitations imposed by fixed-dimension arrays in alarge scale code such as DIF3D is intolerable. Running small problems withunnecessarily large dimensions can be needlessly expensive. Code changes maybe awkward and, from a quality assurance standpoint, risky. DIF3D, therefore,uses a dynamic storage allocation system to manage the core storage of dataduring execution. Core storage is reserved for a particular dimensioned arrayonly during the time the corresponding data are required to be in-core : atother times the space is made available for the storage of other data.

The ARC System dynamic storage allocation routines are contained inthe BPOINTER package36»1+1. BPOINTER is a collection of subprograms which wasdeveloped to alleviate bookkeeping chores associatsd with the use of dynamicstorage allocation techniques. These chores are separated into two functionalcategories:

1. The highly machine-dependent functions of obtaining/releasing largeblocks of workspace called "containers" from/to the operating system.

2. The largely machine-independent bookkeeping functions associated withmanaging array allocations within a given container.

Category 1 tasks are performed by the IGTLCM package, a self-contained setof subroutines that may be used independently of BPOINTER. Consequently,in situations requiring only the IGTLCM functions (e.g. the XCM containerallocation in the CDC 7600 implementation of DOPC aid DRED), inclusion ofthe BPOINTER routines is unnecessary.

4.3.5.1 Programming Considerations

Programs which use the BPOINTER capability tend to be structured insubroutine form. A control routine ib used to define one or two blocksof storage (the containers) and to make the appropriate calls to BPOINTER tocontrol the allocation of space within these containers. Calls to calcula-tional subroutines transmit pointers corresponding to array locations through

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the calling sequences. All BPOINTER capabilities are accessed through anappropriate call to an entry point, subroutine or function subprogram. Thefollowing capabilities are available in the BPOINTER system:

1. Storage of data in and retrieval of data from the container array viauser defined variable arrays.

2. Purge of variable arrays stored in the container array.

3. "Cleanup" of the container array when more storage is required (toavoid fragmentation).

4. Redefinition of array sizes without loss of data already stored inthe array.

5. Dump of selected integer, floating point or Hollerith arrays in anappropriate format.

6. Trace edits of BPOINTER activities.

7. Status reports of the BPOINTER tables.

Detailed program documentation including flow charts, common blockinformation and subprogram descriptions is available in Reference 3f> . Ashorter, functional writeup is included in Appendix A of Reference 41 (memberPOINTR) and gives calling sequences for the BPOINTER routines. This sectionis intended to provide a brief description of how the program package operates.

The short example shown in Figure 4.8 illustrates the structure of aprogram using the BPOINTER package. This example demonstrates the manner inwhich a container is allocated, pointers defined and used, and the containerreleased.

The letters M and B are used as mnemonics within BPOINTER to designateroutines which operate on the FCM and ECM containers, respectively. ThusPUTM allocates an array in the FCM container while PUTB allocates an arraywhich must be referenced on a CDC 7600 as either a LEVEL 2 or a LEVEL 3array. According to CCCC conventions6, arrays allocated in ECM are referencedthrough the standard subroutines CRED/CRIT and DRED/DRIT in exportable sourcecode intended for two-level computers-

On IBM equipment without HIARCHY support (e.g. the 370/195) the twocontainers are both in fast core. The distinctions noted above between thetwo dynamic containers are important on the CDC 7600 where the containersare addressed quite differently and on IBM equipment with HIARCHY supportwhere access to the LCM container (HIARCHY 1, subpool 1) is significantlyslower than access to the MAIN core container (HIARCHY 0, subpool 2).

In the example all dynamically allocated FCM arrays are addressed relativeto the labeled COMMON block /ARRAY/ which contains a single array element,BLK(l). In the short-word version of the code the element must be declaredREAL*8. In the two-level (CDC 7600) version of BPOINTER the ECM container isaddressed relative to the first word of LCM. The pseudo ECM container on IBMequipment is a second container which may be given a HIARCHY 1 location but is

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CSWIMPLICIT REAL*8(A-H,0-Z)REAL*4 BLK4

CSWCOMMON/ARRAY/BLK(1)COMMON/IOPUT/NIN,NOUT,NOUT2DIMENSION BLK4(1)EQUIVALENCE (BLK(1),BLK4(1))DATA FLUX/4HFLUX/, POWER/5HPOWER/, MAXSIZ/10000/, NG/27/,1 14/4/, 18/8/, 10/0/NOUT=6

C ALLOCATE CONTAINER WITH MAXSIZ WORDS OF FCM AND NO ECM.CALL BULK(IO)CALL POINTR(BLK,MAXSIZ,10)

C ALLOCATE SPACE FOR ARRAYS POWER AND FLUX. DETERMINE THEC POINTER FOR SUB-ARRAY CURRENT WHICH FOLLOWS THE FIRST NGC SINGLE-PRECISION WORDS FOR THE ARRAY FLUX. THEN CHECK FORC A BPOINTER ERROR.

CALL PUTM( POWER, NG, 18 ,T.POWR)CALL PUTM(FLUX,2*NG,I4,IFLUX)ICURNT=IPT2(IFLUX,NG,I0)IF( IPTERR(DUMMY).LE.O ) GO TO 10PRINT 500

500 FORMAT(15H0BP0INTER ERROR)STOP

10 CONTINUEC CALL SUBROUTINE INIT TO USE THESE ARRAYS. THEN FREE THEC CONTAINER AND STOP.

CALL INIT(BLK(IFLUX).BLK(IPOWR),BLK4(ICURNT),NG)CALL FREESTOPEND

CSUBROUTINE INIT(PHI,POWER,CURENT.NG)

CSWREAL*8 POWER

CSWDIMENSION PHI(l), POWER(l), CURENT(l)DO 10 l=1,NGPHI(I)=1.0POWER(I)=3.1E+06CURENT(I)=.333

10 CONTINUERETURNEND

Fig. 4.8. A BPOINTER Example

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addressed in precisely the same manner as the first (FCM) container. The oneword assigned to the container by the applications program provides a refer-ence address. At execution time the function routines IGTLCM and IGTSCM areused to obtain the addresses of core which are available to the program forthe allocation of data arrays.

A few codes at the same time use BPOINTER and directly address ECM on two-level machines. In these programs the "LEVEL 2" BPOINTER reference commonblock must start at the first word of LCM. BPOINTER calculates address off-sets based on that assumption. DIF3D and most codes currently under develop-ment do not address ECM directly ; they employ CRED and CRIT to transfer blocksof data between the two levels of memory.

Occasionally it is convenient to exercise the two-level implementation ona one-level machine. In such cases it is necessary to precede the BPOINTERinitialization call by the DOPC initialization call so that the user referenceaddress of the BPOINTER ECM container is initialized prior to the firstcall to CRED/CRIT (BPOINTER employs CRED/CRIT in its two-level implementation).A discussion of IGTLCM/IGTSCM and the associated assembler routines thatallocate these blocks of memory follows.

4.3.5.2 IGTLCM/IGTSCM/IGTXCM

Function IGTLCM and its associated entry points IGTSCM and IGTXCM managethe allocation of the ECM, FCM and XCM containers, respectively. The FCMcontainer always resides in fast memory (e.g. the FCM storage pool). TheECM container and the auxiliary ECM container named XCM both reside in thesame storage pool. On single-level machines they reside in the FCM storagepool along with the FCM container; on two-level machines like the CDC 7600they reside in LCM. If the C1LV language flag is activated in a CDC 7600implementation then the ECM and XCM containers will be allocated in the FCMstorage pool along with the FCM container.

IGTLCM, IGTSCM and IGTXCM route all memory allocation requests throughfunction subroutine JGT which calls the appropriate assembler, Fortran orsystem routines. The calling sequence for IGTLCM is:

LOCECM = IGTLCM( NWORDS )

This call returns the (REAL*4) word address of the requested block of NWORDSwhich constitutes the ECM container. A similar call to IGTSCM or IGTXCMallocates the appropriate container. The function value of -1 is returned ifthe container allocation fails. Subroutine FRELCM with associated entrypoints FRESCM and FREXCM release the corresponding containers. The example inFigure 4.9 illustrates the use of the IGTLCM package. The function LOCFWDprovides the (REAL*4) word address of the reference variable used to addressthe container.

4.3.5.3 IBM Allocation

The assembler routine MYLCM with entry point MYSCM, FREELC and FREESC(called by JGT or FRELCM) uses the standard IBM macro instructions GETMAIN andFREEMAIN to allocate and free consecutive words of core which are availableto the program. The designations subpool 1 and 2 are assigned to the ECM and

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COMMON /REFFCM/ BLK(l)CC ALLOCATE FCM CONTAINERC

LOCFCM = IGTSCM( NWORDS )IF ( LOCFCM .EQ. -1 ) GO TO 10

CC DETERMINE WORD OFFSET OF CONTAINER FROM REFERENCE ARRAY BLK(l)C

LFCREF = LOCFCM - LOCFWD ( BLK(l) )CC INITIALIZE CONTAINERC

DO 1 I=1,NWRDSBLK(LFCREF+I)=0.0

1 CONTINUE

CC FREE CONTAINERC

CALL FRESCM

CC ERROR EXIT

10 CONTINUE

Fig. 4.9. IGTSCM/FRESCM/LOCFWD Example

149

FCM containers, respectively. Since allocations are performed in uuits of256 (REAL*8) words, it is most efficient to request blocks of memory in suchmultiples.

Figure A.10 shows a schematic diagram of a program and SCM container.

4.3.5.4 CDC Allocation

The COMPASS assembler routine JGTSCM with entry point JGTLCM (calledby JGT) uses the standard CDC macro instruction MEMORY to determine and tochange, the job's SCM and LCM field lengths.

The FCM container is placed at the end of the user's SCM field length,as shewn in Figure 4.10. The ECM container is placed at the end of the user'sLCM field. The last word of each container is four words short of the user'sSCM or LCM field length; this is done to avoid I/O problems in systems thatattempc to read ahead. The XCM container is allocated to provide space forindices to the random access records of the DOPC files on the CDC 7600 imple-mentation, only. The implementation uses mass storage routines (READMS.WRITMS, OPENMS and CLOSMS) in the CDC library.

BPOINTER releases containers when they are no longer needed and returnsfield lengths to their original values.

4.3.5.5 CRAY Allocation (CTSS)

Two subroutines (LASTMEM and MEMORY) from the CRAY Time Sharing System(CTSS) Fortran Library at Los Alamos National Laboratory are called by JGT todetermine and change a job's field length, respectively. JGT establishes theuser program length (i.e. the high limit of user code, JCHLM) by an initialcall to LASTMEM. Each time a new container is requested JGT allocates spacein one of two ways:

1. If another container has been previously allocated, and there isenough free space between it and the program, the new container isestablished in the free space. The field length is not changed.

2. If adequate free space is not available MEMORY is called to increasethe field length, and the new container is placed such that theaddress of its last word is the new value of JCHLM.

Figure 4.11 shows a schematic diagram of fast core of a CRAY machine containinga program and two containers.

JGT reduces the field length by an appropriate amount only when thecontainer ending at address JCHLM is released.

4.3.5.6 CRAY Allocation (COS)

Dynamic memory allocation on machines using the standard CRAY OperatingSystem (COS) is implemented in a manner that is functionally equivalent to theCTSS implementation. CTSS subroutines MEMORY (2 arguments) and LASTMEM aresimulated on COS installations by the Fortran subroutine MEMGET and its entrypoint LASTMEM, respectively. A blank COMMON array of length 1 must belocated as follows in order for it to provide a reference point (JCHLM) forthe dynamic memory allocation:

.151

s t a r t of FCMfield length

JCHLM

program

/ARRAY/BLK(1)

moreprogram

FCMcontainer

ECMcontainer

system tablesand buffers

Fig. 4.11. Fast-Core Allocation on a CRAY Machine

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1. Non-overlayed COS systems - place it after all object code (the CFTcompiler does this by default).

2. Segmented loading on COS system - assign it to a second memory levelabove all overlays.

3. COS overlay loading types 1 or 2 - assign it (via the SBCA overlaydirective) to a specified address larger than any address used in theoverlay structure (this number is installation dependent and must bedetermined upon completion of loading).

Subroutine MEMGET calls the COS system routine MEMORY (5 arguments) whichissues calls to the CAL assembler MEMORY macro to increment or decrementJCHLM, the length of the user code area. A corresponding field length changeoccurs simultaneously.

4.4 Ma chine Dependence, Hardware and Software Requirements

4.4.1 General Considerations

Machine dependent features in DIF3D that are not universally supportedin FORTRAN '66 compilers are isolated in accordance with the coding conventionsestablished by the CCCC6. All data transfer, except for BCD input file pro-cessing is performed via the CCCC utility routines described in Section 4.3.4.Dynamic storage allocation of FCM and ECM containers is isolated in the IGTLCMroutines (Section 4.3.5.2). The BPOINTER package manages the dynamic suballoca-ticn of arrays within the ECM and FCM containers. Differences of a globalnature such as word length, compiler dialects or machine storage hierarchyare surrounded with pairs of special "keyword" comment cardstfl that are acti-vated or deactivated depending upon the characteristics of the target machine.

4.4.2 Storage Requirements

Formulas for calculating required ECM and FCM container space are givenin Tables 3.2 and 3.3. At least 325K-bytes of storage are recommended for pro-gram and file buffer storage on the IBM 370 seriesj 40,000 words of SCM arerequired on the CDC 7600. ECM requirements are linearly dependent on thenumber of cells (N) in a mesh plane. The finite-difference option requiresat least 9N (8-byte) words in 2-D problems and at least 25N words in 3-Dproblems. At least 19 mesh lines of data and one group of cross section datamust be stored in SCM on the CDC 7600. External data storage must be availablefor approximately 40 scratch and interface files. Fourteen of these arerandom access scratch files (grouped into six file groups), the remainder aresequential access files with either formatted or unformatted record types.

4.4.3 . Data Access Modes

The calling sequences in the CCCC utility routines REED/RITE and DRED/DRITprovide for asynchronous, sequential and random access I/O. These featureshave been fully exploited on IBM 370 systems by the SIO package discussed inSection 4.4.3.1 (see also Sections 4.3.4.2 and 4.3.4.3). The READMS, WRITMS,OPENMS and CLOSMS routines provide random access I/O capabilities on CDC 7600systems (see Section 4.4.3.2). No asynchronous I/O has been implemented onthis system. Fortran '77 I/O statements are used to implement random accessI/O on the CRAY-1 (see Section 4.4.3.3).

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4.4.3.1 SIO, a random access, asynchronous I/O package for IBM systems

In order to make370 Model 195 or 3033to optimize both itsMost large scientificwhich provides littleSeveral Fortran codesthe availability of a

efficient use of large computers such as the IBM Systemat Argcnne National Laboratory, a program must attempt

central processor and peripheral processor operations,programs are written in Fortran, a high level languageflexibility in specifying efficient I/O methods,have, however, been designed which would profit byprogram package with the following characteristics:

1. permits asynchronous operation;

2. performs random access operations efficiently;

3. handles large records efficiently;

4. performs I/O operations without the need for buffers.

The SIO program package was written to provide a Fortran-callable accessmethod with these characteristics.

The two IBM-supplied Fortran I/O programs which come closest to satisfyingthese requirements are the Fortran IV (H Extended) asynchronous I/O and theFortran IV Direct Access I/O.

The Asynchronous I/O uses V-type records which include control informationin each record. Hence buffers are essential. However, with records longerthan two tracks on standard direct access devices, the buffers become essen-tially useless in increasing I/O efficiency, since almost the entire I/Ooperation must be completed before the user can access the data. Furthermore,these buffers consume large amounts of core, and additional central processoreffort is required to move the data between program locations and the buffer.In addition to buffering the data, the Asynchronous I/O operations are sequen-tial and there are no efficient methods for accessing records in a randommanner.

Fortran Direct Access I/O does permit random access of the data file,but it is essentially limited to track-length records. This could be overcomethrough keeping track of the location of each record in an index table anddoing software spanning. Since Direct Access I/O uses V-type records, buf-fering is required. There is also a substantial overhead incurred in theinitial formatting of the direct access data set when the file is firstopened. Furthermore, asynchronous operation is impossible.

The first step toward attaining a capability with the attributes notedabove was to study the IBM I/O routines accessible through standard systemMacro calls. Of these, the Basic Sequential Access Method (BSAM) was chosenbecause it could be used to randomly access records through the Point Macro ;it supported U-format records which contain no control information withinthem ; and it features chained scheduling which allows several tracks to beaccessed without relinquishing the input/output channel and so decreasingI/O time. As with the Direct Access method, it was necessary to use an indextable which contains the relative location of each record and its length. Acopy of this table resides in core and also occupies the first track of the

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data set. The problem of formatting the data set was overcome by alwaysappending a new record to the end of the data set regardless of which logicalrecord it might be. When records are updated, they are written over theold record if possible, or else appended to the end of the data set like anew record. Asynchronous operation is achieved through subtasking the actualcode to do the I/O.

The SIO program package consists of two central modules (SIO and SIOSUB)along with a few auxiliary routines used for edit and error processing(SIOTRC,SIOERR,SI0WU6). In addition the capability may be invoked usingthe standard I/O routines REED/RITE which branch to the SIO access methodfor datasets defined with the job control record format U, i.e. RECFM=U. Thetwo main modules consist of a subroutine (SIO) which is included in the mainprogram (task) through appropriate linkage editor control statements and aself-contained load module (SIOSUB) which operates as a subtask after beingATTACHed by the subroutine SIO. There are two assembly parameters in themodules SIO and SIOSUB which are of interest to the user. They are NBLKSand MAXFILES. NBLKS sets the length of the index table discussed above(called the File Control Block or FCB) and determines the maximum number ofrecords which may be placed in the file. For NBLKS=1, 431 entries are sllowed ;for NBLKS=2, 943 entries are allowed; for NBLKS=3, 1455 entries are allowed;for NBLKS=4, 1967 entries are allowed, but this option is available only ifthe SIO files are on direct access devices with a track length greater thaneight kilbyotes. The parameter MAXFILES specifies the maximum number offiles which may be open at a single time. The two parameters are routinelyset at NBLKS=2 and MAXFILES=50. The variables must be identically definedboth in the main task (SIO) and the subtask (SIOSUB) and files created with aspecific value of NBLKS may not be accessed by versions of SIO with a differentvalue of NBLKS.

4.4.3.2 Implementation Considerations on the CDC 7600

Random access I/O on the CDC 7600 is implemented using the routinesOPENMS, CLOSMS, READMS and WRITMS found in the Fortran utility library.Auxiliary storage equal in length to the number of records in the file must besupplied during the OPENMS call for each file. An auxiliary ECM containernamed XCM is allocated directly from DOPC by calling entry point IGTXCM in theIGTLCM dynamic storage allocation subroutine package. Consequently, DOPCand DRED/DRIT depend only on IGTXCM for dynamic storage allocation.

The subscript index limitation of 131071 words imposed on CDC 7600LCM arrays is effectively raised to 393213 by employing two routines DRED1and DRED2 each of which addresses a successively higher block of 131070 wordsof ECM. The circumvention is accomplished by passing the initial address ofthe next adjacent block of 131070 words of ECM to the appropriate routine,DRED1 or DRED2.

4.4.4 Vectorization on the CRAY-1

Although DIF3D was not designed for a pipelined computer such as theCRAY-1, an advanced computer performance evaluation project1^ at Argonne ledto the implementation of a vectorized variant of the SLOR algorithm applicableto nonperiodic, orthogonal geometry models. The regular mesh structure andthe fact that at least 75% of the DIF3D scalar execution time is spent in a

155

small kernel of subroutines that perform the SLOR algorithm provided ampleopportunity for vectorizing (with vector lengths J/2) the dominant computationsin DIF3D without changing the DIF3D data structure.

The vector pipeline of the CRAY-1 is exploited by simultaneously solvingthe tridiagonal matrix equations generated for the (J+l)/2 odd lines on a meshplane, and then simultaneously solving the corresponding tridiagonal matrixequations generated for the J/2 even lines on a plane. This odd/even (red/black)SLOR algorithm43'44 was implemented within the existing DIF3D data structureby modifying subroutine OSWEEP and by increasing one auxiliary mesh line array(SOLN) to the size of a mesh plane array. The CRAY-1 version of OSWEEP callsRBOSRC and RBOSOR, the vectorized counterparts of the ROWSRC and SORINVsubroutines, twice for each mesh plane k before processing plane k + 1 ; thefirst pass processes the odd numbered lines on plane k and the second passprocesses the even numbered lines.

A comparison of the relative megaflop rates (millions of floating pointoperations per second) achieved by the scalar (conventionally ordered) and thevector (odd/even ordered) algorithms, when applied to the two-dimensional IAEAbenchmark problem with a (170 x 170) rectangular mesh, is tabulated in Table 4.5.

The results45 in Table 4.5 should be viewed in light of three considera-tions. First, one expects a factor of 2.3 increase in megaflop rates on theCRAY-1 due to machine clock cycle differences (12.5 nanosecs on the CRAY-1 vs.28.5 nanosecs on the IBM 370/195). Second, the ROWSRC subroutine in theso-called scalar algorithm will vectorize on the CRAY-1. Third, the megafloprate of the current, vectorized algorithm is dependent on the problem in tworespects. The vector length depends on the number of lines (J) on a plane;the vector stride (the number of ...emory words between successive vectorelements) of length 21 will cause memory bank conflicts whenever

Table 4.5. Execution Rates for the 2D IAEA Benchmark8

Method/Machine

Vector Fortran(RBOSRC, RBOSOR)

Scalar Fortran(ROWSRC, SORINV)

Scalar Fortran withAssembler SORINV

Cray-1

4.4

1.6

2.7

IBM 370/195

0.83

—

1

aRates are expressed in units of 3.9 megaflops. The2 group model is defined with a 1 cm (170 x 170) mesh.

the line length I is a multiple of 8 on the typical 16 memory bank machine.Work in progress towards implementation of a vector length of J*K/2 shouldyield favorable performance increases for a wider class of problems withoutsignificantly altering the DIF3D data structure.

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5. THE NATIONAL ENERGY SOFTWARE CENTER VERSIONS OF DIF3D

DIF3D is available on magnetic tape through the National Energy SoftwareCenter; versions exist for the IBM 370 series, the CDC 7600 and the CRAY-1computers. This section describes the contents of the tapes and outlinesthe steps necessary to implement the code in a standalone form on the abovementioned computers. Knowledge regarding solution techniques or the codeitself is not assumed. The NESC package includes several benchmark problems ;this section also contains descriptions and solutions of these test problems.

5.1 The DIF3D Package

The NESC package consists of this report and a magnetic tape the character-istics of which are listed in Table 5.1. Tables 5.2 a, b, c respectivelydescribe the contents and approximate length of each BCD file on the tape foreach of the three target computers noted above.

TABLE 5.1. D1F3D Tape Characteristicsand its BCD File Contents

Characteristics

Type 9 trackDensity 1600 bpiLabel unlabeledBlock Size 3200 (1596)a

Record Length 80 (133)a

Format EBCDIC

aParenthesized quantities apply tosample problem output files only.

5.1.1 File 1 - DIF3D FORTRAN Source Images

The source code in files 1 and, if applicable, files 2 and 3 combine toform the DIF3D code. The first file includes the major code blocks summarizedin Table 5.3. FORTRAN source for all machine versions is derived from a singlemaster source file. Statements that are unique to a particular implementationare surrounded by pairs of "keyword" comment cards. Code within the keywordbrackets is selectively "activated" (uncommented) or "deactivated" (commentedout) by a simple preprocessing program1*! at the time a tape is generated.The keywords bracket coding applicable to general machine architecturalfeatures such as long and short word lengths (e.g. CLW or CSW) and one- ortwo-level memory hierarchies (e.g. C1LV or C2LV). Particular manufacturer,compiler or installation dependencies are also bracketted (e.g. CIBM, CDC*,CRAY, CANL, CLBL and CD76). Keywords (CSA, CSEG and COVL) exist for generatingmodular or standalone code appropriate for segmented or overlay loading.

This package is sufficiently large that although the source code on thewill be numbered in a global fast

specified on a subroutine basis, only.tape will be numbered in a global fashion, future code modifications will be B

157

TABLE 5.2a. Contents of NESC Export Tape for IBM 370 Systems

FileNumber Contents

Estimated Numberof Card Images

12345678910

DIF3D FORTRAN Source Code 7919^Machine Dependent Source Code 1498SIOSUB Subtask (IBM) Assembler 1228Loader Directives 194ARCSP021 JCL Procedure 282Sample Problem Input (Cases 1, 2, 3 and 4) 226Sample Problem Input (Cases 5 and 6) 161Sample Problem Output (Cases 1, 2, 3 and 4) 3936Sample Problem Output (Cases 5 and 6) 2392CCCC and Code Dependent File Descriptions 5431

TABLE 5.2b. Contents of NESC Export Tape for CDC 7600 Systems

FileNumber Contents


1234567

DIF3D FORTRAN Source Code 79196Loader Directives 121Sample Problem Input (Cases 1, 2, 3 and 4) 226Sample Problem Input (Cases 5 and 6) 161Sample Problem Output (Cases 1,2,3 and 4) 3936Sample Problem Output (Cases 5 and 6) 2392CCCC and Code Dependent File Descriptions 5431

TABLE 5.2c. Contents of NESC Export Tape for CRAY-1 Systems

FileNumber Contents


12345678

DIF3D FORTRAN Source Code 79196Machine Dependent Source Code (optional) 177Loader Directives 121Sample Problem Input (Cases 1, 2, 3 and 4) 226Sample Problem Input (Cases 5 and 6) 161Sample Problem Output (Cases 1, 2, 3 and 4) 3936Sample Problem Output (Cases 5 and 6) 2392CCCC and Code Dependent File Descriptions 5431

158

TABLE 5.3. DIF3D Code Blocks

PrincipalCode Blocks

D3DRIV (+ utilities)SCANSTUFFGNIP4CHMG4CMODCXSBCDINPS4C10ADIF3DUDOITl.2,3,4

Machine Dependent Source Code

Approximate Numberof Card-Images

9537306730

230434745938

1176262536056

40

5.1.2

Most compilers (except for the FTN compilers on the CDC 7600) do notpermit the intermixing of FORTRAN and assembler source code. File 2, there-fore, segregates assembler code from the FORTRAN coding on File 1 for compu-ters other than the CDC 7600. Some of the assembler code located on File 2is provider solely for the purpose of optimizing CPU performance, and isoptional in this respect.

On the tape destined for IBM installations, file 2 contains IBM assemblercode for dynamic storage allocation and for asynchronous, random access I/Oprocessing. File 3 on thi. tape contains the IBM assembler source code forthe SIOSUB subtask which is required for the DIF3D random access I/O implemen-tation on IBM 370 systems. See the explanation in Section 5.4.3.

On the tepe destined for the CDC 7600, assembler subroutines for dynamicstorage allocation, for transfers between ECM and SCM and for optimizingSORINV (the subroutine which performs the back substitution and overrelaxationtasks in the SLOR solution of the tridiagonal matrix equations) are appropri-ately located with their FORTRAN counterparts and associated routines on file 1

File 2 on the CRAY-1 tape contains an assembler coded optimized versionof the (non-vectorizable) SORINV routine mentioned in the previous paragraph.Subroutines RBOSOR and RBOSRC for the vectorizable (odd/even ordering) SLORalgorithm are present on file 1 (see Section 4.4.4).

5.1.3 Loader Instructions

Instructions for creating the DIF3D overlay or segment structure areincluded for the convenience of the user. Linkage editor instructionsare provided on the NESC tape for IBM 370 systems (see also Appendix E ) .Instructions for the SEGLINK segmented loader at Lawrence Berkeley Laboratoryare included on the CDC 7600 tape (see also Appendix F.I). Type 01 ojverlaydirectives are included with the CRAY-1 tape (see also Appendix F.2). Asnoted in Section 5.1.1 all tapes have overlay calls and directives presentin the FORTRAN source; these are appropriately activated (uncommented) on theCDC 7600 and CRAY-1 tapes (see Section 5.2.1).

159

5.1.A Sample Problem Input aud Output

Six problem cases are supplied; four of these cases arise from two- andthree-dimensional models of the well-known SNR Benchmark Problem »in four energy groups. Solutions for both the finite-difference triangulargeometry option and the nodal hexagonal geometry options are generated forthese two models. Two- and three-dimensional models of the well-known IAEAbenchmark problem with two energy groups provide the remaining two testproblems. Finite-difference solutions of these orthogonal geometry (XY andXYZ) problems are generated. Section 5.3 describes the benchmark problems.

Each sample problem was run on the IBM 370 system at Argonne and thecorresponding output, including carriage control symbols, is provided on theNESC tape. The output files will consequently have a record length of 133characters.

5.1.5 ARCSP021, An Instream JCL Procedure for IBM 370 Systems

ARCSP021, the instream JCL procedure appropriate for running the NESCversion of DIF3D on IBM systems is provided for the convenience of the user.It is listed in Appendix A and a discussion of its parameters appears inSection 3.12.3.

5.1.6 CCCC and Code-Dependent Interface File Descriptions

The file descriptions for the various interface files used in DIF3D areprovided on the tape to allow the us,ar to inexpensively generate additionalcopies. These descriptions also appear in the Appendices B, C and D of thisreport.

5.2 Implementation of the NESC DIF3D as a Stand-Alone Program

5.2.1 Code Structure and Loading Instructions

Table 5.3 lists the major code blocks within the DIF3D code system;functional descriptions of these code blocks appear in Section 4.1. A minimaloverlay structure, other than no overlays at all, uses these major codeblocks as primary overlays and D3DRIV as the root overlay. A detailed overlaystructure is given for the major code blocks GNIP4C, HMG4C and DIF3D inFigures 4.2, 4.3 and 4.4, respectively. On systems restricted to three overlaylevels, a root segment with primary and secondary overlays only (e.g. CDC 7600overlay loader or the type 01 overlay directives on the CRAY-1), subroutineDIF3D is assigned to the root segment as a logical extension of the maindriver D3DRIV. This puts the major overlays of the neutronics solution at thesame (primary overlay) level as the remaining code blocks GNIP4C, HMG4C, etc.

Source code for the major code blocks is on File 1 of the NESC tape;code generated from assembling the machine-dependent source (if present) onFile 2 should be included at load time with the root segment. Loading instruc-tions for the target computers are included in the appropriate files noted inTables 5.2 a, b, c. Also present within the source code are appropriatelyinactivated (e.g. commented) or activated (uncommented) overlay directives forthe CDC 7600 and CRAY-1 computers. Appendices E, F.I and F.2 display the jobcontrol language and the loader directives required to create the DIF3D loadmodules for each computer.

160

SIOSUB, a separate subtask module (file 3), is required to implementthe random access I/O capability used by DIF3D on IBM systems. The nextsection describes its relation to the SIO access method and its placement inthe STEPLIB data set prior to execution.

5.2.2 SIO

The SIO access method provides a random access, asynchronous I/O capabilityon IBM operating systems. Within DIF3D the SIO routines are invoked directlyfrom the CCCC generalized I/O subroutines REED and RITE. The source codefor SIO is included as part of the DIF3D standalone code and requires specialcare with regard to its implementation. In particular, SIO is made up of anassembler language module, SIOSUB, and three assembler subroutines, SIO, RECFMand SIOTRC. The latter routines are assembled and included within the rootsegment of the DIF3D load module in a manner completely analagous to Fortranroutines such as REFD and RITE. The subroutine RECFM is called by REED/RITEto interrogate the DCB of a dataset to determine whether it has been desig-nated with an undefined record format, i.e. RECFM=U. If so, it is consideredan SIO dataset and the subroutine SIO is called to perform the I/O ratherthan the Fortran system routine IBCOM#. The subroutine SIO sets up argumentlists and then passes control to the load module SIOSUB to perform the actualI/O operations. Thus, in addition to the DIF3D load module, a second loadmodule, SIOSUB, must be available to the system at the time of execution ofDIF3D, i.e. SIOSUB must be a member of a partitioned data set referenced inthe STEPLIB data definition JCL of the job step. To create the load moduleSIOSUB, it is necessary to assemble the source code and link edit the resultingobject code using standard procedures. It is however essential that the loadmodule SIOSUB be assigned the "Re-enterable" attribute by the linkage editor.This may be done by assigning the parameter RENT in the PARM field of thelinkage editor execution step as follows:

//LKED EXEC PGM=IEWL,PARM='RENT,...'

5.2.3 File Number Assignments

All sequential binary files (input and output interface files and scratchfiles) used in the DIF3D code system are handled through the CCCC standardsubroutines SEEK, REED and RITE. The assignment of file numbers to filenames and the initialization of the SEEK tables is done from the DIF3D driverD3DRIV (also known as MAIN on IBM systems). Subroutine SEEK is also used toobtain reference numbers for sequential BCD interface files : the subroutineSEKPHL is then used to obtain corresponding logical unit numbers for subsequentuse with FORTRAN READ and WRITE statements. SEKPHL is also called to rewind(close) all BCD data sets. Section 4.3.4 describes these functions.

Fourteen random access scratch files are exclusively referenced by theCCCC standard subroutines DOPC, DRED and DRIT : only the DIF3D neutronicssolution code block references these files. File names RNDM01-RNDM14 correspondto DOPC reference numbers 1-14, respectively. The Argonne implementation ofthe DOPC, DRED and DRIT package uses subroutine SEEK to assign logical unitreference numbers to the 14 DOPC reference numbers. Except for notedexceptions, all DOPC calls are issued from subroutines SSDISK or NHDISK in theDIF3D initialization segment SSINIT. The exceptions are the DOPC initializationand termination calls in subroutine DIF3D, the driver for the DIF3D neutronics

161

module proper, and a DOPC call required in subroutine XSREV, the adjoint crosssection reversal subroutine. In the latter case, DOPC file group 6 is deletedand redefined with a potentially different record size in its lone member file.

Table 5.4 lists all of the files used by the code blocks in the NESCversion of D1F3D and classifies them into one of five different categoriesthat have already been defined in Section 4.2 for the Argonne productionversion of DIF3D. As shown in the table, printer output is written to file 6and optionally to file 10. BCD input data is read from file 5; BCD or binaryinterface files which exist at the start of a job will be read from theirrespective files. The DOPC data sets in Table 5.4 have previously been definedin Table 4.3.

TABLE 5.4. Data Set Classification for the NESC DIF3D

FileReferenceNumber

FileName

FileTypea

FileDescripcion

56910111213151819202223242526272829303132333439

41-56b

66-71 -

76-7880

A.DIF3DA.NIP3A.HMG4CA. ISODIF3DCOMPXSLABELSD3EDITNHFLUXNAFLUXPKEDITGEOD3TISOTXSNDXSRFZNATDNRTFLUXATFLUXFIXSRCRZFLUXPWDINTSEARCHRNDMnnSCR001-6UDOITAUDOIT

BCDBCDBCDBCDBCDBCDBCDBCDCDBCDBCDBCDBCDBCDBCDB

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDOPCSCRCDBBCD

input data for SCAN module •output data all modulesinput data spool from SCANauxiliary output all modulesDIF3D controlGNIP4C controlHMG4C controlBCD ISOTXSDIF3D controlmacroscopic cross sectionslabels, half-heightstabular edits spoolnodal restart (real)nodal restart (adjoint)peak, power/flux interfacegeometry descriptionmicroscopic cross sectionsnuclide/zone referencezone nuclide atom densitiesreal fluxadjoint fluxfixed sourcezone flux averagespower densitySRCH4C controlrandom access scratch filesscratch filesUDOIT versions 1-3UDOIT module input

aSee Section 4.2. CDB denotes a code-dependent binary file.

bTable 4.3 describes the 14 DOPC files. Reference numbers 44 and 50are undefined.

162

File assignments may be easily reassigned by changing source code inD3DRTV; no other routines need be modified. All files are written sequen-tially (one minor exception is noced in Section 4.4.3; it applies t-o adjointcalculations with upscatter). If necessary, all files may be read sequentially.Greater efficiency is achieved when random access I/O methods are employed.Reading the flux file in the inscatter source calculation and the flux andfinite-difference coefficient files during the concurrent inner iteration strategyare the principal I/O operations affected by this access method.

5.2.4 Running the NESC version of DIF3D

DIF3D is designed to run in environments in which codes that follow theCCCC standards may have never before been implemented. If desired, all inputdata may be entered in BCD form. BCD input processors within the DIF3D codesystem will subsequently convert this data to the necessary CCCC and code-dependent binary interface files. Existing BCD or binary interface fileswill also be accepted by DIF3D. Table 4.2 summarizes the input and outputinterface files for each code block within the DIF3D code system. Thecontents and formats of the BCD and binary interface files are given in theinterface file descriptions in Appendices B-D. The sample problem input dataon the NESC tape is entirely in BCD format.

The BCD data format principally consists of sets of card images havinga two-digit card type identifier in columns 1 and 2. Frequently, severalcards of the same type are requiied; the ordering of cards within a given typeis usually fixed. Data associated with a particular file is preceded by thecard image DATASET=filename and terminated by another DATASET=filename cardfor the next file, by a BLOCK=STP021 card or by an end-of-file indicator.Alternative keywords to DATASET (e.g. UNFORM, NOSORT and MODIFY) are describedin Section 3.2; th^se provide free field input, special dataset treatment(e.g. A.ISO), and permit modification of specified card types (replacement ordeletion), respectively. Preceding a collection of DATASETs must be a BLOCK=STP021 card image. Each such BLOCK invokes another execution of DIF3D. OldDATASETS (files) which already exist at the start of a job are specified inthe BLOCK=OLD block. The list of old DATASETs consists of card images of theform DATASET=filename.

Most systems require users to specify memory size and CPU time estimatesin a JOB control statement (see JOB Control examples in Section 3.12, Figs.3.5, 3.8 and 3.9). DIF3D jobs require a fixed amount of storage to containthe longest program overlay and I/O buffers, and a problem-dependent minimumamount of computer memory for the FCM and ECM data storage containers (seeSection 3.9). The FCM and ECM container sizes specified in the sample probleminput are appropriate for the CDC 7600, but they may also be used (lessefficiently) on the other target computers. The length of the longestoverlay is installation dependent and can be obtained by examining the outputfrom a successful loader job. The amount of space required for I/O buffersis also installation and implementation dependent; at a given moment themaximum number of files that are opened is problem dependent, but should notexceed 14 (the number of DOPC files). This number does not include the threeBCD input and output file unit numbers 5, 6 and 10. A practical estimate maybe closer to 6 or 7 simultaneously open files.

163

For IBM and CRAY-1 systems region sizes specified on the JOB card providean upper bound on the allowable memory to be used for both program instructionsand dynamically allocated storage containers. On the CDC 7600, the FCM andECM field length requests should only include space required for the longestoverlay; additional space will be dynamically allocated via calls to IGTLCM orIGTSCM from the BPOINTER package. The sample problem discussions which followinclude container size and CPU time estimates for each problem.

5.3 Sample pioblems

Six problem cases are derived from two benchmark source situations.Summarized in Table 5.5 are estimates of typical FCM and ECM container sizesthat are appropriate for running the sample problems on the designatedcomputers. For implementations on the IBM 3033 or CRAY-1 computers theseestimates may optionally replace the container sizes (on the A.DIF3D type 02card) supplied with the sample problems on the NESC tape. As noted above thesupplied sizes are appropriate for the CDC 7600. The relatively largecontainer sizes suggested for the CRAY-1 (operating under the CRAY TimeSharing System at Los Alamos National Laboratory) reduce expensive 1/0 costsin favor of less expensive memory residence charges. Because sample problems1-4 are combined in a single job (as are sample problems 5-6), JOB regionsize or field length calculations are governed by the largest container sizesin each problem set (i.e. problems 4 or 6).

5.3.1 The SNR Benchmark Problem

The SNR benchmark problemit6» i+7 is a 4-group model of a 300 MWehomogeneous-core LMFBR originally specified in both Cartesian and triangulargeometry. The modified problem 5>H7 solved here is obtained by alteringthe outer boundary of the triangular-geometry model (while preserving thevolume of the core) to allow imposition of boundary conditions along surfacesof hexagons. The model consists of a two-zone core surrounded by radial andaxial blankets without a reflector. The height of the active core is 95 cm,and each axial blanket is 40 cm thick. A total of 11 rings of hexagons(including the central hexagon) are included in the model, with a latticepitch of 11.2003 cm. Jin

=0 boundary conditions are imposed on the outersurfaces of the blankets. The full-core model includes a total of 18 controlrods, with 6 of these rods parked at the core-upper axial blanket interface,and the remaining 12 inserted to the core midplane. As in Ref. 5, all calcu-lations are performed using sixth-core symmetry.

5.3.1.1 The Two-Dimensional Model

r'igure'5.1 displays the BCD input data contained on the NESC tape forthe two-dimensional SNR benchmark problem. Two cases corresponding to thefinite-difference and the nodal solution options are specified. Data followingthe second BLOCK=STP021 in Fig. 5.1 invokes the nodal solution option. TheREM0VE=filename cards located after the second BLOCK=STP021 card turn off theexistence sentinels for the corresponding file names in the SEEK table beforeprocessing begins for the second case. Selected printed and plotted outputfrom these two cases is displayed in Appendices G.I and G.2. Included area geometry map, a mesh cell to region map, macroscopic cross section editsand tabulations of region and area integrals for power density, total fluxand neutron balances.

164

TABLE 5.5. Resource Estimates for Sample Problems 1-6

Problem andComputer

simple 1 - 2D SNRFinite Difference OptionIBM 3033CDC 7600CRAY-1

Sample 2 - 20 SNRNodal OptionIBM 3033CDC 7600CRAY-1

Sample 3 - 3D SNRNodal OptionIBM 3033CDC 7600CRAY-1

Sample 4 - 3D SNRFinite Difference OptionIBM 3033CDC 7600CRAY-1

Container SizeFCM

45036C~550

5504000600

60020000650

55012000650

ECM

4300600011250

570057006100

270002700061000,

15300164000450000

CPU Time(Seconds)13

2.81.71.9

1.81.01.6

211111

1478142

Sample 5 - 2D IAEA ProblemFinite Difference OptionIBM 3033 800CDC 7600 20000CRAY-1 8040

Sample 6 - 3D IAEA ProblemFinite Difference OptionIBM 3033 400CDC 7600 8000CRAY-1 800

62000102000102000

602511

94000166000166000

743619

aUnits are decimal number of longwords (REAL*8 words on IBMsystems). JOB region size calculations are given by:

IBM 3033: REGION = 325K + (FCM + ECM)/(128 words/K byte)CDC 7600: SCM = 100,0008 + FCM (octal words)

LCM = SCM + ECM + buffers (octal words)CRAY-1 : REGION = 200000 + FCM + ECM (decimal words)

(unoverlayed)

bCPU times on the IBM 370/195 are approximately 30 to 50% lessthan on IBM 3033.

//SNR2D3D JOB REGION-1700K,TIHE-8,CLASS-X//*HAIN L1NES-25.0RG-PR0// EXEC ARCSP021//SYSIN DD *BLOCK-STP021UNFORM-A.DIF3D010203040506 1

**** SAMPLE1600 85000 01 0

PROBLEM

0 4300 500 11 111 10 100

I ****

1 0 0l.OE-10 l.OE-10 l.OE-10

.0 0.UHFORH-A.01020304050514141414141415151515152930303030303030303030303030303030303030

001 0.04NIP3

**** SAMPLE0707 4XUYUHIM2H3M4M5H6HiM2H3M5H611.1C1C1C1C1C1C

ocococRBKBRBOCOCRBRBCRCRCF

HOSORT-AOV

1 10000

0 4.5000 1.5000 11112131415161COCRBCRCF '

.2003 111234566 1789108 19 4 59 45 4611 5 611 56 577 37 354 1

.ISOIfiOTXS HH2 <

0.5

PROBLEM0 500

4. 41.01.01.01.01.01.0

1

»GFK 3D

] ****0 0 0

BNCH *

2D SNR BENCI'tARK - RODS IN - FD06

2D SNR BENCHMARK - RODS IN - FD060 1

ID 4 6 0 3 0 1 1 12D *NA COOLED PBR BENCHMARK FOUR GROUP CROSS SECTIONS

* * 11 12 13 14 15 160.768 0.232 0.0 'J.O1.72336E+09 4.02463E+08 7.970033+07 3.15946E+O7 1.OS E+07 8.0010000.

04D 11100.

01

5D .11587.21220

1000.3 6CFK0.00 11 2

.21220.46137

91003

e

.17305 E-01 .39123 E-022.9121737D 0.0

2.8818740.0

.40791 £-05 0.04D 12100.

GFK0.0

2

10

0.012 15

.00 04 1.46137

34571.18286 E-02.879511

.023597.46838 E-02

.0

0.001

0.01

.34571.69059.36334

0.0.42309

0.0

E-031.E-02 .

E-07 .

0.

0.01 0 200

.11587830758E-O3 .92943 E-0292415 £-02 3.036066

.16153 E-0244493 E-07

0 0 11 1 2

5D .11588 .21213.21213 .46770.20476 E-012.9149267D 0.0.46451 E-05 0.04D 13 GFK100. 0.0

0 0 11 1 2

5D .14584.28443.129995E-012.4409777D 0.0.38880 E-05 0.04D 14 GiK100. 0.0

0 01 1

5D .12270.23133

0 0 0 0 03 4 1 1 1

.46770 .35349.35349 .66221 E-031

.48531 E-02 .26377 E-02 .51332 E-022.884945

0.0

0.01 0 200

2.882535.023262 0.0

.43414 E-02 .40724 E-07 .10.0 0.0 0.0 0 0 0 03 4 - 1 1

.407321.11527E-O33,

.11588.S3956 E-03 1.00354E-O2.13238 E-01 3.079063

.15718 E-02.49968 E-07

4.28443 .52703

52703 .4073Z.27688 E-02 .44347 E-04 .12274 E-03

0.01 0 200

2.4231710.0

2.422951.032071 0.0

.58971 E-02 .90018 E-0710.0 0.0 0.0

.14584063463E-O31.002116E-O2.34952 E-03 2.796413

.27776 E-02.45039 E-07

12.23133

.46274

04.46274

.33749

0 01 1.33749

8.2278 E-042

0.01 0 200

.97185 E-02 .19453 E-02 .31065 E-04 .87566 E-042.441880 2.423086 2.422988

.026322 0.0.53536 E-02 .62133 E-0710.0 0.0 0.00

7D 0.0 0.0.28907 E-05 0.04D 15 GFK100.

.12270.170873E-O3 7.64083E-O3.23769 E-03 2.790264

.22889 E-02.33248 E-07

0.00 0 01 1 2

5D .13317 .25355.25355 .58044.168687D. 0.0 0.0.10320 E-05 0.0

0 04 1.58044

.54168

.022946

0 01 1.54168

186696E-O2

0.0

0.01 0 200

.86815 E-02 .70361 E-ll

.13317•126433E-O1 .634405E-O1

.37687 E-02.10489 E-07

Fip. 5.1. Input Data for the Four SNR Benchmark Problem Modpls

10.00 0

.32642.19272

0.00 0

0.00 1

0.01 0 200

.19272 .072206.2163O5E-03 .16880 E-03 .11468 E-02

.012942 0.0 .12871 E-02.34533 E-02 .43633 E-ll .69903 E-08

2D SNR BENCHMARK - RODS IN - NODAL


4D 16 GFK100. 0.0

0 0 01 1 2

5D .072206 .11487.11487 .32642.78660 E-037D 0.0 0.0.68780 E-06 0.0BLOCK-STPO21.3REMOVE-GEODSTREMOVE-COMPXSREMOVE-NDXSRFREMOVE-ZNATDNREMOVE-LABELSBEMOVE-RTFLUXMODIFY-A.DIF3D

01 **** SAMPLE PROBLFM 2 ****02 600 550011 1 40.0 1 87.5 1 135.011 1 175.0UNFORM-A.NIP301 **** SAMPLE PROBLEM 2 ****03 114BLOCK-STP021.3REMOVE-GEODSTREHOVE-COMPXSREMOVE-NDXSRFREMOVE-ZNATDNREMOVE-LABELSREMOVE-RTFLUXREMOVE-NHFLUXREMOVE-DIF3DUNFORM-A.DIF3D01 •*** SAMPLE PROBLEM 3 **** 3D SNR BENCHMARK - RODS IN - NODAL02 2000 60000 003 0 0 0 4500 3004 1 0 0 00 110 10 100 1 0 005 1.0E-7 1.0E-5 1.0E-506 1.0 0.001 0.04 0.511 1 40.0 1 87.5 1 135.011 1 175.0UNF0RM-A.NIP301 **** SAMPLE PROBLEM 3 **** 3D SNR BENCHMARK - 8 PLANES - NODAL02 0 1 8000 0 500 0 0 0 0 003 12404 7 4 0 4 4 405 XU .5000 1 405 YU .5000 1 405 ZL .5000 1 405 ZU .5000 1 409 Z 2 40.0 2 87.5 2 135.009 Z 2 175.014 Ml II 1.014 M2 12 1.014 M3 13 1.014 M4 14 1.0

141415151515151529303030303030

M5M6MlM2M3M4H5M6

15161COCRBABCRCF

1.01.0

11.2003 11 1AB 1 0 0 0.0 175.01C 1 0 0 40.0 135.0AB 2 0 0 0.0 175.01C 2 0 0 40.0 135.0AB 3 0 0 0.0 175.01C 3 0 0 40.0 135.0

3T AB 4 0 0 0.0 175.030 1C 4 0 0 40.0 135.030 AB 5 0 0 0.0 175.030 1C 5 0 0 40.0 135.030 AB 6 0 0 0.0 175.030 1C 6 0 0 40.0 135.030 AB 7 0 0 0.0 175.030 OC 7 0 0 40.0 135.030 AB 8 0 0 0.0 175.030 OC 8 0 0 40.0 135.030 RB 9 0 0 0.0 175.030 RB 10 0 0 0.0 175.030 AB 6 1 1 0.0 175.030 OC 6 1 1 40.0 135.030 RB 8 1 1 0.0 175.030 AB 9 4 5 0.0 175.030 OC 9 4 5 40.0 135.030 AB 9 45 46 0.0 175.030 OC 9 45 46 40.0 135.030 RB 11 5 6 0.0 175.030 RB 11 56 57 0.0 175.030 CF 4 1 1 0.0 135.030 CF 7 3 3 0.0 87.530 CF 7 35 35 0.0 87.530 CR 4 1 1 135.0 175.030 CR 7 3 3 87.5 175.030 CR 7 35 35 87.5 175.0BLOCK-STP021.3REMOVE-GEODSTREMOVE-COMPXSREMOVE-NDXSRFREMOVE-ZNATDNREMOVE-LABELSREMOVE-RTFLUXRKMOVE-NHFLUXMODIFY-A.DIF3D01 **** SAMPLE PROBLEM 4 **** 3D SNR BENCHMARK - RODS IN - FD0636MODIFY-A.NIP301 **** SAMPLE PROBLEM 4 **** 3D SNR BENCHHARK - RODS IN - FD063603 9009 Z 8 40.0 10 87.5 10 135.009 Z 8 175.0

a*

Fig. 5.1. Input Data for the Four SNR Benchmark Problem Models (contd.)

167

5.3.1.2 The Three-Dimensional Model

The third and fourth BLOCK=STP021 cards in Fig. 5.1 signal the start ofthe three-dimensional models solved by the nodal and finite-difference options,respectively. The MODIFY=filename cards permit selective modification of cardtypes within appropriate data sets; previously existing data that are stillpertinent need not be respecified. Appendices G.3 and G.4 display selected,printed output for these two cases.

5.3.2. The IAEA Benchmark Problem

The IAEA benchmark problem1*8 is the well-known 2-group LWR model designedas a severe test for the capabilities of coarse mesh methods and flux synthesisapproximations. The problem solved here has the Jjn=O boundary conditionapplied at external boundaries. Because the DIF3D finite-difference optionrequires a rectangular boundary domain in the XY plane, the irregular outerboundaries on the XY plane that are required by the benchmark specificationsare modelled by assigning the inactive mesh cells to a blackness theoryregion with an appropriate internal black boundary condition constant (B=.5).The dimensions of the quarter-core planar model are 170 x 170 cm. The three-dimensional quarter-core model has 380 cm in the axial dimension. Two fuelregions, a reflector and five inserted rods (one of which is only partiallyinserted) appear in the quarter-core model.

5.3.2.1 The Two-Dimensional Model

Input data for the two-dimensional IAEA problem appear in Figure 5.2.Printed and graphical output selections similar to those chosen for the SNRproblems are displayed in Appendix G.5.

5.3.2.2 The Three-Dimensional Model

Input data for the three-dimensional IAEA problem also appear in Figure5.2; it follows the second BLOCK=STP021 card. Selected printer output isdisplayed in Appendix G.6.

5.4 Suggested Local Modifications

The export package described in this chapter is designed to run in stan-dalone fashion on a variety of machines and operating systems. Because ofthis we cannot take advantage of local system routines and options. In thissection we point to several areas of the code which programmers may wish tomodify to make DIF3D more compatible with the local system.

5.4.1 SEEK Initialization

The initialization of the SEEK tables at the front of the driver ofthe code is done in the manner required by the version of SEEK which accompaniesthe NESC package. Programmers at those installations that have their ownversion of SEEK may wish to modify the initialization procedure coded intothe DIF3D driver. There are no CCCC standards for SEEK initialization.

BLOCK-STP021UNFORM-A.DIF3D01 **** SAMPLE 5 ****02 20000 10200003 0 0 0 0 SO04 1 0 0 11 110 10 100 1 106 0. 0. .01UNFORM-A.NIP301 **** SAMPLE S ****02 0 1 17000 0 200003 4004 3 4 3 405 0. .5 0. .506 RREFL 0. 170.06 RFUEL1 0. 50.06 RFUEL1 50. 90.

90. 110.90. 130.

IAEA 2D BENCHMARK - 2. CM MESH

IAEA 2D BENCHMARK - 2. CM MESH

85 0.20 110.20 90.

170.150.130.110.90.50.130.110.70.30.10.10.90.90.170.150.130.110.

06 RFUEL1 90. 110. 10 10 90.06 KFUEL1 90. 130. 20 20 50.06 RFUEL1 110. 150. 20 25 0.06 RFUEL2 0. 30. 15 65 0.06 RFUEL2 30. 70. 20 50 0.C& RFUEL2 70. 110. 20 35 0.06 RFUEL2 110. 130. 10 15 0.06 RFUE2R 0. 10. 5 5 0.06 RFUE2R 70. 90. 10 5 0.06 RFUE2R 0. 10. 5 10 70.06 RFUE2R 70. 90. 10 10 70.06 BACKGR 70. 170. 50 10 150,06 BACKGR 110. 170. 30 20 130,06 BACKGR 130. 170. 20 10 110,06 BACKGR 150. 170. 10 20 70,

10 CBACKG11 1.0 .514 CFUEL1 FUEL1 1.14 CFUEL2 FUEL2 1.14 CFUE2R FUEL2R 1.14 CREFL REFL 1.14 CBACKG BLACK 1.15 CFUEL1 RFUEL115 CFUEL2 RFUEL215 CFUE2R RFUE2R15 CREFL RREFL15 CBACKG BACKGR34 ** .8E-443 1 5.5 5.5NOSORT-A.ISO

OV ISOTXS ISOTXS*IAEA BNCHMK* 1ID 2 6 0 1 1 1 1 12D * 2 GROUP CROSS SECTIONS FOR IAEA BENCHMARK PROBLEM* * FiJELl FUEL2 FUEL2R REFL REFLR BLACK1.00000E+00 0.01.00000E+09 2.20000E+05 1.00000E+07 1.00000E+00 0.0

0 " 3 6 9 12 154D FUEL1 ' IAEA1.00000E+00 3.20000E-I1 0.0 0.0 0.0 0.0

0 0 1 0 0 0 0 0 1 1 01 1 2 1 1

5D 2.22222E-0I 8.33333E-O1 3.00000E-02 8.00000E-02 1.00000E-023.5O000E-O2 0.0 4.50000E-O2 3.00000E+00 3.00000E+007D 0.0 0.0 2.00000E-024D FUEL2 IAEA1.00000E+00 3.20000E-11 0.0 0.0 0.0 0.0

0 0 1 0 0 0 0 0 1 1 01 1 2 1 1

5D 2.22222E-01 8.33333E-01 3.00000E-02 8.50000E-02 1.OOOOOE-024.00000E-02 0.0 4.50000E-O2 3.00000E+00 3.00000E+007D 0.0 0.0 2.OOOOOE-024D FUEL2R IAEA1.00000E+00 3.20000E-11 0.0 0.0 0.0 0.0

0 0 1 0 0 0 0 0 1 1 01 1 2 1 1

5D 2.22222E-01 8.33333E-O1 3.OOOOOE-02 1.30000E-01 1.OOOOOE-028.50000E-02 0.0 4.50000E-O2 3.00000E+00 3.00000E+007D•4D

0.0REFL

1.OOOOOE+00

5D

0 01 1

0,IAEA

.0

3.20000E-11 0.002

l.':>66b7E-0i 1,1.OOOOOE-027D4D

0.0REFLR

1.OOOOOE+000 01 1

0,IAEA

01

.11111E+00

.0

3.2000CE-11 0.002

01

2

014

4

01

.OOOOOE-02

0.00 0

.OOOOOE-02 1

.OOOOOE-02

0.00 0

0.0 0.0

0.0 0.01

5D 1.66667E-01 1.11111E+00 4.OOOOOE-02 5.50000E-02 0.05.5O000E-O27D 0.0 0.0 4.OOOOOE-024D BLACK IAEA

0.01.OOOOOE+00 3.2000OE-11 0.0 0,0 0.0 0.00 0 0 0 0 0 0 0 1 11 1 2 1 1

5D 1.66667E-01 l.lllllE+00 1.OOOOOE+00 1.OOOOOE+00 1.OOOOOE+001.OOOOOE+007D 0.0 0.0 0.0BLOCK=STP021REM0VE-GEODSTREMOVE=COMPXSREMOVE=NDXSRFREMOVE-ZNATDNREMOVE-LABELSREMOVE-RTFLUXMODIFY-A.DIF3D01 IAEA 3D BENCHMARK 10. CM MESH02 8000 16600006 0. 0. .01MODIFY-A.NIP301 IAEA 3D BENCHMARK 10. CM MESH02 0 1 3000 0 1000 0 0 0 0 1

co

Fig. 5.2. Input Data for the IAEA Benchmark Problem Models

03040505050506060606060606060606060606060606060606060606060610110909091414141414141515151515153443

443 4 3 4XU .5YU .5ZL .5ZU .5RREFLRFUEL1RFUEL1RFUEL1RFUEL1RFliELlRFUEL2RFUEL2RFUEL2RFUEL2RFUE2RRFUE2RRFUE2RRFUE2RRFUE2RRREFLRRREFLRRREFLRRREFLRRREFLRBACKGRBACKGRBACKGRBACKGRCBACKG1.0 .5

4 4

0. 170.0. 50.50. 90.90. 110.90. 130.110. 150.0. 30.30. 70.70. 110.110. 130.0. 10.70. 90.0. 10.70. 90.30. 50.0. 10.70. 90.0. 10.70. 90.30. 50.70. 170.110. 170.130. 170.150. 170.

X 17 170.Y 17 170.Z 38 380.CFUEL1CFUEL2CFUE2RCREFLCREFLRCBACKGCFUEL1CFUEL2CFUE2RCREFLCREFLRCBACKG-DELETK-DELETE

FUEL1 1.FUEL2 1.FUEL2R 1.REFL 1.REFLR 1.BLACK 1.RFUEL1RFUEL2RFUE2RRREFLRREFLRBACKGR

022222222222222836363636360000

383636363636363636363636363636383838383838383838

0.110.90.90.50.0.0.C.0.0.0.0.70.70.30.0.0.70.70.30.150.130.110.70.

1701501301109050130110703010109090501010909050170150130110

Fig. 5.2. Input Data for the IAEA Benchmark Problem Models (contd.)

170

5.4.2 Storage Allocation Routines

The BPOINTER container allocation is done in a FORTRAN subroutine namedIGTLCM (with entry point IGTSCM). At individual installations there maybe special system routines available which could be called from IGTLCM toborrow space from the system or to return it. Programmers should look atIGTLCM to see if modifications are in order.

5.4.3 TIMER

The subroutine TIMER is a general timing routine specified by the CCCC.The specifications for the subroutine include elapsed central processortime, remaining "limiting" time, elapsed peripheral processor time, currentdate, user identification, user account, user case identification and wallclock time. Many of these options are installation dependent so that they arenot implemented in the export version of TIMER. The options which are notimplemented are not required for execution of DIF3D although various timingedits are zeroed in the export version of TIMER. Programmers interestedin obtaining proper edits should modify TIMER according to local conventionsto Implement the desired options.

5.4.4 GNIP4C Graphics

The graphics region map options in the GNIP4C input processor are notoperational in the NESC version of DIF3D; they are not crucial to the executionof the code, and graphics systems vary from system to system. An effort wasmade, hov/ever, to make it as simple as possible to implement these options.

1. All graphics calls for the orthogonal geometry maps are made throughthe subroutine 0RTPC2, and all graphics calls for maps of arrays ofhexagons are made through HEXPC5. It should be possible to limitcode modifications to these two routines.

2. The graphics map routines were coded and checked out for threedifferent graphics systems: CALCOMP, DISPLA and the local A"gonnegraphics primitives. Code peculiar to CALCOMP and DISPLA werecommented out but are identified by comment cards of the form:

C**** DISPLA GRAPHICSor

C**** CALCOMP GRAPHICS

It should not be hard to reactivate the DISPLA or CALCOMP options.

3. On some systems additional, initialization calls may have to be made.

5.4.5 Random Access 1/0 Routines DOPC, DRED and DRIT

In the implementation of DOPC thac accompanies the NESC package eachcode block using DOPC initializes it in their respective driver subroutines.On IBM systems DRED (DRIT) call REED (RITE) to perform asynchronous, randomaccess I/O. On CDC 7600 systems, the mass storage routines READMS, WRITMS,OPENMS and CLOSMS are used. On the CRAY-1 FORTRAN '77 I/O statements providerandom access capabilities. Installations with asynchronous, random accesscapabilities superior to those previously mentioned may simply replace DOPC,DRED, DRIT, CRED and CRIT. The latter two routines must be replaced ormodified to maintain ECM referencing consistent with any replacement DOPCimplementations.

171

ACKNOWLEDGEMENTS

A number of people have contributed significantly to the programming inthe DIF3D code package. C. H. Adams chiefly managed the evolution of theGNIPAC input processor from the FX2 input processor; the broader picture ofthe evolution of the CCCC routines was also greatly influenced by him.GNIP4C was touched by many others including B. J. Toppel, R. P. Hosteny,Herb Henryson II and several summer students. R. P. Hosteny coded the HMG4Ccode block. The nodal solution option overlays are the work of R. D. Lawrence.I am indebted to D. ^. Ferguson who originally outlined the basic codestructure of DIF3D and chose the iteration strategies. Contributions to thisreport were made by C. H. Adams, H. Henryson II, R. P. Hosteny and B. J.Toppel. Users whose feedback uncovered bugs during the development stagesare gratefully acknowledged. A. R. Hinds made several fine tuning suggestionsto improve the running times of the inner iteration kernal, SORINV, on theIBM 370/195. Significant CPU time reductions were also achieved on the CDC7600 with a COMPASS assembler version of SORINV written by F. E. Dunn. For theassistance of L. Rudsinski with the implementation of DIF3D on the CRAY-1 atNCAR, and F. Brinkley and D. McCoy on the CRAY-1 with CTSS at Los Alamos I amindebted. The work of Karen Leffler and Eileen Johnson in typing this reportis greatly appreciated.

172

REFERENCES

1. D. R. Ferguson and K. L. Derstine, "Optimized Iteration Strategies andData Management Considerations for Fast Reactor Finite DifferenceDiffusion Theory Codes," Nucl. Sci. Eng., 64_, 593 (1977).

2. K. L. Derstine, "DIF3D: A Coda to Solve One-, Two-, and Three-DimensionalFinite Difference Diffusion Theory Proulems," ANL-82-64, Argonne NationalLaboratory, 1983.

3. R. D. Lawrence, "A Nodal Interface Current Method for Multigroup DiffusionCalculations in Hexagonal Geometry," Trans. Am. iJucl. S o c , 39, 461 (1981).

4. R. D. Lawrence, "A Nodal Method for Three-Dimensional Fast ReactorCalculation in Hexagonal Geometry," Proceedings of the Topical Meeting onAdvances in Reactor Computations, Vol. II, p. 1030, Salt Lake City,American Nuclear Society, March, 1983.

5. R. D. Lawrence, "The DIF3D Nodal Neutronics Option for Two- and Three-Dimensional Diffusion Theory Calculations in Hexagonal Geometry,"ANL-83-1, Argonne National Laboratory, 1983.

6. P. Douglas O'Dell, "Standard Interface Files and Procedures for ReactorPhysics Codes, Version IV", UC-32, Los Alamos Scientific Laboratory(September 1977).

7. B. J. Toppel, "The Fuel Cycle Analysis Capability, REBUS-3," ANL-83-2,Argonne National Laboratory, 1983.

8. R. W. Hardie and W. W. Little, Jr.., "3DB, A Three-Dimensional DiffusionTheory Burnup Code," BNWL-1264, Battelle-Pacific Northwest Laboratories(1970).

9. D. R. Vondy, T. B. Fowler, and G. W. Cunningham, "VENTURE: A Code Blockfor Solving Multigroup Neutronics Problems Applying the Finite-DifferenceDiffusion-Theory Approximation to Neutron Transport," ORNL-5062, Oak RidgeNational Laboratory (1975).

10. W. R. Cadwell, "PDQ-7 Reference Manual," WAPD-TM-678, Bettis Atomic PowerLaboratory (lf . / ) .

11. D. R. Ferguson, Personal communication.

12. L. A. Hageman, "Numerical Methods and Techniques Used \n the Two-Dimensiona Neutron Diffusion Program PDQ-5," WAPD-TM-364, Bettis AtomicPower Laboratory (1963).

13. L. A. Hageman and C. J. Pfeifer, "The Utilization of the Neutron DiffusionProgram PDQ-5," WAPD-TM-395, Bettis Atomic Power Laboratory (1965).

14. C. H. Adams, Personal communication. VARI3D performs perturbation theorycalculations and is still under development a,. Argonne.

173

15. C. H. Adams,"SYN3D: A Single-Channel, Spatial Flux Synthesis Code forDiffusion Theory Calculations", ANL-76-21, Argonne National Laboratory,1976.

16. T. B. Fowler, D. R. Vondy and G. W. Cunningham, "Nuclear ReactorCore Analysis Code: CITATION," ORNL-TM-2496, Oak Ridge NationalLaboratory, Tenn. (1971).

17. T. A. Daly et al., "The ARC System Two-Dimensional Diffusion TheoryCapability, DARC2D," ANL-7716, Argonne National Laboratory (1972).

18. R. S. Varga, Matrix Iterative Analysis, Chap. 3, Prentice-Hall, Inc.,Englewood Cliffs, New Jersey (1962>.

19. A. F. Henry, Nuclear Reactor Analysis, Cambridge, Mass. (1975).

20. K. L. Wachspress, Iterative Solution of Elliptic Systems and Applicationsto the Neutron Diffusion Equations of Reactor Physics, Chap. 2.,Prentice-Hall : n c , Englewood Cliffs, New Jersey (1966).

21. R. S. Varga, Proc. Symp. Appl. Math., 11, 164, American MathematicalSociety, Providence, Rhode Island (1961).

22. G. Birkhoff and R. S. Varga, J. Soc. Ind. Appl. Math., 6_, 354 (1958).

23. R. Froehlich, "A Theoretical Foundation for Coarse Mesh VariationalTechniques," Proc. Int. Conf. Research Reactor Vitalization and ReactorMathematics, Mexico, D.F., 1, 219 (May 1967).

24. E. L. Wachspress, Iterative Solution of Elliptic Systems and Applicationsto the Neutron Diffusion Equations of Reactor Physics, pp. 77-80, 83 and270-287, Prentice-Hall Inc., Englewood Cliffs, New Jersey (1966).

25. D. A. Flanders and G. Shortley, J. Appl. Phys., 21, 1326 (1950).

26. R. S. Varga, Matrix Iterative Analysis, Chap. 5, Prentice-Hall, Inc.,Englewood Cliffs, New Jersey (1962).

27. R. S. Varga, Matrix Iterative Analysis, Chap. 4, Prentice-Hall, Inc.,Englewood Cliffs, New Jersey (196?).

28. B. J. Toppel, C. H. Adams, R. D. Lawrence, H. Henryson II, and K. L.Derstine, "Validation of Alternative Methods and Data for a BenchmarkFast Reactor Depletion Calculation," Proceedings of the Topical Meetingon Advances in Reactor Physics and Core Thermal Hydraulics, (held inKiamesha Lake, NY), NUREG/CP-0034, Vol. 1, p. 177, U.S. NuclearRegulatory Commission, Washington, D.C., August 1982.



174

31. I. Stakgold, Boundary Value Problems of Mathematical Physics, Vol. I,pp. 79-81, MacMillan, Toronto (1969).

32. E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Chap. 2,Wiley, New York, 1966.

33. M. R. Wagner, "GAUGE - A Two-Dimensional Few Group Neutron Diffusion -Depletion Program for a Uniform Triangular Mesh," GA-8307, Gulf GeneralAtomic, 1968.

34. D. A. Meneley, "Acceleration of External Source Problems in Near-CriticalSystems," Applied Physics Division Annual Report: July 1, 1970, to June30, 1971, ANL-7910, pp. 513-515.

35. E. Issaacson and H. B. Keller, Analysis of Numerical Methods, pp. 98-102,Wiley, New York (1966).

36. L. C. Just, H. Henryson II, A. S. Kennedy, S. D. Sparck, B. J. Toppeland P. M. Walker, "The System Aspects and Interface Data Sets of theArgonne Reactor Computation (ARC) System," ANL-7711, Argonne NationalLaboratory (1971).

37. G. E. Bosler, R. D. O'Dell, and W. M. Resnik, "LASIP-III, A GeneralizedProcessor for Standrd Interface Files," LA-6280-MS, Los Alamos ScientificLaboratory (1976).

38. H. Henryson II, B. J. Toppel, and C. G. Stenberg, "MC2-2: A Code toCalculate Fast Neutron Spectra and Multigroup Cross Sections," ANL-8144,Argonne National Laboratory (1976).

39. M. K. Drake, ed., Data Formats and Procedures for the ENDF NeutronCross Section Library, Brookhaven National Laboratory, BNL 50274(Oct. 1970).

40. H. Henryson II, Personal communication.

41. C. H. Adams, K. L. Derstine, H. Henryson II, R. P. Hosteny and B. J.Toppel, "The Utility Subroutine Package Used by Applied Physics ExportCodes," ANL-83-3, Argonne National Laboratory, 1983.

42. L. Rudsinski, "Production Runs on the CRAY-1," ANL-79-68, Argonne NationalLaboratory (1979).

43. D. Boley, B. Buzbee, and S. Parter, "On Block Relaxation Techniques,"University of Wisconsin, Mathematics Research Center Report 1860 (June1978).

44. D. Boley, "Vectorization of Block Relaxation Techniques: Some NumericalExperiments," Proceedings of the 1978 LASL Workshop on Vector and ParallelProcessors, LA-7491 (September 1978).

45. K. L. Derstine, "An Experience with the Conversion of the Large-ScaleProduction Code DIF3D to the CRAY-1," Scientific Computer InformationExchange Meeting, Livertnore, CA, pp. 116-127 (September 1979).

.175

46. G. Buckel, K. Kufner, and B. Stehle, "Benchmark Calculations for aSodium-Cooled Breeder Reactor by Two- and Three-Dimensional DiffusionMethods," Nucl. Sci. Engr. 64_, 75 (1977).

47. "Benchmark Problem Book," ANL-7416, Supplement 3, Argonne NationalLaboratory, to appear, 1984.

48. "Benchmark Problem Book," ANL-7416, Argonne National Laboratory (1968),

14. Other Programming or Operating Information or Restrictions: An optim-ized assembler version of the (finite-difference) tridiagonal matrixsolution and overrelaxation routine is available for the CDC andCRAY systems. DIF3D is maintained as a single unified source file.Particular machine versions are configured at distribution time viaactivation and deactivation of coding bracketted by in-stream languageflag comment cards.

15. Name and Establishment of Authors:K. L. Derstine and R. D. Lawrence ,.Applied Physics DivisionArgonne National LaboratoryArgonne, Illinois 60439

Major contributions to the finite-difference option of DIF3D were madeby D. R. Ferguson.

16. Material Available: Restricted Distribution Magnetic Tape Transmittal

a) User's Manual

b) Magnetic Tape Containing

i) Source Code

ii) Sample Problem Data Card-Images

iii) Sample Problem Output

iv) Code Dependent BCD and Binary Card-Image File Descriptions

v) Linkage Editor, Segmented Loader or Overlay Loader ControlCard-Images

vi) JCL Procedure for Execution.

17. Category: C

Keywords: block overrelaxationchebyshev accelerationcoarse mesh diffusion theoryhexagonal geometrymultigroup diffusion theorynodal diffusion theory

18. Sponsor: Division of Reactor Research and Technology, U. S. Departmentof Energy

xv

Appendix A

ARCSP021 INSTREAM JCL PROCEDURE FOR IBM 370 SYSTEMS

//ARCSP02I PROC ATCYL-5,ATDSP-'(.DELETE)'.ATFLUX",&ATFLUX,,// ATVOL-.DEST-'*,.DEST2-F,DMPDEST-F,// DMYICYL-21,DMY2CYL-7,DMY5CYL-4,// FDCCYL-20,FLXCYL-I.HALFTRK-6I36,// ISOCYL-1.ISODSP-,(MOD,KEEP),.ISOVOL-,// ISOTXS-'&ISOTXS' ,MODEDCB-'RF.CFM»U' ,// MODLIBI-'SYSl.DUMMYLIB,,// MODLIB2-'C116.NESC.MODLIB',// NACYL-5,NADSP-'(.DELETE)',NAFLUX-,&NAFLUX'.NAVOL-// NHCYL-5,NHDSP-'(,DELETE)',NHFLUX-,&NHFLUX',NHVOL=// PATH-'STP021',// POSTLIB-'SYSl.DUMMYLIB,.PRELIB-'SYS1.DUMMYLIB,,// PSICYL-5,PSUCYL-3,QRTRTRK«3064,REGN-1000K,// RTCYL-5,RTDSP-'(.DELETE)'.RTFLUX-'&RTFLUX,,// RTVOL-.TIMLIM-,(600,0)'.TWELTRK-1016,// SRFCYL-12,// UNITS-BATCHDSK.UNITSCR-SASCR.//' ZOKCYL-1//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//*//•II*

A * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

•CATALOGED PROCEDURE FOR 1. 2 OR 3D DIFFUSION CODE DIF3D 3.0 **LAST MODIFIED 6/09/83, PREVIOUSLY MODIFIED 5/16/83 ** ****************************************************************

******************************************

PARAMETER DEFAULT VALUE

PATHTIMLIMRKGNMODLIB1MODLIB2PRF.LIBPOSTLIBDESTDEST2DMPPESTATCYLATDSPATFIJ'XATVII1,

ISOCYI.

STP021(600,0)inOOKSYSI.DUMMYLIB

USACE

PROGRAM NAMESTEP TIME LIMITSTEP REGION SIZESECOND STEP LIBRARY

CI16.NESC.MODLIB NESC SYSTEM LIBRARYSYS1.DUMMYLIBSYS1.DIIMMYLIB*FF

(.DELETE)

(.ATF'.HX

FIRST STEP LIBRARYLAST STEP LIBRARYOUTPUT DEST. (PRINTER)OUTPUT DESTINATION FICHF.ROUTE DUMP TO FICHF.NO. OF CYL. FOR ATFLUXDISPOSITION OF ATFLUXMSN KOR DATASKT ATFI.UXVOI.HMK KllR ATFU'X

N O . CYL. FOR I S O T V S

FTNNF001

FXEC

EXEC

EXEC

STEPI.IB

STEPLIB

STEPLIB

STEPLIB

0610

SYSUDUMP

3'

31

1 !

31

27

/ / *II*II*If*II*II*II*II*II*11*'I*'I*II*II*II*II*II*II*II*II*II*II*11*II*II*11*II*I '*II*II*I '*II*I '*II*II*II*II*II*'I*il*II*II*II*II*//STI//STIIIIIII

KoDSP ("Oll.KKKP) DISPOSITION "V I s o T * si>-'nr\s iisoTvs nss, KOR DATASKT ISOTXS

ISOVnL VDI.i' f- KOR JSOT VS

NADSP f.liH.FTF) DISPOSITION ny NAF1.I"

SAK1 I'K J.NAK1 I'X MSN KOK NAKI.I'X

VAVol VOI.I'MI- KOR NAFI.I'X

SlirYI. S NO. OF CYL. KOR XMFIJ'VNIIDSP .'.MKI.KTK) DISPOSITION OK MIFI.I'XMIKI.I'X iSMKl.l'X MSN KOR NIIFI.i'XVHVOI. VOI.l'HK KOR MIFI.PXRTfYI. S NO. OF CYI . -OR RTFI.I'XKTDSI- ( .DFI.KTK) DISPOSITION OF KTFI.I'X»Tl'l.l'X ARTFI.I'X DSN K'lR DATASKT RTFI.I'XRTVol. VOI.l'MK FOR RTKI.l'XSRFCYI. !2 NO. OF CYL. FOR SURF. FU'XKS

THh KOI.I.OWINC FIVK PARAHKTKRS DFFINK CYLINDER ALLOCATIONAND TIIK I)CB FOR AUXILIARY FLUX, FDCOKF AND ZONMAP DATASKTS

.'7

J4

23

21

VI

KlirrYl.r"l XCY1.VDDH'CBPSITYI.I'SITYI./ONCYI.

20IRFCFM-HS1

1

NO. OF CYL. FOR FDCOK.F DATASKT i SNO. CYL. FOR I OROI'P Kl.l'X F I I . F W i - 4 J , •>! ,DCB FOR MAJOR 1 0 DATASKTS H I . S ^ . S S ,NO. C Y L . KOR FLUX DATASK X S il-i2 ."iNO. CYL. FOR ADJ. I'PSCAT FI.I'X i lNO. CYL FOR 7.ONMAP l)2

TMF FOII.OUINi: THREE PARAMETERS HFFINK CYLINDER MJ.OCATMNFOR [ll'MMY F I 1 F S WHICH ALLOCATE CONTICIIOMS BLOCKS OF SPACETo H^ srBAI.LOCATKI) TO VARIOUS SCRATCH DATA S E T S .

IIMYICYI.DMY2CYL

217

NO, OK CYL. KOR KDCOKK, ZHSMAI' iS.*"!!NO. OF CYL. FOR FI.I'X DATASKTS ( 4 l , i h , S S )

( 4 2 , 4 7 , S h ) ( i H . S l . S - )

NO. OF CYL. KOR Kl.l'X DATASKTS ( i 1 , 4 < ) )

TIIK KOLLOW1NC SIX 1'ARAMFTKKS DKFINK UNIT AND R1.KSI7.K KORA VARIETY OF I1ATASKTS

IIAI.FTKK"HTRTRKTUI'I.TRKI'M r si'NI fSCR

| O l hBATCHDSK<ASCR

HALF TRACK KI.OCKINCOI'ARTKK TRACK HI.OCKINCTVH.FTH TRACK HI.OCKINCI'.ENERIC I'NIT NAMKCENKRir I'NIT NAME

o.,i i-vrc I'(:M»M'ATH,TI"I-"(.TIMLIM,RK(:ION-ARK(:NI ' l l H III) n S N - M ' R K I I K . I I I S I ' - S I I K

111) ' ) K \ = . f . « o n i . l K I , I 1 I S P - S I I R1)1) D S N ' d M l i n l . l K? . D I S P - S 1 I KIII) IISS»M'OSTI.IH,I1|SI'»SIIP

/ / n U M M Y I n n DSN-&&DUMMYI , S P A C E - ( C \ i . , ( 4 D M Y I C Y L , 1 ) , , C O N T I C ) ,/ / UNIT-MINITSCR X/ / SHARED RY FDCOF:F(45) ,ZONMAP( 52 )//DUMMY2 DD DSN-4&DUMMY2,SPACE-(CYL,(&nMY2CYL,1),.CONTIG),// UNIT«(4UNITSCR,SEP-(DUMMY1)) X// SHARED BY PSIOLD(4 1 ) ,PSIGO(55), FRNOLD(4f>)//DUMMY! DD DSN-&&DUMMY3,SPACE-(CYL,(4DMY2CYL, 1 ), .CONTIC),// UNIT-(SUNITSCR,SEP-(DUMMY1.DUMMY2)) X// SHARED BY PSINEW(42) ,PSIGN(5f>) ,FRNNEU(47)//DUMMY4 DD DSN-«,aDUMMY4,SPACE-(CYL,(4DMY2CYL,t),,CONTIG),// UNIT-(MINITSCR,SEP-(nUMHVl ,nUMMY2,m!MMY3)) X// SHARED BY FRNMI(48),SRCNEW(51),FSRC(54)//DUMMY5 DD DSN-4ADUMMY5,SPACE-(CYL,(4DMY5CYL,1),,CONTIC),// UNIT«(4JNITSCR,SEP»(DUMMYl,DUMMY2,DUMMY3,DUMMY4)) X// SHARED BY FRNM2(49),PSIUP(43)//FT05F00I DO DDNAME-SYSIN X// BCD INPUT./ /FT06F001 DD SYSOUT-4DEST,DCB-(RECFM-FBA,LRECL-I33,riLKSIZE'l596) X/ / PRINTED OUTPUT./ / F T O 9 F ( W 1 DD i m i T » & U N I T S C R , S P A C E - < C Y L , ( l , ] ) ) ,/ / DCB-(RF.CFM-VBS,LRECL-84,BLKSIZE-4QRTRTRK) X// ARC SYSTEM SPOOLED OUTPUT.//FTlOFnni DD DCB-(RECFM-FBA,LRECL-133,BLKSIZE-1596),SYSOUT=4DEST2 X// ALTERNATE PRINT FILE.//*//* DATASETS 11 TO 17 ARE MODULE DEPENDENT BCD DATASETS//*/ / F T l l F f W l DD D S N = 4 4 A D I F 3 D , 1 ' N I T - 4 U N I T S C R , S P A C E - ( T R K , ( 1 , 5 ) ) ,/ / DCB="(RECFM-VBS,LRECL»84,3LKSIZE=4TUELTRK) X// 1,2 OR 3D DIFFUSION MODULE DEPENDENT BCD DATASET.//FT12FOO1 DD DSN-&4ANIP3.UNIT-4UNITSCR,SPACF»(TRK,(4,1)),// DCB-(RECFM»VBS,LRECL=«R4,BI.KSIZE-4QRTRTRK) X// THE ARC SYSTEM GENERAL NEUTRONICS BCD DATASET.//FTI3FOO1 fin DSN-46AHMC4C,UNIT=4UNITSCR,SPACE-(TRK,(I ,0)),// DCB-(RECFM-VBS,LRECL»84,BLKSIZE-4TWELTRK) X// CCCC HOMOGENIZATION MODULE DEPENDENT BCD DATASET.//FT15F001 DD DSN-44AISO,UNIT-4UNITSCR,SPACE=(CYI.,( 1 ,1)),// DCB-(RECFM-VBS,LRECL«84,eLKSIZE-4QRTRTRK) X// THE ISOTXS BCD DATASET.//*//* DATASKTS 18 TO 25 ARE MODULE DEPENDENT BINARY DATASKTS.//*/ / F T I 8 F 0 0 1 DD D S N - 4 & D I F 3 D , U N I T " 4 U N I T S C R , S P A f . r > ( T R K , ( l , n ) ) ,/ / DCB-(RECFM-VBS,LREC1.-X,BLKSIZE=&ORTRTRK) X// 1 , 2 OR 3D DIFFUSION MODULE DEPENDF.NT BINARY DATASET.//FT19F001 DD DSN'iiCOMPXS ,UNIT=-&llNITSCR,Sl'ACE-( CYl.,( 1 .1 )) ,// DCB=(RECEM-VBS,LRECL*X,BLKSIZE»&HA!.FTKK) X// COMPOSITION MACROSCOFIC CROSS-SECTION DATASET.//FT20F001 DD DSN-&ALABE1.S ,UNIT-4UNITSCR,SPACK=-(TRK ,( 3 ,0) ),// ' DCB»(RECFM»VBS,LRECL=X,BLKSI7.E=(.TWELTRK) X// A.NIP3 LABELS AND AREA DEFINITIONS.//FT22FOOI DD DSN»&D3EDIT,UNIT=-4IINITSCR ,SPACE'(CYL, (1 ,1 ) ) ,// DCB-(RECFM=VBS,LRECL=X,BLKSIZE-&HALFTRK) X// D1F3D EDITS INTFRFACE DATASET.

//FT23FO(1I/ // // ///FT24FOO1////////FT25Fnni//////*//*//*//FT26FOO1//////FT27F0ni////////FT28F(H11/ // ///FT29FOO1//////FT30Fnol////////FT3IFnni////////FT32FOO1//////FT33FOOI/ // // / F T U F O n i

//FT39FOOI/ // // / */ / */ / */ /FT41 RIO I/ /

DD DSN=4NHFLUX,DISP=4NHDSP,SPACK'(CYL,(SNHCYL,1)),UNIT-&UNITS,VOL=SER»&NHVOL,DCB»( RECFM-VBS, LRECL-X , BI.KS IZE=&HALFTRK)RESTART FILE FOR REAL NODAL HEX CALCULATION.

DD DSN»SNAFLUX,DISP-&NADSP,SPACE«(CYL,(&NACYL,1)),UNIT-&UNITS.VOL-SER-4NAV0L,DCB»( RECF»»VHS,I.RECL-X , BLKSIZE-&HALFTRK )RESTART FILE FOR ADJOINT NODAL HEX CALCULATION.

DD DSN=&PKEDIT,UNIT-&UNITSCR,SPACE"(CYL,(I , ! ) ) ,DCB-(RECFM-VBS,LRECL-X,BLKSIZE-&HALFTRK)PEAK POWER DENSITY AND FLUX INTERFACE DATASET.

DATASETS 26 TO 40 ARE i ^ INTERFACE FILES.

DD DSN-&r.EODST.UNIT«&UNITSCR,SPACE-(CYL,(01 ,1)),DCB-(RECFM-VBS,LRECL-X,BLKSTZE-4HALFTRK)CCCC GEOMETRY DESCRIPTION DATASET.

DD DSN-&ISOTXS,DISP-4IS0DSP,SPACE-(CYL,(&I^OCYL.l)),UNIT-&UNITS.VOL-SER-&ISOVOL,DCB-(RECFM=VBS,LRECL-X,BLKSIZE-&HALFTRK)CCCC NUCLIDE-ORDERED MICROSCOPIC CROSS SECTIONS.

DD DSN-&NDXSRF,HNIT-&UNITSCR,SPACE=<TRK,(O3.0)),DCB-(RECFM-VBS,LRECL-X,BLKSIZE-&HALFTRK)CCCC NUCLIDE/CROSS SECTION REFERENCING DATA.

DD DSN-&ZNATDN,UNIT»4UNITSCR,SPACE-(CYL,(O1,1)),DCB-(RECFM-VBS,LRECL-X,BLKSIZE-&HALFTRK)CCCC ZONE NUCLIDE ATOM DENSITIES.

DD DSN-&RTFLUX ,DISP-&RTOSP, SPACE-( CYL, ( &RTCY1.. 1 ) ) ,UNIT-&UNITS.VOL-SER-&RTVOL,DCB-(RECFM-VBS,LRECL-X,BLKSIZE-&HALFTRK)CCCC REAL FLUX INTERFACE DATASET.

DD rSN-SATFLUX,DISP-&ATDSP,SPACE-(CYL,(&ATCYL,1)),UNIT-4UNITS.V0L-SER-&ATV0L,DCB- (RF.CFM-V BS, LRECL-X , BLKS I ZF.-4HAt.FTRK )CCCC ADJOINT FLUX INTERFACE DATASET.

DD RSN-4FIXSRC,IINIT-4UNITS,SPACE»(CYL,(O1 ,1 )) ,DCB»( RECFM-VBS .l.RECI.-X, BLKSIZE-6.HALFTRK)CCCC FIXED SOURCE DATASET.

DD DSN-4RZF1.UX,UNIT-4UNITS,SPACE-(TRK,(O1 ,1 )),DCR-(RECFM-VBS,LRECL-X,BLKSIZE-4HALF~RK)CCCC ZONE AVERAGED FLUX INTERFACE DATASET.

DD DSN-4PWDINT.IINIT-4UNITS.SPACE-(CY1.,(O1,1)),DCB-( RECFM-VBS, LRECL-X , Bl.KSIZE-4HAt.FTRK)CCCC POWER DENSITY INTERFACE DATASET.

DD DSN=-4SEARCH,UNIT-&UNITSCR,SPACE=(TRK,(03,n)) ,DCB-(i!ECFM-VBS,l.RECL-X,Bl.KSI/.E=(.HAl.FTRK)CCCC CRITICAI.ITY SEARCH DATA.

DATASETS 41 TO f.0 ARE SCRATCH DATASETS.

DD l>SN-f>&P.S IOLD,SUBALLOC-( CYL, (SPSICYI. , 1),DUMMY2 ) ,DCB=&MODEI)CB

/ / FLUX ITERATE SCRATCH DATASET.//FT42FOPI DD DSN=(.4PSINEW,SIIBAI.I.OC-(CYL,(4PSICYl.,n,ni!MMY3),

~\

Appendix B

DIF3D BCD INPUT FILE DESCRIPTIONS

B.I A.DIF3D

C***********************************************************************

cC. • REVISED 12/15/82

C

A.DIF3D

ONE-, TWO-, AND THREE-DIMENSIONAL DIFFUSION THEORY

MODULE-DEPENDENT BCD INPUT

THIS BCD DATASET MAY BE WRITTEN EITHER

IN FREE FORMAT (UNFORM-A.DIF3D) OR

ACCORDING TO THE FORMATS SPECIFIED FOR EACH

CARD TYPE (DATASET-A.DIF3D).

COLUMNS 1-2 MUST CONTAIN THE CARD TYPE NUMBER. -

A BLANK OR ZERO FIELD GIVES THE DEFAULT OPTION -

INDICATED.

NON-DEFAULTED DATA ITEMS ON THE A.DIF3D

DATA SET ALWAYS OVERRIDE THE CORRESPONDING

DATA ON THE RESTART DATA SET DIF3D.

PROBLEM TITLE (TYPE 01)

FORMAT (12,4X ,11A6)

CONTENTS...IMPLICATIONS, IF ANY

01

ANY ALPHANUMERIC CHARACTERS (1 CARD ONLY).

C

CR

ca.c.en

STORAGE AND DUMP SPECIFICATIONS (TYPE 02)

FORMAT (I2,4X,3Th)

COLUMNS CONTKNTS... IMPLICATIONS, IF ANY

mi

CI)CPen

CI)C!)CDCI)

enCI)CI)enccc—

CRCCI.cCI)en

en

en

en

en

en

en

en

en

en

CI)

CI)en

en

en

en

en

en

en

enCM

enenCM

en

en

i-: 02

7— i 2 POINTR CONTAINER ARRAY SIZH IN FAST CORK "KMORY (FCM)IN RKAI.*8 WiJRDS (DKFAULT-IOOOO).

11-18 POINTR CONTAINER ARRAY SIZE IN EXTENDED CORFMEMORY (KCM) IN RKAI.*R WORMS (nKFAULT-IOOOO).

19-24 POINTR DEBUGGING EDIT.r>...NO I)KBM(XING PRINTOUT (DEFAULT).I...DEBUGGING DUMP PRINTOUT.2...DEBUGGING TRACK PRINTOUT.1...BOTH DUMP AND TRACE PRINTOUT.

PROBLEM CONTROL PARAMKTF.RS (TYPE 03)

FORMAT (12 ,4X , 1 1 1ft )

COLUMNS CONTENTS...IMPLICATIONS, IF ANY

1-2 03

7-12 PROBLEH TYPE.O...K-EFFECTIVF. PROBLEM (DEFAULT).I...FIXED SOURCE PROBLEM.

n - 1 1 SOLUTION TYPE.O...REAI. SOLUTION (DEFAULT) .1...AD.I0INT SOLUTION.2...BOTH REAL ANn ADJOINT SOLUTION.

19-24 CMKBYSHEV ACCELERATION OF OUTER ITERATIONS.

O...YES, ACCELERATE THE tlUTER ITERATIONS (DEFAULT).1...NO ACCELERATION.

2S-1O MINIMUM PI.ANK-HI.OCK (RECORD) SIZK IN REAI.*H WORDS FORI/O TRANSFER IN THE CONCURRENT INNER ITERATIONSTRATEGY. THE DEFAULT C-4S00) IS HIGHLY RECOMMENDED.

11-Th OUTER ITERATION CONTROL.- 1 . . . BYPASS III FID MODULE.-'. .CALCULATE DATA MANAGEMENT PARAMETERS AND PERFORM

NKIITRONICS EDITS ONLY.-I...CALCULATE DATA MANAGEMENT PARAMETERS, CALCULATE

OVKRRELAXATION FACTORS AND PERFORM NEUTRONICS

Oβ

CI)CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

EDITS ONLY..GE.O...MAXIMUM NUMBER OF OUTER ITERATIONS (DEFAULT-3O).

37-42 RESTART FLAG.O...THIS IS NOT A RESTART (DEFAULT).1...THIS IS A RESTART PROBLEM.

43-48 JOB TIME LIMIT, MAXIMUM (CP AND PP(OR WAIT)) PROCESSOR -SECONDf (DEFAULT-1000000000).

49-54 NUMBER OF UF.^CATTER ITERATIONS PER OUTER ITERATION(DEFAULT'S). PERTINENT TO UPSCATTER PROBLEMS ONLY.

55-60 CONCURRENT ITERATION EFFICIENCY OPTION.0...PERFORM THE ESTIMATED NO. OF INNER ITERATIONS FOR -

EACH GROUP.1...AVOID THE LAST PASS OF INNER ITERATIONS IN THOSE

GROUPS FOR WHICH THE NO. OF ITERATIONS IN THE LAST -PASS ARE LESS THAN A CODE DEPENDENT THRESHOLD.

61-66 ACCELERATION OF OPTIMUM OVERRELAXATION FACTORCALCULATION.0...N0 ACCELERATION (DEFAULT).1...ASYMPTOTIC SOURCE EXTRAPOLATION OF POWER ITERATIONS-

USED TO ESTIMATE THE SPECTRAL RADIUS OF EACH INNER -(WITHIN GROUP) ITERATION MATRIX.

67-72 OPTIMUM OVF.RRELAXATION FACTOR ESTIMATION ITERATIONCONTROL. THE DEFAULT (-50) IS STRONGLY RECOMMENDED.

THE MAXIMUM NUMBER OF OUTER ITERATIONS SENTINELSPECIFIES THE NUMBER OF OUTERS THAT CAN BE PERFORMED(COLS. 31-36) EACH TIME THE DIF3D MODULE IS INVOKED.

THE DIF3D TERMINATION PROCEDURE WILL ALWAYS:l...(RE)WRITE THE APPROPRIATE FLUX FILF.S

(RTFLUX OR ATFLUX).2...(RE)WRITE THE RESTART FILE DIF3D.

TO FACILITATE AUTOMATIC RESTART, THE RESTART FLAGON THE DIF3D RESTART CONTROL FILE WILL BE TURNED ONAUTOMATICALLY UPON DETECTION OF:

1...MAXIMUM NUMBER OF OUTER ITERATIONS.2...TIME LIMIT.

TO RESTART THE FLUX CALCULATION:EITHER

PROVIDE THE RESTART DATA SET DIF3D ANDTHE APPROPRIATE FLUX DATA SET (RTFLUX OR ATFLUX)AND SPECIFY THEM UNDER "BLOCK-OLD" IN THE BCDINPUT DATA

OR1...SET THE RESTART FLAG (COLS. 37-42) TO 1 ON

THE TYPE 03 CARD. THIS PERMITS IMMEDIATE

CN RESUMPTION OF OUTER ITERATION ACCELERATION.CN 2...INCLUDE THE LATEST K-EFFECTIVE ESTIMATECN (COLS. 13-24) AND THE DOMINANCE RATIOCN ESTIMATE ON THE TYPE 06 CARD (COLS. 61-72).CN 3...INCLUDE THE OPTIMUM OVERRELAXATION FACTORSCN FOR EACH GROUP (TYPE 07 CARD).CN 4...PROVIDE THE APPROPRIATE FLUX DATA SET (RTFLUX -CN OR ATFLUX) AND SPECIFY IT UNDER "BLOCK'OLD"CN IN THE BCD INPUT DATA.CNCN A NON-ZERO TIME LIMIT (COLS. 43-48) OVERRIDESCN THE ACTUAL TIME LIMIT DETERMINED INTERNALLYCN BY SYSTEM ROUTINES IN THE ANL AND LBL PRODUCTIONCN IMPLEMENTATIONSCNCN THE TIME LIMIT PARAMETER (COLS. 43-48) IS PERTINENTCN TO EACH ENTRY TO THE DIF3D MODULE.CNCN IT IS RECOMMENDED THAT AN ODD NUMBER OF UPSCATTERCN ITERATIONS BE SPECIFIED (COLS. 49-54) TO AVOIDCN ADDITIONAL I/O OVERHEAD.CNCN THE USER IS CAUTIONED TO MONITOR THE POINT-WISECN FISSION SOURCE CONVERGENCE TO ENSURE THAT MONOTONICCN CONVF.RGENCE IS OBTAINED WHEN THE EFFICIENCY OPTIONCN (COLS. 55-60) IS ACTIVATED.CNCN THE OPTIMUM OVERRELAXATION FACTOR ACCELERATION OPTION -CN IS PRIMARILY INTENDED FOR PROBLEMS KNOWN TO HAVE HIGH -CN O1.8) OPTIMUM OVERRELAXATION FACTORS.CNCN ITERATION CONTROL (COLS. 67-72) OF THE OPTIMUMCN OVERRELAXATION FACTOR ESTIMATION IS PRIMARILY INTENDED -CN FOR USE IN CONJUNCTION WITH THE ASYMPTOTIC ACCELERATION-CN OPTION (COLS. 61-66).C

CR c.nn OPTIONS (TYPE 04)c.CA. FORMAT ( 1 2 , 4 X , 1 0 1 6 )

CC!) COLUMNS CONTENTS.. . IMPLICATIONS, I F ANY

CD 1-2 04CDCD 7-12 PROBLEM DESCRIPTION EDIT (IN ADDITION TO USER INPUTCI) SPECIFICATIONS WHICH ARE ALWAYS EDITED.CD O...NO EDITS (DEFAULT).CD 1...PRINT HDITS.CD 2...WRITE EDITS TO AUXILIARY OUTPUT FILE.CD 3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILK-

CDCDCD

cnCDCDCDCDCDcnCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

13-18 GEOMKTRY (REGION TO MESH INTERVAL) MAP EDIT.O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

19-24 GEOMETRY (ZONE TO MESH INTERVAL) MAP EDIT.O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

25-30 MACROSCOPIC CROSS SECTION EDIT.ENTER TWO DIGIT NUMBER SP WHERE

S CONTROLS THE SCATTERING AND PRINCIPAL CROSS SECTIONS -P CONTROLS THE PRINCIPAL CROSS SECTIONS EDIT ONLY.

THE INTEGERS S AND P SHOULD BE ASSIGNED ONE OF THEFOLLOWING VALUES (LEADING ZEROES ARE IRRELEVANT).O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

31-36 BALANCE EDITSENTER 3 DIGIT NUMBER GBR Wf-'RS

G CONTROLS GROUP BALANCE EDITS INTEGRATED OVER THEREACTORB CONTROLS REGION BALANCE EDIT BY GROUPR CONTROLS REGION BALANCE EDIT TOTALS

(INCLUDING NET PRODUCTION AND ENERGY MEDIANS)

THE INTEGERS G, B, AND R SHOULD BE ASSIGNED ONE OF THE -FOLLOWING VALUES (LEADING ZEROES ARE IRRELEVANT)O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

37-42 POWER EDITSENTER 2 DIGIT NUMBER RM WHERE

R CONTROLS REGION POWER AND AVERAGE POWER DENSITY EDITS-M CONTROLS POWER DENSITY BY MESH INTERVAL EDIT (PWDINT)-

THE INTEGERS R AND M SHOULD BE ASSIGNEDONE OF THE FOLLOWING VALUES (LEADING ZEROES AREIRRELEVANT)O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.

CI)

cnCDCDCDCI)cncncncncnCDCDcnCDCDcnCDcnCDCDcncncnenCDcncncncncncncncnCDCDcncncncnCDcnCDcncncncncCNCNCNCNCNCN

3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILF-

43-48 FLUX EDITSENTER 3 DIGIT INTEGER RMB WHERE

R CONTROLS FLUX EDIT BY REGION AND CROUPINCLUDING GROUP AND REGION TOTALS

M CONTROLS TOTAL (CROUP INTEGRATED) FLUX EDITBY MESH INTERVAL

B CONTROLS TOTAL FLUX EDIT BY MESH INTERVAL AND GROUP -(RTFLUX OR ATFLUX)

THE INTEGERS R, M, AND B SHOULD BE ASSIGNEDONE OF THE FOLLOWING VALUES (LEADING ZEROES AREIRRELEVANT)0...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

49-54 ZONE AVERAGED (REAL) FLUX EDIT.O...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRJTE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

55-60 REGION AVERAGED FLUX EDIT.0...NO EDITS (DEFAULT).1...PRINT EDITS.2...WRITE EDITS TO AUXILIARY OUTPUT FILE.3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

61-66 STANDARD INTERFACE FILES TO BE WRITTEN IN ADDITIONTO RTFLUX AND/OR ATFLUX.0...NONE (DEFAULT).1...WRITE PWDINT.2...WRITE RZFLUX. •--. -3...WRITE BOTH PWDINT AND RZFLUX.

67-72 MASTER DIF3D EDIT SENTINEL DURING CRITICALITY SEARCHES --I...SUPPRESS ALL DIF3D EDITS EXCEPT THE ITERATION

HISTORY AND ERROR DIAGNOSTICS0...EOIT INPUT DATA ON 1ST SEARCH PASS, OUTPUT

INTEGRALS UPON CONVERGENCE OR UPON ACHIEVING THEMA:IMUM SEARCH PASS LIMIT.

N...£LSO INVOKE SPECIFIED DIF31 EDITS EVERY N-THSEARCH PASS.

MULTI-NIGIT EDIT SPECIFICATION EXAMPLES.

ENTERING THE INTEGER 201 IN COLUMNS 31-36 YIELDSTHE GROUP BALANCE EDIT ON THE AUXILIARY FILE ANDTHE REGION BALANCE EDIT ON THE PRIMARY PRINT FILE.

CNCNCNCC —

C-CRCCLCCDCOenenCDenCDCDCDCDCDCDCDCDCCNCNCNCNCC

CRCCLCCDCDCDCDCDCDCDenCDCDCDCDCDCD

ENTERING THE INTEGER 30 IN COLUMNS 31-36 YIELDSTHE REGION BALANCE EDIT BY GROUP ON BOTH THE PRINT ANDTHE AUXILIARY OUTPUT FILES.

CONVERGENCE CRITERIA (TYPE 05)

FORMAT (I2.1OX.3E12.5)


1-2

13-24

25-36

37-48

05

EIGENVALUE CONVERGENCE CRITERION FOR STEADY STATECALCULATION (DEFAULT VALUE - l.OE-7 IS RECOMMENDED).

POINTWISE FISSION SOURCE CONVERGENCE CRITERIONFOR STEADY STATE SHAPE CALCULATION(DEFAULT VALUE • 1.OE-5 IS RECOMMENDED).

AVERAGE FISSION SOURCE CONVERGENCE CRITERIONFOR STEADY STATE SHAPE CALCULATION(DEFAULT VALUE - 1.OE-5 IS RECOMMENDED).

IN UPSCATTERING PROBLEMS IT IS RECOMMENDED THATTHE EIGENVALUE CONVERGENCE CRITERION (COLS. 13-24)BE .1 TIMES THE POINTWISE FISSION SOURCE CONVERGENCECRITERION (COLS. 25-36).

OTHER FLOATING POINT DATA (TYPE 06)

FORMAT (I2.10X.5E12.5)


1-2 06 " ————»—--»«--

13-24 K-EFFECTIVE OF REACTOR (DEFAULT IS OBTAINED FROMTHE APPROPRIATE RTFLUX OR ATFLUX FILE, IF PRESKNT.OTHERWISE DEFAULT - 1.0).

2S-36 ANY POINTWISE FISSION SOURCE WILL BE NEGLECTED IN T'!>. -POINTWISE FISSION SOURCE CONVERGENCK TEST IF IT ISI.KSS THAN THIS FACTOR TIMES THE R.M.S. FISSIONSOURCE (DEFAULT VALUE • .00! IS RECOMMENDED).

37-4B ERSOR REDUCTION FACTOR TO BF. ACHIEVED BY EACH SERIES

CDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCCNCNCNCNCNC-

C —CRCCLCCDCDr.DCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCN

OF INNER ITERATIONS FOR EACH GROUP DURING A SHAPECALCULATION - STRONGLY RF.COMMENDED THAT THE DEFAULTVALUE OF (.04) BE USED.

49-60 STEADY STATE REACTOR POWER (WATTS). (DEFAULT » 1.0).

61-72 DOMINANCE RATIO (FOR RESTART JOBS ONLY).

K-F.FFECTIVE SPECIFICATIONS (COLS. 13-24):1...F0R K-EFFECTIVE PROBLEMS, SUPPLY ESTIMATED

K-F.FFECTIVE OF REACTOR.2...FOR RESTARTED K-EFFECTIVE PROBLEMS, SUPPLY

I.ATEST K-EFFECTIVE ESTIMATE SUPPLIED ON THEITERATION HISTORY EDIT.

3...FOR SOURCE PROBLEMS, SUPPLY K-EFFECTIVE OFTHK REACTOR.

DEFAULT IS OBTAINED FROM THE APPROPRIATE RTFLUX ORATFLUX FILE, IF PRESENT. OTHERWISE DEFAULTS.0 .

NON-MONOTON1C POINTWISE FISSION SOURCE CONVERGENCEIS USUALLY INDICATIVE OF THE NEED TO TIGHTEN THE ERROR -REDUCTION FACTOR(COLS. 37-48). THIS IS FREQUENTLY TRUE-IN TRIANGULAR GEOMETRY PROBLEMS WHERE A VALUE OF .01 IS-USUALLY SUFFICIENT TO OBTAIN MONOTONIC CONVERGENCE.

OPTIMUM OVERRELAXATION FACTORS (TYPE 07)

FORMAT (I2,10X,5E12.5)


1-2 07

13-24 OPTIMUM OVERRELAXATION FACTOR FOR GROUP 1.

2S-36 OPTIMUM OVERRELAXATION FACTOR FOR GROUP 2.

37-4R OPTIMUM OVERRELAXATION FACTOR FOR GROUP 3.

49-fcO OPTIMUM OVERRELAXATION FACTOR FOR GROUP 4.

61-72 OPTIMUM OVKKRELAXATION FACTOR FOR GROUP 5.

REPEAT 5 VAUIF.S PER CARD FOR AS MANY TYPE 07 CARDSAS ARE NF.F.DF.D.

THE OPTIMUM OVERRELAXATION FACTORS ARE NORMALLYOBTAINED FROM THE RESTART INSTRUCTIONS PRINTEDIMMEDIATELY AFTER THE DIF3D ITERATION "TSTORY KDIT.IN THK RESTART INSTRUCTIONS, THE FACTORS ARE ALWAYSEDITTED IN THF. —REAL PROBLEM— ORDERING AND SHOULD BF.

-ps

CNCNCNCNCNCNCNCNCNCNCNCC —

ENTERED ON THE TYPE 07 CARD -IN THE RESTART INSTRUCTIONS.

-EXACTLY— AS EDITTED

CCRCRCCCCCCCC •

CLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCC

THE PERMISSIBLE FACTOR RANGE IS BOUNDED BY 1.0 AND 2.0INCLUSIVE. A ZERO OR BLANK FACTOR ENTRY DEFAULTSTO 1.0. FACTORS ARE COMPUTED FOR THOSE CROUPS HAVINGA FACTOR OF 1.0; FACTORS GREATER THAN 1.0 ARE NOTRECOMPUTED.

TYPE 07 CARDS ARE PRIMARILY INTENDED FOR RESTART JOBSONLY (STRONGLY RECOMMENDED).

NEAR CRITICAL SOURCE PROBLEM ASYMPTOTIC EXTRAPOLATIONPARAMETERS (TYPE 08)

***** WARNING....SELECT THIS OPTION ONLY IF THE ********** ASYMPTOTIC EXTRAPOLATION IS REQUIRED FOR ********** THIS PROBLEM. *****

FORMAT (I2,4X,I6,E12.5)


1-2 08

7-12 NUMBER OF OUTER (POWER) ITERATIONS PERFORMED PRIOR TOASYMPTOTIC EXTRAPOLATION OF NEAR CRITICAL SOURCEPROBLEM (DEFAULT-5).

13-24 EIGENVALUE OF THE HOMOGENEOUS PROBLEM CORRESPONDINGTO THE NEAR CRITICAL SOURCE PROBLEM. THIS EIGENVALUEMUST BE LESS THAN ONE.

25-30 INITIAL FLUX GUESS SENTINEL.O...FLAT FLUX GUESS-1.0 (DEFAULT)l.-.FLAT FLUX GUESS-0.0

THE TYPE 08 CARD IS REQUIRED TO ACTIVATE AN ALTERNATESPECIAL ACCELERATION SCHEME FOR NEAR CRITICALSOURCE PROBLEMS.

IF COLS. 13-24 ARE ZERO OR BLANK, THE HOMOGENEOUSPROBLEM EIGENVALUE WILL BE ESTIMATED. IN THIS CASE, ITIS RECOMMENDED TO INCREASE THE NUMBER OF ITERATIONS INCOLS. 7-12 TO AT LEAST 10.

CLCCDCDCDCDCDCDCDCDCDCDCCNCNCNCNC~

CCRCCLCCDcnCDCDCDCDCDcnCDCDCDCDCDcncnCDcnCDcnCDcncncnCDcnc.CN

SN TRANSPORT OPTIONS (TYPE 09)

FORMAT (I2,4X,2I6,6X,E12.4)


1-2 09

7-12 SN ORDER.

13-18 MAXIMUM ALLOWED NUMBER OF LINE SWEEPS PER LINE PERINNER ITERATION (DEFAULT-10).

25-36 LINE SWEEP CONVERGENCE CRITERION (DEFAULT-1.OE-4).

TO INVOKE THE DIF3D TRANSPORT OPTION, THE TYPE 09 CARDMUST BE PRESENT WITH A NONZERO SN ORDER. FOR THE TIMEBEING, USERS MUST ALSO CONTINUE TO 'PRELIR' TODATASET 'C116.B99983.MODLIB, TO INVOKE THIS OPTION.

PARAMETERS FOR NODAL HEXAGONAL GEOMETRY OPTION (TYPE !0)

FORMAT (I2.4X.5I6)


1-2 10

7-12 ORDER OF NODAL APPROXIMATION IN HEX-PLANE.2...NH2 APPROXIMATION.3...NH3 APPROXIMATION.4...NH4 APPROXIMATION (DEFAULT).

13-18 ORDER OF NODAL APPROXIMATION IN Z-DIRECTION.2...QUADRATIC APPROXIMATION.3...CUBIC APPROXIMATION (DEFAULT).

19-24 COARSE-MESH REBALANCE ACCELERATION CONTROL.-1...NO COARSE-MESH REBALANCE ACCELERATION.

.GF..O...NUMBER OF COARSE-MESH REBALANCE ITERATIONS PEROUTER ITERATION (DEFAULT-2).

25-30 ASYMPTOTIC SOURCE EXTRAPOLATION OF OUTER ITERATIONS.0...APPLY ASYMPTOTIC SOURCE EXTRAPOLATION TO OUTKR

ITERATIONS (DEFAULT).1...NO ASYMPTOTIC SOURCE EXTRAPOLATION.

31-3h NUMBER OF AXIAL PARTIAL CURRENT SWEEPS PER GROUPPER OUTER ITERATION (DEFAULT-2).

THF. TYPE 10 CARD IS PERTINENT ONLY WHEN THF: NODA1.

IIII//FT43FOOIIIII//FT45F001IIII//FT46F001IIII//FT47F00IIIII//FT48F001IIII//FT49F001IIII//FT51F001IIII//FT52FOO1IIII//FT53FOO1IIII//FT54FO01IIII//FT55FOOIIIII//FT06FOniIIIIII*II*II*//FT66FnOlIIII//FT67FOO1IIII//FTftHFOOlIIII//FT69F00IIIII//FT7OFDOI

DCB-&MODEDCBFLUX ITERATE SCRATCH DATASET.

DD DSN=&&PSIUP,SUBALLOC-(CYL,(&PSUCYL,1),DUMMY5),DCB-SMODEDCBAUXILIARY FLUX OATASET FOR ADJOINT UPSCATTER ITERATIONS

DD DSN-&&FDCOEF,SUBALLOC-(CYL,(&FDCCYL,5).DUMMY 1),DCB-&MODEDCBFINITE DIFFERENCE COEFFICIF.NTS SCRATCH DATASET.

DD DSN-&&FRNOLD,SUBALLOC-(CYL,(&FLXCYL,1),DUMW2),DCB-&MODEDCBFISSION SOURCE SCRATCH DATASET

DD DSN-&&FRNNEW,SUBALLOC-(CYL,(&FLXCYL,1).DUMMY3),DCB-&MODEPCBFISSION SOURCE SCRATCH DATASET

DD DSN-&& FRNM1,SUBALLOC-(CYL,(&FLXCYL,1),DUMM{k),DCB-&MODEDCBFISSION SOURCE SCRATCH DATASET.

DD DSN-&&FRNM2,SUBALLOC-(CYL,(&FLXCYL,1),DUMMY5),DCB-&MODEDCBFISSION SOURCE SCRATCH DATASET.

DD DSN-&&SRCNEW,SUBALLOC=(CYL,(&FLXCYL,1).DUMMY4),DCB-&MODEDCBTOTAL SOURCE SCRATCH DATASET.

DD DSN-&&ZONMAP,SUBALLOC-(CYL,(&ZONCYL,I),DUMMY 1),DCB-&MODEI1CBZONE MAP SCRATCH DATASET.

DD DSN-&&CXSFXT,UNIT-&UNITSCR,SPACE-(CYL,(01,1)),DCB-&MODEDCBCOMPOSITION CROSS SECTIONS SCRATCH DATASET.

DD DSN-4&FSRC,SUBALLOC-(CYL,(&PSICYL,1),DUMMY4),DCB-&MODEDCBFIXED SOURCE SCRATCH DATASET.

DD DSN-&&PSIGO,SUBALLOC-(CYL,(&FLXCYL,1),DUMMY2),DCB-&MOnFDCBFLUX ITERATE SCRATCH 0/TASET ONE GROUP.

DD DSN-&&PSIfiN,5UBALL0C-(CYL,(&FLXCYL,1).DUMMY3),DCB»4MODEDCBT U X ITERATE SCRATCH DATASET ONE GROUP.

DATASETS 66 TO 71 ARE SCRATCH DATASETS

nr> DSN-&SCROO] , I I N I T - & U N I T S C R , S P A C E 'DCB-(RECFM-VBS,LRECL-X,BLKSIZE'SCRATCH FILE 1.

DD DSN-&SCROO2.UNIT-&UNITSCR.SPACE'DCB-( RECFM-VBS, LRECL-X, T"KSI/,E!

SCRATCH FILE 2 .f>n OSN-&SCROn3,UNIT-&UNITSCR,SPACE'

DCB-(RECFM-VBS.LRKC1.-X .BLKSIZE'SCRATCH FILE 3.

I)D DSN-&SCROn4,UNIT-&UNITSCR,SHACK'DCB-(RECFM-VBS,LRF.CL-X, BLKSIZESCRATCH FILE 4.

DD DSN=&SCROO5,UNIT=iUNITSCR,SPACE'

•(CYL,USRFCYL,2)),'&HALFTRK)

•(CYI.,(4SRFCYL,2)),'4HALFTRK)

'(CYL,(01 ,1)),'&HALFTRK)

•(CYL,(01,1)).•&HALFTRK)

= (CYL,(01 ,1)),

// DCB-(RECFM=VBS.LRECL-X,BLKSIZE'&HALFTRK)// SCRATCH FILE 5.//FT71F001 DD DSN-&SCR006,UNIT-4UNITSCR,SPACE-(CYL,(01,1)),// DCB-(RECFM-VBS,LRECL-X,BLKSIZE-4HALFTRK)// SCRATCH FILE 6.//*//* DATASETS 76 TO 80 ARE UDOIT INTERFACE DATASETS//*//FT76F001 no DSN-&UD0IT1.UNIT-4UNITSCR,SPACE»(CYL,(01,1)),// DCB-( RECFM-VBS, LRECL-X, BLKSUE*&HALFTRK)// UDOIT INTERFACE FILE VERSION 1.//FT77FOO1 DD DSN-4IIDOIT2 ,UNIT=&UNITSCR,SPACE-(CYL,(01,1 ) ),// DCB-(RECFM-VBS,LRECL-X,BLKSIZE-4HALFTRK)// UDOIT INTERFACE FILE VERSION 2.//FT78F001 DD DSN-&UD0IT3 ,UNIT-&UNITSCR,SPACF.-(CYL,(01 ,1 )) ,// DCB-(RECFM-VBS,LRECL-X,BLKSIZE'&KALFTRK)// UDOIT INTERFACE FILE VERSION 3.//FT80F001 DD DSN-&AUD0IT,UNIT-&UNITSCR,SPACE-(TRK,(3,1)),// DCB-(RECFM-VBS,LRECL-84,BLKSIZE-&QRTRTRK)// BCD INPUT DATASET FOR UDOIT MODULES.//SYSIIDIIMP DD SYSOUT-&DMPDEST// SYSTEM DUMP DATASET FOR ABNORMAL JOB TERMINATION.// PEND

CNCNCNCNCNCNCNCNCC

HEXAGONAL GEOMETRY OPTION (A.NIP3 TYPE 03 CARDGEOMETRY-TYPE SENTINEL VALUES BETWEEN 110 AND 128)IS SPECIFIED.

IT IS RECOMMENDED THAT THE DEFAULT VALUES FOR THEORDER OF THE NODAL APPROXIMATION IN THE HEX-PLANE(COLS. 7-12) «ND FOR THE ORDER OF THE NODAL APPROXI-MATION IN THE I-DIRECTION (COL^. 13-18) BE SPECIFIED.

CCRCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCc—

AXIAL COARSF.-MESH REBALANCE BOUNDARIES FOR NODALHEXAGONAL GEOMETRY OPTION (TYPE 11)

-(I2,10X,3(I6,E12.5))


1-2 11

13-18 NUMBER OF AXIAL COARSE-MESH REBALANCE INTERVALS.

19-30 UPPER 2-COORDINATE.


37-48 UPPER 7.-C00RDINATE.


55-66 UPPER Z-COORDINATE.

THE TYPE 11 CARD IS PERTINENT ONLY WHEN THE THREE-DIMENSIONAL NODAL HEXACONAL GEOMETRY OPTION (A.NIP3TYPE 03 CARD GEOMETRY-TYPE SENTINEL VALUES BETWEEN120 AND 128) IS SPECIFIED.

IF NO TYPE 11 CARDS ARE PRESENT, THE AXIAL COARSE-MESHREBALANCE INTERVALS ARE DEFINED BY THE 7.-C00RDINATKVALUES SPECIFIED ON A.NIP3 CARD 09.

BOUNDARIES ARE SPECIFIED VIA NUMBF.R PAIRS.EACH NUMBER PAIR IS OF THE FORM (N(I), 7.(1)). THEREARE N(I) AXIAL COARSE-MESH REBALANCE INTERVALS BETWEEN7.(1-1) AND 7.(1), WHEPE Z(0) IS THE LOWER REACTORBOUNDARY TN THE 7.-DIRECTION. NUMBER PAIRS MUST BEGIVEN IN ORDER OF INCREASING MESH COORDINATES. ALLAXIAL COARSE-MESH REBALANCE BOUNDARIES MUST COINCIDEWITH THE MESH LINES WHICH BOUND MESH INTERVALS.

B.2 A.HMC4C

C***********************************************************************

CCCCFCECCNCNCNCNCNCNCNCNC

PREPARED 9/26/79 AT ANL

A.HMG4C

INPUT FOR CCCC TO ARC SYSTEM CROSS SECTION HOMOGENIZATION -

THIS IS A USER-SUPPLIED BCD DATA SET.THE LIST FOR EACH RECORD IS GIVEN IN TERMSOF THE BCD FORMAT OF THAT DATA CARD.COLUMNS 1-2 NORMALLY CONTAIN THE CARD TYPENUMBER.A BLANK FIELD GIVES THE DEFAULT OPTIONINDICATED.ALL INPUT CARDS ARE OPTIONAL.


FORMAT (I2.4X.1IA6)


C-CRCCLCCD COLUMNSCD - — —CD 1-2CDCO 7-72CCNC

c

01

ANY ALPHANUMERIC CHARACTERS.

UP TO SIX TYPE 01 CARDS MAY BE USED.

ato

CEOF

C.CRCCLCCDCDCDCDCDCDCI)CI)CI)CDCDCD

PROBLEM OPTIONS (TYPE 02)

FORMAT (I2.4X.8I6)


1-2 02

7-12 SI7.E OF MAIN CORE CONTAINER ARRAY IN REAL*" WORDS(SINGLE WORDS ON CDC SYSTEMS). (DEFAULT-20000).

H-18 PRINT FILE MASTER CONTROL FLAG.0...PRINT GENERAL RUN INFORMATION AND REQUESTED EDITS

(DEFAULT).1...SUPPRESS ALL PRINTING EXCEPT DIAGNOSTICS.

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

19-24 COMPXS EDIT FLAG.0...NO EDIT (DEFAULT).1...PRINT COMPLETE EDIT OF THE CREATED COMPXS FILE.2...WRITE COMPLETE EDIT OF THE CREATED COMPXS FILE

ON THE AUXILIARY OUTPUT FILE.3...COMPXS EDIT WRITTEN ON BOTH PRINT AND AUXILIARY .

OUTPUT FILES.

25-30 ISOTXS EDIT FLAG.0...N0 EDIT (DEFAULT).1...PRINT RUNNING EDIT OF ISOTXS (I.E. NOT EVERY

ISOTOPE ON THE FILE IS PRINTED, ONLY THOSEACTUALLY REFERENCED).

2...WRITE RUNNING EDIT OF ISOTXS ON THE AUXILIARYOUTPUT FILE.

3...RUNNING EDIT OF ISOTXS WRITTEN ON BOTH PRINTAND AUXILIARY OUTPUT FILES.

31-36 POINTR DEBUGGING EDIT FLAG.0...N0 DEBUGGING PRINTOUT (DEFAULT).1...DUMP PRINTOUTS ONLY.2...TRACE PRINTOUTS ONLY.3...BOTH TRACE AND DUMP PRINTOUT.

NOTE THAT HMG4C CONTAINS NO DUMPS, I.E. 1 IS NOTA RELEVANT VALUE FOR THIS FLAG.

37-42 PROHPT FISSION SPECTRUM OPTION FLAG.0...IGNORE ISOTOPE FISSION VECTORS, IF PRESENT IN

ISOTXS, AND USE THE SET FISSION VECTOR FOR ALLCOMPOSITIONS (DEFAULT). IF A SET FISSION SPECTRUMIS NOT PRESENT IN ISOTXS, THE COMPOSITION FISSIONSPECTRA WILL BE COMPUTED BY THE TOTAL FISSIONSOURCE WEIGHTING METHOD USING ISOTOPE FISSIONVECTORS.

1...USE ISOTOPE FISSION VECTORS, IF PRESENT IN ISOTXS,TO COMPUTE COMPOSITION FISSION VECTORS WITH TOTALFISSTON SOURCE WEIGHTING, I.E., UNDER ASSUMPTIONTHAT FLUX IS GROUP INDEPENDENT. THIS IS THEPREFERRED WEIGHTING METHOD. IF AN ISOTOPE FISSIONVECTOR IS NOT PRESENT, THE SET FISSION VECTOR WILLBE USED IN ITS PLACE.

2...USE ISOTOPE FISSION VECTORS, IF PRESENT IN ISOTXS,TO COMPUTE COMPOSITION FISSION VECTORS WITHNII*SIGMA( FISSION) WEIGHTING. THIS METHOD OFCOMPUTING A FISSION SPECTRUM IS NOT RECOMMENDED.IF AN ISOTOPE FISSION VECTOR IS NOT PRESENT, THESET FISSION VECTOR WILL BE USED IN ITS PLACE.

43-48 AUXILIARY OUTPUT FILE MASTER CONTROL FLAG.0...SUPPRESS ALL OUTPUT TO AUXILIARY FILE (DEFAULT).1...WRITE GENERA. RUN INFORMATION AND REQUESTED

EDITS ON AUXILIARY OUTPUT FILE.

NOTE THAT ERROR DIAGNOSTICS ARE NOT WRITTEN ON THEAUXILIARY OUTPUT FILE.

49-54 EDIT FLAG FOR A SUPPLIED COMPXS FILE.0...NO EDIT (DEFAULT).1...PRINT COMPLETE EDIT OF SUPPLIED COMPXS FILE.2...WRITE COMPLETE EDIT OF SUPPLIED COMPXS FILE ON

THE AUXILIARY OUTPUT FILE.3...EDIT OF SUPPLIED COMPXS WRITTEN ON BOTH PRINT AND

AUXILIARY OUTPUT FILES.

CDCDCDCDCDCDCDCD

cnCDCC-

cCRCCLCCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCC

CEOF

B.3 A.ISO (SEE ISOTXS FILE DESCRIPTION)

SCATTERING CROSS SECTION TRUNCATION OPTION (TYPE 03)

FORMAT (I2.4X.E12.5)


1-2 03

7-18 SCATTERING MATRIX TRUNCATION FRACTION (DEFAULT-1.0)

THE SCATTERING CROSS SECTION BANDWIDTH OF ACOMPOSITION IN FILE COMPXS IS TRUNCATED ATTHE POINT WHERE THE INPUT FRACTION (COL 7-18)OF THE TOTAL SCATTERING CROSS SECTION HASBEEN ACCUMULATED. A VALUE OF .999 ISGENERALLY SUFFICIENT TO RETAIN THE RIGOROF A CALCULATION WHILE SIGNIFICANTLY REDUCINGTHE SCATTERING BANDWIDTH AND HENCE, THE I/OTIMES ASSOCIATED WITH THE SCATTERING SOURCEDETERMINATION IN A NEUTRONICS CALCULATION.

CO•toI

B.4 A.NIP3

C**********************************************************************-

CPREPARED 8/28/75 AT ANLLAST REVISED 09/30/83

A.NIP3NEUTRONICS MODEL INPUT FOR CODES WHICH REOUIRE CCCCINTERFACE FILES

THIS BCD DATA SET MAY BE WRITTEN EITHERIN FREE FORMAT (UNFORM-A.NIP3) OR ACCORDING TO -THE FORMATS SPECIFIED FOR EACH CARD TYPE(DATASET-A.NIP3).

COLUMNS 1-2 MUST CONTAIN THE CARD TYPENUMBER.

UNLESS OTHERWISE STATED, BLANKS ARE NOTMEANINGFUL IN A6 LABEL FIELDS.

*** CARD TYPE DIRECTORY ***

CONTENTS

PROBLEM TITLE

INPUT PROCESSING SPECIFICATIONSPROBLEM GEOMETRYEXTERNAL BOUNDARY CONDITIONSEXTERNAL BOUNDARY CONDITION CONSTANTSREGION BOUNDARIES FOR ORTHOGONAL GEOMETRIESAREA SPECIFICATIONSVARIABLE-MESH STRUCTUREINTERNAL BLACK ABSORBER CONDITIONSINTERNAL BLACK ABSORBER CONDITION CONSTANTSFINITE-GEOMETRY TRANSVERSE DISTANCESMATERIAL SPECIFICATIONSCOMPOSITION (ZONE) SPECIFICATIONSREGION/COMPOSITION CORRESPONDENCEREGION OR MESH DISTRIBUTED INHOMOGF.NEOUS SOURCESEARCH EDIT OPTIONS AND CONVERGENCE CRITERIASEARCH PARAMETER DATACONCENTRATION MODIFIERS FOR CRITICALITY SEARCHMESH MODIFIERS FOR CRITICALITY SEARCHBUCKLING MODIFIERS FOR CRITICALITY SEARCHALPHA MODIFIERS FOR CRITICALITY SEARCHHEXAGON DIMENSIONREGION DEFINITIONS FOR ARRAYS OF HEXAGONSBACKGROUND REGION FOR ARRAYS OF HEXAGONSCOMPOSITION- AND CROUP-DEPENDENT BUCKLINGSDIRECTIONAL DIFFUSION COEF. SCHEMEDIRECTIONAL DIFFUSION COEF./COMPOSITION CORRESPONDENCE

cccCFCECECCNCNCNCNCNCNCNCNCNCNCCCNCNCN

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

TYPI

0102030405060709101!1213141519212223242526293031343536

FISSION ENERGY CONVERSION FACTORSCAPTURE ENERGY CONVERSION FACTORSNUCLIDE SET ASSIGNMENTSSOURCE EDIT, SYNTHESIS TRIAL FUNCTION SOURCENATURAL DECAY INHOMOGF.NEOUS SOURCESOURCE SPECTRAGRAPHICS OUTPUT CONTROLASSIGNMENT OF REGION TO CONTROL ROD BANK

£***•***********************«******************************************-

CNCNCNCNCNCNCNCNC

3738394041424344

CRCCLCCDCDCDCDCDCCNCc—

c—CRCCLCCOCDCDCDCDCDCDCDcnCDCDCDCDCDCI)CDCDCDCDCDCD


FORMAT (I2.4X.11A6)


1-2 01

7-72 ANY ALPHANUMERIC CHARACTERS.

ANY NU..3ER OF TYPE 01 CARDS MAY BE USED.

IINPUT PROCESSING SPECIFICATION (TYPE 02)

FORMAT (I2.1OX.8I6)


1-2 02

13-18 POINTR DEBUGGING EDIT FOR GEOMETRY PROCESSING MODULE.0...NO DEBUGGING PRINTOUT (DEFAULT).1...DEBUGGING DUMP .-RINTOUT.2...DEBUGGING TRACE PRINTOUT.3...FULL DEBUGGING PRINTOUT (DUMP+TRACE).

19-24 GEOMETRY PROCESSING MODULE EDIT.0...NO EDITS (DEFAULT).1...PRINT GEOMETRY EDITS.2...WRITE GEOMETRY EDITS TO AUXILIARY OUTPUT FILE.3...GEOMETRY EDITS GO TO BOTH PRINT AND AUXILIARY

OUTPUT FILES.

OPTIONS 2 AND 3 ARE OPERATIVE ONLY FOR THOSE CODESWHICH ' "OGNIZE AUXILIARY OUTPUT FILES.

25-30 SIZE OF MAIN CORE STORAGE ARRAY FOR GEOMETRY

CD

cnenCn 31-36enCDCDCD 37-42CDCDCD 43-48CDCDCD 49-54CDCDCDcnCDCDCD 55-60CDCDCDCDCDCDCD 61-66CDCDCDCDCDCDCDCD 67-72CDCDCDCDCDCDcnCNCNCNCNCNCNC

PROCESSINC MODULE (GNIP4C) IN REAL*8 WORDS(DF.FAULT-inOOO).

RTZE OF BULK CORE STORAGE ARRAY FOR GEOMETRYPROCESSING MODULE (GNIP4C) IN REAL*8 WORDS(DEFAULT-0).

STZE OF MAIN CORE STORAGE ARRAY FOR CROSS SECTIONPROCESSING MODULES IN REAL*8 WORDS (DhfAULT - 20000). -

SIZE OF BULK CORE STORAGE ARRAY FOR CROSS SECTIONPROCESSING MODULES IN REAL*8 WORDS (DEFAULT-0).

POINTR DERUGGINo EDIT FOR CROSS SECTION PROCESSINGMODULES.0...N0 DEBUGGING PRINTOUT (DEFAULT).!.,.DEBUGGING DUMP PRINTOUT.:...DEBUGGING TRACE PRINTOUT.3...FULL DEBUGGING PRINTOUT (DUMP+TRACE).

CROSS SECTION PROCESSING EDIT.O...NO EDITS (DEFAULT).1...PRINT CROSS SECTION EDITS.2...WRITE CROSS SECTION EDITS TO AUXILIARY OUTPUT FILE.-3...CROSS SECTION EDITS GO TO BOTH PRINT AND AUXILIARY -

OUTPUT FILES.

REGION/MESH INTERVAL PRINTER-PLOTTER MAP EDIT DURINGGEOMETRY PROCESSING.O...NO MAP (DEFAULT).1...PRINT REGION MAP.2...WRITE REGION MAP TO AUXILIARY OUTPUT FILE.3...WRITE REGION MAP TO BOTH PRINT AND AUXILIARY OUTPUT-

FILES.

ZONE(COMPOSITION)/MESH INTERVAL PRINTER-PLOTTER MAPEDIT DURING GEOMETRY PROCESSING.O...NO MAP (DEFAULT).1...PRINT ZONE MAP.2...WRITE ZONE MAP TO AUXILIARY OUTPUT FILE.3...WRITE ZONE MAP TO BOTH PRINT AND AUXILIARY OUTPUT -

FILES.

EDIT OPTIONS 2 AND 3 ARE OPERATIVE ONLY FOR THOSKCODES WHICH RECOGNIZE AUXILIARY OUTPUT FILES.

THE PRINTER-PLOTTER MAP OPTIONS (COLS. 61-72) AREENTIRELY SEPARATE FROM THE GRAPHICS MAP OPTIONSIN COLS. 7-48 OF THE TYPE 43 CARD.

CMCCLCCDCDCDCDCDCDcnCDCDCDCDcncncnCDcncnCDCDCDcncncncnCDCDCDCDCDCDcnCI)cncncncncncncnCI)cncnCDcncnc.c.

PROBLEM GEOMEiKY SPECIFICATION (TYPE 03)

FORMAT (12 , IOX , 16)

COLUMNS

1-2 03

CONTENTS...IMPLICATIONS, IF ANY.

13-18 GEOMETRY TYPE.10...SLAB20...CYLINDER30...SPHERE40...X-Y44...X-Y-Z50...R-Z60...R-THETA62.,.R-THETA-Z64...THETA-R66...THETA-R-Z70...TRIANGULAR, RHOMBIC BOUNDARY, CORF. CENTER AT

60 DEGREE ANGLE (SIXTH CORE SYMMETRY).72...TRIANGULAR, RECTANGULAR BOUNDARY, HALF CORE

SYMMETRY.74...TRIANGULAR, RHOMBIC BOUNDARY, CORF. CENTER AT

120 DEGREE ANGLE (THIRn CORE SYMMETRY).76...TRIANGULAR, 60 DECREE TRIANGULAR BOUNOARY,

SIXTH CORE SYMMETRY.78...TRIANGULAR, RECTANGULAR BOUNDARY, QUARTER

CORE SYMMETRY.80...TRIANGULAR, RECTANGULAR BOUNDARY, FULL CORE.90...TRIANGULAR-Z, RHOMBIC BOUNDARY IN PLANE, CORE

CENTER LINE AT 60 DEGREE ANCLE.92...TRIANGULAR-Z, RECTANGULAR BOUNDARY IN PLANE,

HALF CORE SYMMETRY IN PLANE.94...TRIANGL'LAR-Z, RHOMBIC BOUNnARY IN PLANE, CORE

CENTER LINE AT 120 nF.fiREE ANGLE.96...TRIANGULAR-Z, 60 nEGREF. TRIANGULAR BOUNDARY

IN PLANE.98...TRIANf;IILAR-Z, RECTANGULAR BOUNDARY IN PLANE,

QUARTER CORE SYMMETRY IN PLANE.100...TRIANGUI.AR-7., RECTANGULAR BOUNnARY IN PLANE,

FULL CORE IN PLANE.110...HEXAGONAL, FULL CORE.114...HEXAGONAL, SIXTH CORF. SYMMETRY.116...HEXAGONAL, THIRn CORE SYMMETRY.120...HEXAGONAL-;,., FULL CORE IN PLANE.124...HEXAGONAL-Z, SIXTH CORE SYMMETRY IN PLANE.126... HEX AGONAL-7., THIRD CORE SYMMETRY IN PLANE.

Ito

C

c-CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCfCNCNCNCNCNCNCNCNCNCNCNCNCN

EXTERNAL BOUNDARY CONDITIONS (TYPE 04)

FORMAT (I2.10X.616)


1-2 04

13-18 BOUNDARY CONDITION AT LOWER "X" BOUNDARY OF REACTOR.

19-24 BOUNDARY CONDITION AT UPPER "X" BOUNDARY OF REACTOR.

25-30 BOUNDARY CONDITION AT LOWER "Y" BOUNDARY OF REACTOR.

31-36 BOUNDARY CONDITION AT UPPER "Y" BOUNDARY OF REACTOR.

37-42 BOUNDARY CONDITION AT LOWER Z BOUNDARY OF REACTOR.

43-48 BOUNDARY CONDITION AT UPPER Z BOUNDARY OF REACTOR.

2...PHI-0.3...PHI PRIME-0.4...D * PHI PRIME + A * PHI - 0.6...REPEATING (PERIODIC) WITH OPPOSITE FACE.7... REPEATING (PERIODIC) WITH NEXT ADJACENT BOUNDARY

(SEE DISCUSSION BELOW).8...INVERTED REPCATING ALONG THIS FACE

(180 DEGREE ROTATION).9...INCOMING ANGULAR FLUX ZERO (TRANSPORT ONLY).10..REFLECTIVE (TRANSPORT ONLY).11..PERIODIC (TRANSPORT ONLY).12..WHITE (TRANSPORT ONLY).

PHI PRIME IS THE DERIVATIVE OF THF. FLUX IN THEDIRECTION OF THE REACTOR OUTWARD NORMAL. D IS THKDIFFUSION COEFFICIENT IN THE MESH INTERVALIMMEDIATELY INSIDE THE REACTOR BOUNDARY. IF COLS.43-48 ARE 4 AND NO TYPE 05 CARD IS SUPPLIED TO SPECIFYTHE CONSTANT A, THE VALUE 0.46920 WILL BE USKD BYDEFAULT.

CONDITIONS 2-8 APPLY TO DIFFUSION THEORY PROBLEMS,AND 9-12 APPLY TO TRANSPORT THEORY PROBLEMS.

"X" REPRESENTS THF. FIRST DIMENSION COORDINATE (X INX-Y GEOMETRY, R IN R-Z, ETC.). "Y" REPRESENTS THESECOND DIMENSION COORDINATE (Y IN X-Y GEOMETRY, 7. INR-Z, ETC.). WHEN THE MODEL IS THREE-DIMENSIONAL, THETHIRD DIMENSION IS ALWAYS Z.

REPEATING CONDITIONS (6,7,8) ARE ONLY APPLICABLE TO

CNLNCNCNCNCNCNCNCNCNCNCNCNCC —

THF. FIRST TWO DIMENSIONS.

NOTE FOR REPEATING CONDITION 7. LET XL DENOTE THF.LOWER "X" BOUNDARY, XU DENOTE THE UPPER "X" BOUNDARY,YL DENOfE THE LOWER "Y" BOUNDARY AND YD DENOTE THEUPPER Y BOUNDARY. FOR REPEATING BOUNDARY CONDITIONS(CONDITION 7), THE SEQUENCE OF BOUNDARIES IMPLIED BYTHE TERM "NEXT ADJACENT BOUNDARY" IS XL, YL, XU, YU.OF THE TWO BOUNDARIES INVOLVED, THE ONE APPEARINGFIRST IN THE SEQUENCE IS ASSIGNED THE BOUNDARYCONDITION (7), THE SECOND IS IGNORED. FOR EXAMPLE,IF XL AND YL ARE THE PERIODIC BOUNDARIES, COLS. 13-18MUST CONTAIN A 7, COLS. 25-30 WILL BE IGNORED.

CRCCLCcnCDCDCDCDCDCDCDCDCDCI)CDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCN

EXTERNAL BOUNDARY CONDITION CONSTANTS (TYPE 05)

FORMAT (I2,8X,A2,E12.5,12X,2I6)


1-2

11-12

13-24

17-42

43-48

05

BOUNDARY DESIGNATOR.XI...XII..YL..YU..

"X" LOWER."X" UPPER."Y" LOWER."Y" UPPER.

u>

ZI 7. LOWER.

ZU...Z UP^ER.

VALUE OF CONSTANT A REFERRED TO ON CARD TYPE 04.

HIGHER-ENERGY GROUP NU'BF.R FOR WHICH CONSTANTS APPLY. •

LOWER-ENERGY GP" P NUMBER FOR WHICH CONSTANTS APPLY.

AS MANY TYPE 05 CARDS AS NECESSARY MAY BE 1'SED TOSPECIFY THF. EXTERNAL BOUNDARY CONDITIONS.

IF NO "HIGHER-ENERGY GROUP NUMBER" IS SUPPLIED (COLS.37-42 ARE BLANK), THF. CONSTANTS GIVEN APPLY TO ALLENERGY GROUPS. IF NO "LOWER-ENERGY GROUP NUMBER" ISSUPPLIED (COLS. 43-48 ARE BLANK), THE CONSTANTS GIVENAPPLY TO THE "HIGHER-ENERGY GROUP" ONLY. IF NO GROUPNUMBERS ARF SUPPLIED (COLS. 37-48 ARE BLANK), THF.CONSTANTS GIVEN APPLY TO ALL ENERGY GROUPS.

DATA ON THIS CARD MAY BE OVERI.AYED. THAT IS, BOUNDARYCONSTANTS DEFINED ON LATER TYPE S CARDS SUPERCEDF. DATAFOR ENERGY RANGES PREVIOUSLY SPECIFIED.

CNCNCNCNCNCNC

CRCRCCLCCDcnCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

cnCDCDCDCDCDCCNCNCMCNCNCNCNCN

"X" REPRESENTS THE FIRST DIMENSION COORDINATE (X INSECOND DIMENSION COORDINATE (Y IN X-Y GEOMETRY, Z INX-Y GEOMETRY, R IN R-Z, ETC.). "Y" REPRESENTS THER-7., ETC.). WHEN THE MODEL IS THREE-DIMENSIONAL, THETHIRD DIMENSION IS ALWAYS Z.

REGION BOUNDARY COORDINATES AND CONSTANT MESH STRUCTURE(TYPE 06)

FORMAT (I?,4X,A6,2E12.5,2I6,2E12..,')


1-2 06

7-1? REGION LABEL (REPEATED ON ADDITIONAL TYPE 06 CARDS).

13-24 "X--DIRECTION LOWER-BOUNDARY COORDINATE.

25-36 "X"-DIRECTION UPPER-BOUNDARY COORDINATE.

37-42 FOR ONE-DIMENSIONAL AND TWO-DIMENSIONAL GEOMETRIES,NUMBER OF INTERVALS IN "X"-DIRECTION.

** OR **

TOR THREE-DIMENSIONAL GEOMETRIES, LOWER 7. MESHLINE NUMBER OF THE REGION.

43-48 FOR TWO-DIMENSIONAL GEOMETRIES, NUMBER OF INTERVALSIN ^"-DIRECTION.

** OR **

FOR THREE-DIMENSIONAL GEOMETRIES, UPPER 7. MESHLINE NUMBER OF THE REGION.

49-60 "Y"-DIRECTION LOWER-BOUNDARY COORDINATE.

61-72 "Y"-DIRECTION UPPER-BOUNDARY COORDINATE.

CARP TYPE 06 IS NOT PERTINENT FOR TRIANGULAR,TRIANGULAR-Z, HEXAGONAL, OR HEXAGONAL-Z GEOMETRIES.SKF. CARD TYPE 30.

"X" REPRESENTS THE FIRST DIMENSION COORDINATE (X INX-Y GEOMETRY, R IN R-Z, ETC.). "Y" REPRESENTS THESECOND DIMENSION COORDINATE (Y IN X-Y GEOMETRY, 7. INR-7., ETC.). WHEN THE MODEL IS THPEK-DIMENSIONAL, THE

CNCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNC.

THIRD DIMENSION IS ALWAYS Z.

IN GEOMETRIES INVOLVING AN ANGULAR DIMENSION (THETA)THE ANGULAR VARIABLE MUST BE GIVEN IN RADIANS.

REGIONS MAY BE DEFINEr USING THE OVERLAY PRECEDURE,WITH THE LATEST REGION ASSIGNMENT OVERLAYING THEPREVIOUS CONFIGURATION, OR USING THE USUAL PROCEDURE,WITH EACH REGION'S BOUNDARIES GIVF.N EXPLICITLY.REGION LABELS MUST BE NON-BLANK.

THE MESH FOR A DIRECTION MUST BE COMPLETELY SPECIFIEDEITHER ON THE TYPE 06 OR 09 CARDS. IF MESH DATA ARESUPPLIED ON BOTH TYPE 06 AND 09 CARDS, THE TYPE 09DATA WILL BE USED.

FOR ONF.-DIMENF.i.NAL PROBLEMS, ONLY THE "X"-t>IRECTIONUPPER BOUNDARI , NEED BE GIVEN FOR REGIONS AFTER THEFIRST. IF THIS OPTION IS USED THE TYPE 6 CARDS MUSTBE ARRANGED SO AS TO DEFINE REGIONS SEQUENTIALLY,MOVING FROM LEFT TO RIGHT. IN OTHER WORDS THEX-DIRECTION UPPER BOUNDARIES MUST BE IN ASCENDINGORDER.

FOR THREE-DIMENSIONAL GEOMETRIES, THE DEFINITION OFTHE MESH STRUCTURE MUST BE SUPPLIED ON TYPE 09 CARDS.

THE LOWEST 7. MESH LINE NUMBER (CORRESPONDING TO THEFIRST Z BOUNDARY) OF TliE MODEL IS 0 (ZERO). THELARCEST Z MESH LINE NUMBER (CORRESPONDING TO THESECOND 7. BOUNDARY) IS EQUAL TO THE NUMBER OF Z MESHINTERVALS.

a

C —CRCCI.CCI)cnCI!CDCI)CDCOCDCDCDCI)CDCD

SPECIFICATIONS (TYPE 07)

FORMAT (I2.4X.11A6)


1-2 07

7-12 AREA LABEL (REPEATED ON ADDITIONAL TYPE 07 C*RDS).

1 )-|8 LABEL OF RF.GI <N COMPRISING AREA.

19-24 LABEL OF REGION COMPRISING AREA.

2<)-3O LABEL Or REGION COMPRISING AREA.


CDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCC —

C-CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCI)CDCDCDCDCDCDCCNCN

37-42 LABEL OF REGION COMPRISING AREA,






AREA LABELS MUST BE NON-BLANK. THE FIRST BLANK REGIONLABEL ENCOUNTERED TERMINATES READING OF THE DATA ONTHAT PARTICULAR TYPE 07 CARD. A REGION CAN BE PLACEDIN AS MANY AREAS AS THE USER DESIRES.

THE CONCEPT OF AREAS DOES NOT EXIST IN THE CCCCENVIRONMENT. ONLY CERTAIN CODES WRITTEN AT ANL MAKEUSE OF AREAS, AND IN THOSE CODES AREAS ARE USED FOREDIT PURPOSES ONLY.

VARIABLE-MESH STRUCTURE (TYPE- 09)

FORMAT (I2,9X,A1,3(I6,E12.5))


1-2 09

12 COORDINATE DIRECTION.X...-X" COORDINATE DIRECTION.Y..."Y" COORDINATE DIRECTION.Z...Z-COORDINATE DIRECTION.

13-18 NUMBER OF INTERVALS.

19-30 UPPER COORDINATE.


37-4H UPPER COORDINATE.


55-66 UPPER COORDINATE.

NOTE THAT A 7. IN COL. 12 IS PERTINENT ONLY IF THEGEOMETRY IS THREE-DIMENSIONAL.

CNCNCNCNCNCNCCNCNCNCNCNCNCNCNCNCC —

"X" REPRESENTS THK FIRST DIMENSION COORDINATE (X INX-Y GEOMETRY, R IN R-7., ETC.). "Y" REPRESENTS THESECOND DIMENSION COORDINATE (Y IN X-Y GEOMETRY, Z INR-Z, ETC.). WHEN THE MODEL IS THREE-DIMENSIONAL, THETHIRD DIMENSION IS ALWAYS Z.

IN GEOMETRIES INVOLVING AN ANGULAR DIMENSION (THETA)THE ANGULAR VARIABLE MUST BE GIVEN IN RADIANS.

EACH NUMBER PAIR IS OF THE FORM (N(I), X ( D ) . THEREARE N(I) INTERVALS BETWEEN X(I-l) AND X(I), WHERE X(0)IS THE LOWEX REACTOR BOUNDARY IN THIS DIRECTION.NUMBER PAIRS MUST BE GIVEN IN ORDER OF INCREASINGMESH COORDINATES. ALL REGION BOUNDARIES MUST COINCIDEWITH THE MESH LINES THAT BOUND MESH INTERVALS.

CCRCCLCCDcnCDCD

cnCDCD

cnCDcncnCDcncncnCOcnCI)cncncncncncnCI)cncnCD

cn

INTERNAL BLACK ABSORBER CONDITIONS (TYPE 10)

FORMAT (12 ,1 OX, 10A6 )


1-2 10

13-18 LABEL OF COMPOSITION (CCCC ZONE) WHICH IS TO BETREATED WITH INTERNAL BLACK BOUNDARY CONDITION.


25-30 LABEL OF COMPOSITION (CCCC 7.0NF.) WHICH IS TO BETREATED WITH INTERNAL BLACK BOUNDARY CONDITION.


37-42 '.ABEL OF COMPOSITION (CCCC ZONE) WHICH IS TO BETREATED WITH INTERNAL BLACK BOUNDARY CONDITION.


49-')4 LABEL OF COMPOSITION (CGCC ZONE) WHICH IS TO BETREATt-T WITH INTERNAL BLACK BOUNDARY CONDITION.

55-f>n LABEL OF COMPOSITION (CCCC ZONE) WHICH [S TO BETREATED WITH INTERNAL BLACK BOUNDARY CONDITION.

61-66 LABEL OF COMPOSITION (CCCC ZONE) WHICH IS TO BE

CO

CDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC—

C —CRCRCCLCCDCOCDcncnCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCN

TREATED WITH INTERNAL BLACK BOUNDARY CONDITION.


AS MANY TYPE 10 CARDS CAN BE USED AS ARE NECESSARY TOSPECIFY ALL OF THE DESIRED COMPOSITION (CCCC ZONE)LABELS.

EACH REGION WHICH IS COMPOSED OF ANY COMPOSITIONLISTED ON TYPE 10 CARDS WILL BE TREATED AS A BLACKABSORBER ACCORDING TO THE INTERNAL BOUNDARY CONDITIONSGIVEN ON TYPE 11 CARDS TO FOLLOW.

THE REGIONS WHICH ARE COMPRISED OF THESE COMPOSITIONSARE SPECIFIED ON TYPE 15 CARDS.

THE FIRST BLANK COMPOSITION LABEL TERMINATES READINGOF THE DATA ON THAT PARTICULAR TYPE 10 CARD.

INTERNAL BLACK ABSORBER CONDITION CONSTANTS(TYPE 11)

FORMAT (I2,1OX,2E12.5,24X,2I6)


1-2 11

13-24 THE CONSTANT A, DEFINED BELOW.

25-36 THE CONSTANT B, DEFINED BELOW.

61-66 HIGHER-ENERGY GROUP NUMBER FOR WHICH CONSTANTS APPLY. -

67-72 LOWER-ENERGY GROUP NUMBER FOR WHICH CONSTANTS APPLY.

THE INTERNAL BLACK BOUNDARY CONDITION IS SPECIFIED AS -

A*PHI PRIME + B/D*PHI - 0.

IF NO "HIGHER-ENERGY GROUP NUMBER" IS SUPPLIED (COLS. -61-66 ARE BLANK), THE CONSTANTS GIVEN APPLY TO ALLENERGY GROUPS. IF NO "LOWER-ENERGY GROUP NUMBER" ISSUPPLIED (COLS. 67-72 ARE BLANK), THE CONSTANTS GIVEN -APPLY TO THE "HIGHER-ENERGY GROUP" ONLY. IF NO GROUPNUMBERS ARE SUPPLIED (COLS. 61-72 ARE BLANK), THECONSTANTS GIVEN APPLY TO ALL ENERGY CROUPS.

DATA ON THIS CARD MAY BE OVERLAYED. THAT IS, CONSTANTS -

CNCNCNCNCNCNCC-

C-CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNON

DEFINED ON LATER TYPE 11 CARDS SUPERCF.DE DATA FORENERGY RANGES PREVIOUSLY SPECIFIED.

ANY GROUP FOR WHICH NO INTERNAL BLACK ABSORBERCONDITION CONSTANTS ARE SPECIFIED ON TYPE 11 CARDSWILL BE TREATED AS BEING NON-BLACK.

FINITE-GEOMETRY TRANVERSE DISTANCES (TYPE 12)

FORMAT (I2,4X,A6,4E12.5)

COLUMNS CONTENTS..,IMPLICATIONS, IF ANY

1-2 12

7-12 REGION OR AREA LABEL.

13-24 ACTUAL TRANSVERSE HALF-HEIGHT OR RADIUS.

25-36 TRANSVERSE EXTRAPOLATION DISTANCE.

37-48 ACTUAL TRANSVERSE HALF-HEIGHT IN THE SECOND DIRECTION -FOR A FINITE ONE-DIMENSIONAL RECTANGULAR SLAB.

49-60 TRANSVERSE EXTRAPOLATION DISTANCE IN THE SECONDDIRECTION FOR A FINITE ONE-DIMENSIONAL RECTANGULARSLAB.

THE DATA ON THE TYPE 12 CARDS ARE USED TO CALCULATEREGION VOLUMES AND, IN THE ABSENCE OF TYPE 34 CARDS,BUCKLINGS. REGION VOLUMES ARE CALCULATED USINGACTUAL HALF-HEIGHTS (EXCLUDING THE EXTRAPOLATIONDISTANCE).

AN AREA LABEL IN COLS. 7-12 IMPLIES ALL THE REGIONSASSIGNED TO THAT AREA.

THE REGION-DEPENDENT DATA THAT IS PROVIDED ON THISCARD IS CONVERTED BY THE GNIP4C INPUT PROCESSOR TOCOMPOSITION-DEPENDENT DATA. THIS IS A POTENTIALPROBLEM FOR USERS IF THKY HAVE ASSIGNED ONECOMPOSITION TO TWO OR MORE REGIONS WITH DIFFERENTHALF HEIGHTS.

IF THERE IS NO REGION LABEL (COLS.7-12 ARE BLANK), THE -DATA ON THE CARD APPLY TO ALL REGIONS OF THE REACTOR. -IF THERE IS NO REGION LABEL AND IF THERE ARE NO TYPE 34-CARD (COMPOSITION AND GROUP DEPENDENT BUCKLINGSPECIFICATIONS), THE DATA ON THIS CARD WILL BE USED TO -CALCULATE A SPACE- AND ENERGY-INDEPENDENT BUCKLING AND -

Cv

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC —

CCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCN

TO CALCULATE REGION VOLUMES. IN THIS MODE OF INPUTONLY ONE TYPE 12 CARD SHOULD BE SUPPLIED.

IF MORE THAN ONE TYPE 12 CARD IS PRESENT (EACH CARDWITH A VALID REGION OR AREA LABEL IN COLS. 7-12), THEDATA ON THE CARDS WILL BE USED TO CALCULATE REGIONVOLUMES.

DATA ON THIS CARD MAY BE OVERLAYED. THAT IS,TRANSVERSE DISTANCES DEFINED ON LATER TYPE 12CARDS SUPERCEDE DATA FOR REGIONS PREVIOUSLYSPECIFIF.D.

IF TYPE 34 CARDS ARE PRESENT, BUCKLINGS WILL BE TAKENFROM TYPE 34 CARDS AND WILL NOT BE CALCULATED FROMTYPE 12 CARD DATA. EVEN IF BUCKLINGS ARE TAKEN FROMTYPE 34 CARDS, REGION VOLUMES ARE CALCULATED USINGTYPE 12 CARD DATA WHEN TYPE 12 CARDS ARE PRESENT.

IN THE ABSENCE OF TYPE 12 AND TYPE 34 CARDS NOBUCKLINGS WILL BE USED AND REGION VOLUMES WILL BECALCULATED USING UNIT TRANSVERSE HEIGHTS.

MATERIAL SPECIFICATIONS (TYPE !3)

FORMAT (I2,1OX,A6,3(A6,E12.5))


1-2 13

13-18 MATERIAL LABEL (REPEATED ON ADDITIONAL TYPE 13 CARDS).

19-24 UNIQUE ISOTOPE LABEL.

25-36 ISOTOPE ATOM DENSITY (ATOMS/CC * 1.F.-24).

37-42 UNIQUE ISOTOPE LABEL.

43-54 ISOTOPE ATOM DENSITY (ATOMS/CC * l.E-24).

55-60 IINIOUE ISOTOPE LABEL.

61-72 ISOTOPE ATOM DENSITY (ATOMS/CC * l.E-24).

MATERIAL LABELS MUST BE NON-BLANK.

MATERIALS CAN BE DEFINED ON A TYPE 13 CARD IN TERMSOF ISOTOPES AND/OR IN TERMS OF OTHER MATERIALS. IN THELATTER CASE THE "ISOTOPE LABF.L" IS A MATERIAL LABEL

CNCNCNCNCNCNCC —

CCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

AND THF. "ISOTOPE ATOM DENSITY" IS A VOLUME FRACTION.

THE CONCEPT OF MATERIALS DOES NOT EXIST IN THF. CCCCENVIRONMENT, AND THE IDENTITY OF INDIVIDUAL MATERIALSIS LOST WHEN THE CCCC FILES ARE CREATED. TYPE 13CARDS ARE PROVIDED AS AN INPUT CONVENIENCE ONLY.

COMPOSITION SPECIFICATIONS (TYPE 14)

FORMAT (I2,1OX,A6,3(A6,E12.5))


1-2 14

13-18 COMPOSITION LABEL (REPEATED ON ADDITIONAL TYPE 14CARDS).

19-24 MATERIAL LABEL.

25-36 MATERIAL VOLUME FRACTION.





COMPOSITION LABELS MUST BE NON-BLANK.

WHEN A "MATERIAL LABEL" HAS NOT BEEN SPECIFIED(COLS.13-18 OF A TYPE 13 OR TYPE 14 CARD), THE"MATERIAL" WILL BE INTERPRETED AS AN ISOTOPE ANDTHE 'VOLUME FRACTION" WILL BE INTERPRETED AS AN ATOMDENSITY.

WHEN AN ISOTOPE (OR MATERIAL) IS REFERENCED MORE THANONCE FOR A SINGLE COMPOSITION, THE ATOM DENSITIES(OR VOLUME FRACTIONS) ARE SUMMED.

TWO TYPE: OF COMPOSITIONS (PRIMARY AND SECONDARY) CANBE DEFINED ON TYPE 14 CARDS. SECONDARY COMPOSITIONSARE MIXTURES OF MATERIALS AND/OR ISOTOPES. PRIMARYCOMPOSITIONS ARE MIXTURES OF SECONDARY COMPOSITIONS,MATERIALS AND/OR ISOTOPES. ONLY PRIMARY COMPOSITIONSMAY BE ASSIGNED TO REGIONS ON THE TYPE 15 CARDS.

SECONDARY tPOSITIONS ARE TREATED AS CCCC SUBZONES.

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

C

C —

THOSE CONSTITUENTS OF A PRIMARY COMPOSITION WHICH ARENOT THEMSELVES SUBZONES (I.E. ISOTOPES AND MATERIALSDIRECTLY ASSIGNED TO PRIMARY COMPOSITIONS) ARECOMBINED INTO CCCC PRIMARY ZONE ASSIGNMENTS.

AN EXAMPLE OF A SET OF TYPE 13 AND 14 CARDS

C-

CR

CR

C

CL

C

CD

CD

CD

CD

CD

CD

CD

CD

CI)CDCDCDCD

13131313141414141414

FUELl

FUEL2

SSCOOL

MIXl

MIX2

C0MP1

COMP2

C0MP3

C0MP3

U238

U238

FENA23

FUELl

FUELl

HIX1

MIXl

COOL

.020

.015

.055

.022

1.00.50.40.40.20.2

PU239

PU239

CRSS

FUEL2

SSSSMIX2

.003

.004

.015

0.1

0.50.20.20.2

016016NI

COOL

COOL

SS

.042

.042

.012

0.40.40.2

14 C0MP4 NA23 .022

THE MATERIAL COOL IS DEFINED IN TERMS OF AN

ISOTOPE (NA23) AND A MATERIAL (SS).

MIXl AND MIX2 ARE SECONDARY COMPOSITIONS.

C0MP1, C0MP2, COMP3 AND C0MP4 ARE PRIMARY

COMPOSITIONS.

IN THE CCCC FILES MIXl WILL BE ASSIGNED AS

SUBZONES TO BOTH COMP1 AND COMP3. THE PRIMARY

ZONE ASSIGNMENTS OF C0MP1, COMP2 AND C0MP3

WILL CONSIST OF SS AND COOL. C0MP4 WILL HAVE

NO SUBZONES.

ASSIGNMENT OF REGION TO COMPOSITION (CCCC ZONE)

(TYPE 15)

FORMAT (12 ,4X, 11A6)


1-2 15

7-12 COMPOSITION (CCCC ZONE) LABEL (REPEATED ON ADDITIONALTYPE 15 CARDS).

13-18 REGION LABEL OR AREA LABEL DEFINING REGION(S)

CONTAINING SPECIFIED COMPOSITION.

19-24 REGION LABEL OR AREA LABEL DEFINING RF.CION(S)


CDCDCDCDCDCDCDCDCDCDCDCDCDCD '

CDCDCDCDCDCDCDCDCDCCNCNCNCNCNCN

CMCNCNCNCNCNCNCNCN

CNCNCNCNCNCNCNCNCNC

2S-3O

31-36

37-42

43-48

49-54

55-60

61-66

67-72

RECION LABEL OR AREA LABEL DEFINING RECION(S)CONTAINING SPECIFIED COMPOSITION.

REGION LABEL OR AREA LABEi, DEFINING PEGION(S)


RECION LABEL OR AREA LABEL DEFINING REGION(S)


REGION LABEL OR AREA LABEL DEFINING REGION(S)










AN AREA LABEL IN COLS. 13-72 IMPLIES ALL THE REGIONS

ASSIGNED TO THAT AREA. AREAS ARE DEFINED ON THE

TYPE 07 CARD.

WHEN A PARTICULAR REGION OR AREA IS REFERENCED ON

MORE THAN ONE TYPE 15 CARD, THE LAST REFERENCE

TO THAT REGION (EITHER DIRECTLY, OR THROUGH AN AREA)

ESTABLISHES THE COMPOSITION ASSIGNMENT.

I.E. A REGION/COMPOSITION CORRESPONDENSE ESTABLISHED

ON ONE TYPE 15 CARD CAN BE OVERWRITTEN BY A

REFERENCE ON A LATER TYPE 15 CARD.

COMPOSITION LABELS MUST BE NON-BLANK. THE FIRST

BLANK REGION LABEL ENCOUNTERED TERMINATES READING

OF THE DATA ON THAT PARTICULAR TYPE 15 CARD.

ONLY PRIMARY COMPOSITION LABELS (SEE CARD TYPE i4)

CAN APPEAR IN COLS. 7-12. FRIMARY COMPOSITIONS ARE

EQUIVALENT TO CCCC ZONES. A REGION CAN CONTAIN ONLY

ONE PRIMARY COMPOSITION.

WHEN THERE ARE NO TYPE 14 CARDS (THE MACROSCOPIC

CROSS SECTIONS ALREADY EXIST) THE COMPOSITION

I.ABEL FIELDS SHOULD CONTAIN COMPOSITION NUMBERS

INSTEAD (I2,4X,I6,10A6).

Cβ

09

CRCR

C

CL

C

C

cnCO

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

C

CD

CD

CD

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

C

CN

CN

CN

DISTRIBUTED ISOTROPIC INHOMOGF.NEOUS SOURCE DATA DEFINEDEITHER BY REGION OR MESH INTERVAL (TYPE 19)

FORMAT (12,4X A6.2I6,4E12.5)

COLUMNS

1-2


19

7-12 LABEL OF REGION OR AREA (BLANK IF DATA ARE GIVEN BY

MESH INTERVALS). IF THE GEOMETRY HAS BEEN SPECIFIED

BY AN INPUT GEODST FILE (AND NOT BY A.NIP TYPE 06

OR 30 CARDS) USE THE REGION NUMBER (16) INSTEAD OF

THE REGION LABEL.

13-18 HIGHER-ENERGY GROUP NUMBER.

19-24 LOWER-ENERGY GROUP NUMBER.

25-36 ISOTROPIC SOURCE VALUE IN THE SPECIFIED MESH INTERVAL,

REGION OR AREA FOR THIS ENERGY RANGE. (NEUTRONS PER

SECOND PER UNIT VOLUME).

37-48 LOWER "X" DIRECTION COORDINATE OF MESH INTERVAL

CONTAINING THIS SOURCE.

49-60 LOWER "Y" DIRECTION COORDINATE OF MESH INTERVAL


61-72 LOWER Z DIRECTION COORDINATE OF MESH INTERVAL


AN AREA LABEL IN COLS. 7-12 IMPLIES ALL THE REGIONS

ASSIGNED TO THAT AREA.

It THERE IS NO REGION LABEL (COLS. 7-12 ARE BLANK),

THE SOURCE SPECIFIED IN COLS. 25-36 IS PLACED IN THE

MF.SH BOX DEFINED BY COLS. 37-48, 49-60 AND 61-72.

IF THERE IS A REGION LABEL (COLS. 7-12 ARE NON-BLANK),

THE MESH COORDINATE FIELDS (COLS. 37-48, 49-60 AND

61-72) ARE IGNORED AND THE SOURCE SPECIFIED IN COLS.

25-36 IS PLACED IN EVERY MESH BOX IN THF. REGION.

"X" REPRESENTS THE FIRST DIMENSION COORDINATE (X IN

X-Y GEOMETRY, R IN R-Z, ETC.). "Y" REPRESENTS THE

SECOND DIMENSION COORDINATE (Y IN X-Y GEOMETRY, 7. IN

R-Z, ETC.). WHEN THE MODEL IS THREE-DIMENSIONAL, THE

THIRD DIMENSION IS ALWAYS Z.

IN GEOMETRIES INVOLVING AN ANGULAR DIMENSION (THF.TA)

THE ANGULAR VARIABLE MUST BE GIVEN IN RADIANS.

CN

CN

CN

CN

CN

CN

CN

CN

CN

CH

CN

CN

CN

CN

C

CR

C

CL

C

CD

CD

CP

CD

CD

CD

CD

CD

CD

CD

CI)

CD

CD

CD

CD

cnCD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

cnCD

CD

CD

IF NO "HICHrR-ENF.RGY GROUP NUMBER" IS SUPPLIED (COLS.

13-18 ARE BLANK), THE SOURCE VALUE GIVEN APPLIES TO

ALL ENERGY GROUPS. IF NO "LOWER-ENERGY GROUP NUMBER"

IS SUPPLIED (COLS. 19-24 ARE BLANK), THE SOURCE VALUE

GIVEN APPLIES TO THE "HIGHER-ENERGY GROUP" ONLY. IF

NO GROUP NUMBERS ARE SUPPLIED (COLS. 13-24 ARE BLANK),

THE SOURCE VALUE GIVEN APPLIES TO ALL ENERGY GROUPS.

DATA ON THIS CARD MAY BE OVERLAYEn. THAT IS, SOURCE

VALUES DEFINED ON LATER TYPE 19 CARDS SUPERCEDE DATA

FOR REGIONS AND GROUPS PREVIOUSLY SPECIFIED.

AN EDIT OF THE OUTPUT FIXSRC FILE MAY BE OBTAINED BY

SUPPLYING THF. EDIT SENTINEL ON THE TYPE 40 CARD.

SEARCH EDIT OPTIONS AND CONVERGENCE CRITERIA (TYPE 21)

FORMAT (I2,10X,2I6,2E12.5,2I6)


1-2 21

13-18 SEARCH FILE PROCESSING EDIT SENTINEL

0, NO EDITS (DEFAULT).1, PRINT EDITS.

2, WRITE EDITS TO AUXILIARY OUTPUT FILE.

3, WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT

FILE.

19-24 MAXIMUM NUMBER OF SEARCH PASSES (DEFAULT-4).

25-36 DESIRED KEFF, KEFF(O) (DEFAULT-1.0).

37-4R CONVERGENCE CRITERION, EPSILON: RELATIVE ERROR BOUND

FOR KEFF (0EFAULT-.01).

ABSOLUTE VALUE OF ((KEFF-KF.FF(O)) / KEFF(O)) .LF..

EPSILON.

49-54 SEARCH (MODULE) PARAMETER EDIT OPTIONS

ENTER TWO-DIGIT NUMBER (IF) WHERE

I CONTROLS INTERMEDIATE PASS PARAMETER EDITS

F CONTROLS FINAL SEARCH PASS PARAMETER EDITS

THK INTEGERS I AND F ARE ASSIGNED ONE OF THE

FOLLOWING VALUES (LEADING ZEROES ARE IRRELEVANT)

0...N0 EDITS

1...PRINT EDITS (DEFAULT FOR F)

Cβ

VO

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCCNCNCC —

55-60

f* • .

CRCCLCcnCDCDCDCDCDCDCDCDCDCDCDCDCDCNCNCCNCNCNCN

2...WRITE EDITS TO AUXILIARY OUTPUT FILE

3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

SEARCH (MODULE) OUANTITY EDIT OPTIONS

ENTER TWO-DIGIT NUMBER (IF) WHERE

I CONTROLS INTERMEDIATE PASS QUANTITY EDITSF CONTROLS FINAL SEARCH PASS QUANTITY EDITS

THE INTEGERS I AND F ARE ASSIGNED ONE OF THEFOLLOWING VALUES (LEADING ZEROES ARE IRRELEVANT)O...NO EDITS (DEFAULT)1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE

3...WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT FILE-

EACH SEARCH PASS REQUIRES THE SUCCESSFUL COMPLETION

OF AN EIGENVALUE PROBLEM BY A NEUTRONICS MODULE.

SUCCESSFUL NEUTRONICS MODULE COMPLETION IS INDICATED BY-1. OUTER ITERATIONS CONVERGED OR2. MAXIMUM NUMBER OF OUTER ITERATIONS ATTAINED.

NONZERO DATA ON THIS CARD OVERRIDES DATA IN AN EXISTING-SF.ARCH FILE DURING A SF.ARCH PROBLEM RESTART.

SEARCH PARAMETER DATA (TYPE 22)

FORMAT (I2.1OX.5E12.5)


1-2 22 — — — — — — —

13-24 INITIAL ESTIMATF. OF X (DEFAULT-0.0) .

25-36 SECOND ESTIMATE OF X (IGNORED IF COLS, ftl-72 ARF.

NON-ZERO) (DF.FAULT-0.1 (X-0.0) , -1.1*X (X NE 0.(0)

37-48 LOWER BOUND FOR X (DEFAULT-O.O).

49-60 UPPER BOUND FOR X (DEFAULT-1.0).

61-72 DERIVATIVE OF KEFF WITH RESPECT TO X (OPTIONAL).

(PROVIDES AN ALTERNATE METHOD FOR OBTAiNING SECONDESTIMATE OF X IN COLS. 25-36).COLS. 25-36 ARE IGNORED IF COLS. 61-72 CONTAIN OTHERTHAN BLANK OR 0.0.

GENERAL SEARCH EXPRESSION: P(X) - P(0) + X * M,

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC

CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

WHFRE P IS THE QUANTITY BEING VARIED, X IS THE SEAR'.H -PARAMETER, AND M IS THE QUANTITY MODIFIER OBTAINEDFROM INFORMATION CONTAINED ON ONE OF THE MUTUALLYEXCLUSIVE CARD TYPES 23, 24, 25, OR 26. X IS TO BEVAR.'KD UNTIL THE DESIRED KEFF IS REACHED. THE SEARCH -WILL BE TERMINATED IF X EXCEEDS ITS BOUNDS OR IF THEMAXIMUM NUMBER OF SEARCH PASSES ARE REACHED.(SOME CODES MAY ALSO TRIGGER JOB TERMINATION BETWEENSEARCH PASSES IF IT IS ESTIMATED THAT .'OB TIME LIMITWOULD BE EXCEEDED DURING THE NEXT SEARCH PASS).

FOR EFFICIENT SEARCHING, SCALE THE SEARCH OUANTITYSUCH THAT THE MAGNITUDES OF THE SEARCH PARAMETERESTIMATES LIE IN THE INTERVAL (.1,10.)

NONZERO DATA ON THIS CARD OVERRIDES DATA IN AN EXISTING-SEARCH FILE DURING A SEARCH PROBLEM RESTART.

CONCENTRATION MODIFIERS FOR CRITICALITY SEARCH (TYPE 23)

FORMAT (I2.4X.11A6)


1-2 23

7-12 COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO BE USED AS THE MODIFIER M IN THE SEARCH FORMULA.

13-18 COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER M IS ADDED AS A SUBZONE.




37-42 COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER M IS ADDED AS A SUBZONF.

43-48 COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPF 14)TO WHICH MODIFIER M IS ADDED AS A SUBZONE.

49-54 COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER H IS ADDED AS A SUBZONE.

Cβ

CDCOCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC

55-60

61-66

67-72

COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER M IS AODED AS A SUBZONE.

COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER M IS ADDED AS A SUBZONE.

COMPOSITION LABEL OF COMPOSITION (FROM CARD TYPE 14)TO WHICH MODIFIER M IS ADDED AS A SUBZONE.

IN THE SEARCH FORMULA P(X) » P(0) + X * M,P(0) DENOTES THOSE PRIMARY COMPOSITIONS (ZONES,COLS. 13-72) TO WHICH THE MODIFIER COMPOSITIONS (M,COLS. 7-12) ARE ADDED AS SUBZONES,X IS THE VOLUME FRACTION APPLIED TO THE MODIFIERCOMPOSITIONS (CCCC ZONES OR SUBZONES) COMPRISING M,AND P(X) DENOTES THE RESULTANT COMPOSITIONS.CARD TYPE 23 DEFINES P(0) AND M IN TERMS OF COMPOSITION-LABELS DEFINED ON CARD TYPE 14.

THE MODIFIER COMPOSITION (CCCC ZONE OR SUBZONE) NAMEIN COLS. 7-12 MUST BE A SUBZONE OR AN UNASSIGNED (NOT -ASSIGNED TO A REGION ON A TYPE 15 CARD) PRIMARY ZONECONTAINING NO SUBZONES.

THE MODIFIER COMPOSITIONS (M) BECOME SUBZONES OFEACH ZONE SPECIFIED IN COLS. 13-72. WHEN A SUBZONE IS -SPECIFIED IN COLS 13-72, THE MODIFIER COMPOSITIONS (M) -BECOME SUBZONES IN EACH ZONE CONTAINING THE Sl'^ZONEIN COLS. 13-72. IN BOTH CASES THE VOLUME FRACTIONOF THE ADDED SUBZONES IS X.

A MODIFIER COMPOSITION (M) CANNOT MODIFY ANOTHERMODIFIER COMPOSITION OR A COMPOSITION WHICH ALREADYCONTAINS THE MODIFIER COMPOSITION AS A ZONE OR SUBZONE.-

AN EXAMPLE OF A SET OF TYPE 23 CARDS USING THE SAMPLE -TYPE 14 CARDS PRESENTED IN THE TYPE 14 CARD DESCRIPTION-FOLLOWS:

23 COMP4 COMP1 MIX223 MIX1 COMP2 ,

tIN THE CCCC FilLES COMP4 WILL BECOME A SUBZONEOF COMP1, COMP2 AND COMP3. MIX1 WILL BECOMEA SUBZONE OF COMP2.

REPEAT TYPF. 23 CARDS AS NEEDED.

C —ORC

MESH MODIFIERS FOR CRITICALITY SEARCH (TYPE 24)

CI.CcnencncncnCDCDcncncnCDcncncncncCNCNCNCNCNCNCNCNCNCNCC —

CRCRCCLCcncncncncncncnccncncCNCNCNCNCN

FORMAT (I2.9X.A1 ,3F.!2.5)


1-2

12

13-24

25-36

37-48

24

COORDINATE DIRECTION.X..."X" COORDINATE DIRECTION.Y..."Y" COORDINATE DIRECTION.Z..."Z" COORDINATE DIRECTION.

LOWER (COARSE MESH) COORDINATE.

UPPER (COARSE MESH) COORDINATE.

MESH MODIFIER, M, FOR EACH MESH INTERVAL BETWEENTHE ABOVE COORDINATES.

IN THE SEARCH FORMULA P(X) - P(0) + X * M,P(X) IS THE RESULTING MESH INTERVAL,P(0) IS THE INITIAL MESH INTERVAL, ANDM IS THE MESH INTERVAL MODIFIER.

DATA ON THIS CARD MAY BE OVERLAYED. THAT IS MESHMODIFIERS DEFINED ON LATER TYPE 24 CARDS SUPERCEDEDATA FOR REGIONS SPECIFIED PREVIOUSLY.

REPEAT TYPE 24 CARDS AS NEEDED.

W

COMPOSITION DEPENDENT BUCKLING MODIFIERS FOR CRITICALITYSEARCH (TYPE 25)

FORMAT (12 , 4X, A6 , F. 1 2 .5 )


1-2 25

7-12 COMPOSITION (ZONE) LABEL.

13-24 BUCKLING MODIFIER, M, IN FIRST TRANSVERSE DIRECTION.

25-36 BUCKLING MODIFIER, M, IN SECOND TRANSVERSFVniRF.CTIONFOR A FINITE ONK-DIMENSIONAL RECTANGULAR SLAB.

IN THE SEARCH FORMULA P(X) - P(O) + X * M,P(X) IS THF RESULTING BUCKLING, P(0) IS THE INITIALBUCKLING. AND M IS THE BUCKLING MODIFIER.P(O) WTI.I. BE EVALUATED FROM THE TRANSVERSE HEIGHTSCIVKN ON CARD TYPF. 12 OR TAKEN DIRECTLY FROM BUCKLINGS

CNONCNCNCNCNC

C-CRCCLCCDCDCDCDcnCDCCNCNCNCC —

GIVEN ON CARD TYPE 34.

IF COLS. 7-12 ARE BLANK, THE DATA IN COLS. 13-24 APPLYTO ALL COMPOSITIONS (ZONES) OF THE REACTOR.

REPEAT TYPE 25 CARDS AS NEEDED.

ALPHA MODIFIER FOR CRITICALITY SEARCH (TYPE 26)

FORMAT (I2.1OX.EI2.5)


1-2 26

13-24 ALPHA MODIFIER, M.

IN THE SEARCH FORMULA P(X) - P(O) + X * M,P(X) IS THE RESULTING ALPHA, P(O) IS THE INITIAL ALPHA,AND M IS THE ALPHA MODIFIER.

CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCN

HEXAGON DIMENSION (TYPE 29)

FORMAT (12,1OX,El 2.5,216)


1-2 29

13-24 DIMENSION OF HEXAGON ACROSS FLATS.

25-30 TOTAL NUMBER OF HEXAGONAL RINGS IN THE REGION OFSOLUTION.

31-36 FOR TRIANGULAR AND TRIANGULAR-7. GEOMETRIES, THENUMBER OF EOUAL PARTS INTO WHICH EACH SIDE OF THEBASIC EQUILATERAL TRIANGLES MAKING UP THE HEXAGONS ARESUBDIVIDED. THUS E.G., IF COLS 31-36 CONTAIN 3, THEHEXAGON CONTAINS 54 MESH POINTS INSTEAD OF THE NORMAL6.

IF THE NUMBER OF RINGS IS NOT PROVIDED IN COLS. 25-30,IT IS DERIVED FROM THE TYPE 30 CARDS.

IF COLS. 31-36 ARE BLANK, THE TRIANGLES ARE NOT

CNCNCNCNCNCNCNCC ~

CRCRCCLCcnCDCDcnCDcnCDcncncnCDcnCDcnencncCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

SUBDIVIDED.

THE TYPE 29 CARD IS PERTINENT ONLY IF COLS. 13-18 ONCARD TYPE 03 ARE GREATER THAN OR EQUAL TO 70.

FOR TRIANGULAR-7. AND HFXACONAL-7. GEOMETRIES THKAXIAL (Z) MESH MUST BE SPECIFIED ON TYPE 9 CARDS.

LOCATIONS OF REGIONS FOR TRIANGULAR, TRIANGULAR-7.,HEXAGONAL, AND HEXAGONAL-7, CEOMETRIES (TYPE 30)

FORMAT (I2,4X,A6,3I6,2E12.5)


1-2 30

7-12 REGION LABEL (REPEATED ON ADDITIONAL TYPE 30 CARDS).

13-18 HEXAGONAL RING NUMBER WHERE REGION IS LOCATED.

19-24 STARTING HEXAGON POSITION FOR THIS REGION.

25-30 FINAL HEXAGON POSITION FOR THIS REGION.

31-42 LOWER Z BOUNDARY OF REGION.

43-54 UPPER Z BOUNDARY OF REGION.

REGION LABELS MUST BE NON-BLANK.

IF THE STARTING POSITION (COLS. 19-24) IS BLANK ORZERO, THE REGION LABEL IS ASSIGNED TO THE WHOLE RING.

IF THE FINAL POSITION (COLS. 25-30) IS BLANK OR ZERO,THE REGION LABEL IS ASSIGNED TO THE POSITION IN 19-24OF THE RING IN 13-1fi.

DATA ON THIS CARD MAY BE 0VER1.AYED. THAT IS, REGIONASSIGNMENTS DEFINED ON LATER TYPE 30 CARDS SUPERCEDEDATA FOR RINGS AND POSITIONS PREVIOUSLY SPECIFIED.

THE KKGIO.v LOWER AND UPPER 7. BOUNDARIES MUST COINCIDEWITh MESH LINES, WHICH BOUND MESH INTERVALS.

THE FIGURE BELOW ILLUSTRATES THE ORDER OF NAMINGRINGS AND HEXAGONS IN THE RINGS. THE FIRST NUMBER OFEACH NUMBERED PAIR IS THE RING NUMBER, AND THE SECONDNUMBER IS THE HEXAGON NUMBER IN THAT RING.

CNCNCNCNCNCNCNCNCNCNCNCN

. CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC —

THE REGION OF SOLUTION DEPENDS ON THE VALUE IN COLS.13-18 ON CARD TYPE 03 AS FOLLOWS.

C —CRCRCCL

COLS. 13-18 ON CARD TYPE 03 REGION OF SOLUTION

8072787074110114116

ENTIRE FIGURE AS SHOWN BF.LOWIN THE 180 DEGREE SECTOR A-BIN THE 90 DEGREE SECTOR A-CIN THE 60 DEGREE SECTOR A-DIN THE 120 DEGREE SECTOR A-EENTIRE FIGURE AS SHOWN BELOWIN THE 60 DEGREE SECTOR F-CIN THE 120 DEGREE SECTOR F-G

D -

-3,5 - -3,4 - -3,3

-3,6 -2,3 - -2,2 - -3,2

-3.7 - -2,4 - -1,1 - -2,1 - -3,1 - * * * F -

-3,8 - -2,5 - -2,6 - -3,12-

-3,9 - -3,10- -3,11-

A -

ALTHOUGH THE RECIONS OF SOLUTION DIFFER FOR THETRIANGULAR AND HEXAGONAL GEOMETRY MODELS, TYPE 10CARDS COMPOSED FOR TRIANGULAR GEOMETRY MODELS CAN ALSOBE USED FOR HF.XAGONAI. GEOMETRY MODELS.

BACKGROUND REGION NAME FOR TRIANGULAR, TRIANGULAR-Z,HEXAGONAL, AND HEXAGONAL-Z GEOMETRIES (TYPE 31)

FORMAT (I2.4X.A6)

CCDCDCDCDCDCCNCNCNCNCNCNCNCNCNC

c—CRCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCN


1-2 '31

7-12 BACKGROUND REGION NAME.

ANY PORTION OF THE REACTOR NOT SPECIFIED ON THETYPE 30 CARDS WILL BE IN THE BACKGROUND REGION.

IF THE BACKGROUND REGION NAME (COLS. 7-12) IS BLANK,OR IF THERE IS NO TYPE 31 CARD, THE BACKGROUND REGIONWILL BE ASSIGNED A REGION NUMBER 0 (ZERO). NOTE THATSOME CCCC CODES EXCLUDE SUCH A REGION FROM THE REGIONOF SOLUTION, WHILE OTHER CCCC CODES MAY NOT ALLOWZERO REGION NUMBERS.

COMPOSITION AND GROUP DEPENDENT BUCKLING SPECIFICATIONS(TYPE 34)

FORMAT (I2,4X,A6,2(E12.5,2I6))

COLUMNS .CONTENTS...IMPLICATIONS, IF ANY

1-2 34

7-i2 COMPOSITION LABEL.

H-24 BUCKLING (B**2).

25-30 HIGHER ENERGY BROAD GROUP NUMBER TO WHICH BUCKLINCIN COLS. 13-24 APPLIES.

31-36 LOWER ENERGY BROAD GROUP NUMBER TO WHICH BUCKLINGIN COLS. 13-24 APPLIES.

37-48 BUCKLING (B**2).

49-54 HIGHER ENERGY BROAD GROUP NUMBER TO WHICH BUCKLINGIN COLS. 37-48 APPLIES.

55-60 LOWER ENERGY BROAD GROUP NUMBER TO WHICH BUCKLINGIN COLS. 37-48 APPLIES.

IF THERE IS NO COMPOSITION LABEL (COLS. 7-12 AREBLANK), THE BUCKI.INGS ON THIS CARD WILL APPLY TOALL COMPOSITIONS.

IF NO "HIGHER-ENERGY GROUP NUMBER" IS SUPPLIED INCOLS. 25-30, THE BUCKLING GIVFN IN COLS. 13-24 APPLIES

CDCDCDC!>CDCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCMCNCNCNCNCNCNCNCNCNCC —

C —CRCCLCCDCDCDCDCDCDCDCDCDCDCD

TO ALL ENERGY CROUPS. IF THERE IS A "HICHER-ENERGYGROUP NUMBER" IN COLS. 25-30, BUT NO "LOWER-ENERGYGROUP NUMBER" IS SUPPLIED IN COLS. 31-36, THE BUCKLINC -GIVEN IN COLS. 13-24 APPLIES TO THE "HICHER-ENERCYGROUP" ONLY.

IF NO "HIGHER-ENERGY GROUP NUMBER" IS SUPPLIED INCOLS. 49-54, THE DATA IN COLS. 37-60 ARE IGNORED. IFTHERE IS A "HIGHER-ENERGY GROUP NUMBER" IN COLS. 49-54,-BUT NO "LOWER-ENERGY CROUP NUMBER" IN COLS. 55-60,THE BUCKLING GIVEN IN COLS. 37-48 APPLIES TO THE"HIGHER-ENERGY GROUP" ONLY.

BUCKLINGS CAN BE OVERLAYED THAT IS, BUCKLINGS DEFINED -ON LATER TYPE 34 CARDS SUPERCEDE DATA FOR COMPOSITIONS -AND/OR ENERGY RANGES PREVIOUSLY DEFINED. THE EXCEPTION -TO THIS RULE IS THE SITUATION DESCRIBED IN THE PRE-CEDING PARAGRAPHS WHERE DATA IS SPECIFICALLY IGNORED. -

4 7EXAMPLE 34343434

**COMP1C0MP1C0MP2

001 1.003.004.005

313

.0025

THIS EXAMPLE IS IN FREE-FORMAT - ** IMPLIES A BLANKLABEL. COMPOSITION COMP1 IS BUCKLED .003 IN GROUPS1-2, .004 IN GROUP 3, .003 IN GROUPS 4-5, .002 INGROUPS 6-7, AND ZERO IN ALL OTHER GROUPS.COMPOSITION COMP2 IS BUCKLED .005 IN ALL GROUPS. ALLOTHER COMPOSITIONS ARE BUCKLF.D .001 IN GROUPS 1-3,.002 IN GROUPS 4-7 AND ZERO IN ALL OTHER GROUPS.

WHEN ANY TYPE 34 CARDS EXIST, BUCKLINGS WILL NOT BECALCULATED FROM FINITE GEOMETRY DATA ON TYPE 12 CARDS.

DIRECTIONAL DIFFUSION COEFFICIENT FACTOR SCHEME (TYPE 35) -

FORMAT (I2,4X,A6,6F6.2,2I6)


1-2 35 * """ "*"_

7-12 DIRECTIONAL DIFFUSION COEFFICIENT FACTOR SCHEME LABEL. -

13-18 FIRST DIMENSION DIFFUSION COEFFICIENT MULTIPLIER, Al. -

19-24 FIRST DIMENSION DIFFUSION COEFFICIENT ADDITIVETERM, 81.

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN

25-30 SECOND DIMENSION DIFFUSION COEFFICIENT MULTIPLIER, A2. -

31-36 SECOND DIMENSION DIFFUSION COEFFICIENT ADDITIVETERM, B2.

37-42 THIRD DIMENSION DIFFUSION COEFFICIENT MULTIPLIER, A3. -

43-48 THIRD DIMENSION DIFFUSION COEFFICIENT ADDITIVETERM, B3.

49-54 HIGHER ENERGY BROAD GROUP NUMBER TO WHICH DATA INCOLS. 13-48 APPLY.

55-60 LOWER ENERGY BROAD GROUP NUMBER TO WHICH DATA INCOLS. 13-48 APPLY.

IF MORE THAN ONE TYPE 35 CARD IS NEEDED FOR A GIVENDIFFUSION COEFFICIENT FACTOR SCHEME, THE LABEL INCOLS. 7-12 MUST BE REPEATED ON EACH ADDITIONAL CARD.

FIRST, SECOND AND THIRD DIMENSIONS REFER TO THEDIMENSIONS IN THE ORDER THEY ARE NAMED ON CARD TYPE 3. -E.G. FOR R-Z GEOMETRY R IS THE FIRST DIMENSION, AND7. IS THE SECOND.

THE FIRST DIMENSION DIFFUSION COEFFICIENT, Dl, ISCALCULATED FROM THE HOMOGENEOUS DIFFUSION COEFFICIENT, -D, AS FOLLOWS:

Dl - A1*D+B1

THE OTHER TWO DIMENSIONS ARE HANDLED IN A SIMILAR WAY. -

IF T r "HIGHER ENERGY BROAD GROUP NUMBER" IS NOT

PROVIDED (COLS. 49-54 ARE BLANK OR ZERO), THECONSTANTS SPECIFIED IN COLS. 13-48 WILL APPLY TO ALLBROAD GROUPS FOR THE PARTICULAR SCHEME.

IF THE "LOWER ENERGY BROAD GROUP NUMBER' .S NOTPROVIDED (COLS. 55-60 ARE BLANK OR ZERO), THECONSTANTS SPECIFIED IN COLS. 13-48 WILL APPLY TO THEHIGHER ENERGY BROAD GROUP NUMBER (COLS. 49-54) ONLY.

THE CONSTANTS DEFINING A PARTICULAR SCHEME CAN BEOVERLAYED. THAT IS, FACTORS DEFINED ON LATER TYPE 35CARDS SUPERCEDE DATA FOR ENERGY RANGES PREVIOUSLYDEFINED.

DIRECTIONAL DIFFUSION COEFFICIENT FACTOR SCHEMES AREASSIGNED TO COMPOSITIONS ON TYPE 36 CARDS.

IF NO TYPE 36 CARDS ARE SUPPLIED, AND ONLY ONE SC1IEMK -IS DEFINED (THE SAME LABEL APPEARS IN COLS. 7-12 OFALL TYPE 35 CARDS), THE FACTORS WILL BE USED IN ALL

Dβ

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNC

c—

c—CRCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

COMPOSITIONS.

I? NO TYPE 36 CARDS ARE SUPPLIED AND MORE THAN ONESCHEME IS DEFINED, THE FACTORS FOR THE FIRST DEFINEDSCHEME (I.E. THAT SCHEME LABEL WHICH APPEARS ON THEFIRST TYPE 35 CARD) WILL BE USED IN ALL COMPOSITIONS.

THE CALCULATION OF TRANSVERSE LEAKAGE BY THE DIF3DCODE WILL USE THE THIRD DIMENSION DIFFUSIONCOEFFICIENT FOR THE PSEUDO ABSORPTION,

D-B-SQUARED - (A3*D+B3)*B**2REGARDLESS OF THE PROBLEM DIMENSIONS. OTHERCODES USING THE COMPXS FILE MAY BEHAVE DIFFERENTLY -IT IS UP TO THE USER TO CHOOSE THE PROPERCOEFFICIENT TO MODIFY.

DIRECTIONAL DIFFUSION COEFFICIENT FACTORS-COMPOSITIONCORRESPONDENCE (TYPE 36)

FORMAT (I2,4X,11A6)


1-2 36

7-12 DIRECTIONAL DIFFUSION COEFFICIENT FACTOR SCHEME LABEL(SEE CARD TYPE 35).

13-18 COMPOSITION TO fflICH DIFFUSION COEFFICIENT FACTORS ARE -ASSIGNED.

19-24 COMPOSITION TO WHICH DIFFUSION COEFFICIENT FACTORS ARE -ASSIGNED.


31-36 COMPOSITION TO WHICH DIFFUSION COEFFICIENT FACTORS ARF -ASSIGNED.




55-60 COMPOSITION TO WHICH DIFFUSION COEFFICIENT FACTORS ARE -

CDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC

C —CRCCLCCI)CDCDCDCDCDCDCDCDCDCDCDCDCDCD

61-66

67-72

ASSIGNED. '

COMPOSITION TO WHICH DIFFUSION COEFFICIENT FACTORS AREASSIGNED

OPPOSITION TO WHICH DIFFUSION COEFFICIENT FACTORS AREASSIGNED.

IF MORE THAN ONE TYPE 36 CARD IS REQUIRED TO ASSIGNGIVEN DIFFUSION COEFFICIENT FACTORS TO COMPOSITIONS,THE LABEL IN COLS. 7-12 MUST BE REPEATED ON THEADDITIONAL CARDS.

IF NO TYPE 36 CARDS ARE SUPPLIED, AND ONLY ONEDIRECTIONAL DIFFUSION COEFFICIENT FACTOR SCHEME ISDEFINED (THE SAME LABEL APPEARS IN COLS. 7-12 OF ALLTYPE 35 CARDS), THE FACTORS WILL BE USED IN ALLCOMPOSITIONS.

IF NO TYPE 36 CARDS ARE SUPPLIED AND MORE THAN ONESCHEME IS DEFINED, THE FACTORS FOR THE FIRST DEFINEDSCHEME WILL BE USED IN ALL COMPOSITIONS.

IF NO COMPOSITIONS ARE DEFINED IN COLS. 13-72, .THESCHEME IDENTIFIED BY THE LABEL IN COLS. 7-12 WILL BEUSED FOR ALL COMPOSITIONS.

THE SCHEME-COMPOSITION CORRESPONDENCE DATA CAN BEOVERLAYED. THAT IS, DATA GIVEN ON LATER TYPE 36 CARDSSUPERCEDES DATA PREVIOUSLY DEFINED. in

FISSION ENERGY CONVERSION FACTOR DATA (TYPE 37)

FORMAT (I2,10X,3(A6,E12.5))


1-2 37

13-18 COMPOSITION LABEL.

19-30 ENERGY CONVERSION FACTOR FOR THIS COMPOSITION(FISSIONS/WATT-SEC.).




CDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC —


IF TYPE 37 OR TYPE 38 CARDS ARE PROVIDED FOR AA PARTICULAR COMPOSITION, THE ENERGY CONVERSIONFACTORS IN DATA SET ISOTXS WILL BE IGNORED FOR THATCOMPOSITION, AND THE DATA ON THE TYPE 37 AND TYPE 38CARDS WILL BE USED INSTEAD.

IF THE FIRST LABEL (COLS. 13-18) ON A TYPE 37 CARD ISBLA?rK, THE ASSOCIATED CONVERSION FACTOR WILL BEENTTRED FOR ALL COMPOSITIONS.

IF COLS. 31-36 ARE BLANK THE DATA IN COLS. 37-66 ARENEGLECTED. IF COLS. 49-54 ARE BLANK THE DATA INCOLS. 55-66 ARE NEGLECTED.

DATA ON THIS CARD MAY BE OVERLAYED. THAT IS, FACTORSDEFINED ON LATER TYPE 37 CARDS SUPERCEDE DATA FORCOMPOSITIONS PREVIOUSLY SPECIFIED.

THE ENERGY CONVERSION FACTOR FOR ANY COMPOSITION NOTREFERENCED ON A TYPE 37 OR TYPE 38 CARD WILL BEDETERMINED FROM DATA IN ISOTXS.

CCRCCLCenCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCN

CAPTURE ENERGY CONVERSION FACTOR DATA (TYPE 38)

FORMAT (I2,10X,3(A6,E12.5))


1-2 38


19-30 ENERGY CONVERSION FACTOR FOR THIS COMPOSITION(CAPTURES/WATT-SEC.).





IF TYPE 37 OR TYPE 38 CARDS ARE PROVIDED FOR A

CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNC

C —CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDC!)CDCDCDCDCDCD

A PARTICULAR COMPOSITION, THF. ENERGY CONVERSIONFACTORS IN DATA SET ISOTXS WILL BE IGNORED FOR THATCOMPOSITION, AND THE DATA ON THE TYPE 37 AND TYPE 38

WILL BE USED INSTEAD,

IF THE FIRST LABEL (COLS. 13-18) ON A TYPE 38 CARD ISBLANK, 1..E ASSOCIATED CONVERSION FACTOR WILL BEENTERED FOR ALL COMPOSITIONS.

IF COLS. 31-36 ARE BLANK THE DATA IN COLS. 37-66 AKENEGLECTED. IF COLS. 49-54 ARE BLANK THE DATA INCOLS. 55-66 ARE NEGLECTED.

DATA ON THIS CARD MAY BE OVERLAYED. THAT IS, FACTORSDEFINED ON LATER TYPE 38 CARDS SUPERCEDE DATA FORCOMPOSITIONS PREVIOUSLY SPECIFIED.

THE ENERGY CONVERSION FACTOR FOR ANY COMPOSITION NOTREFERENCED ON A TYPE 37 OR TYPE 38 CARD WILL BEDETERMINED FROM DATA IN ISOTXS.

NUCLIDE SET ASSIGNMENTS (TYPE 39)

FORMAT (I2.4X.11A6)


1-2 39

7-12 NUCLIDE SET LABEL.

13-18 ISOTOPE TO BE ASSIGNED TO THIS NUCLIDE SET.










cCNCNCNCNCNCVCNCNCNCNCNCC —

SOURCE EDIT AND SYNTHESIS TRIAL FUNCTION SOURCESPECIFICATION.(TYPE 40)

CCRCRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

NUCLIDE SET ASSIGNMENTS ARE OPTIONAL. THF.IR USE MAYREDUCE THE SIZE OF THE CCCC ATOM DENSITY FILE (ZNATDN)AND, THEREFORE, THE RUNNING TIME FOR CROSS SECTIONHOMOGENIZATION.

ALL ISOTOPES USED IN A PARTICULAR ZONE OR APARTICULAR SUBZONE MUST BE ASSIGNED TO THE SAMENUCLIDE SET.

WHEN NO TYPE 39 CARDS ARE PROVIDED, ALI ISOTOPES AREASSIGNED TO A SINGLE NUCLIDE SET.

FORMAT (I2.4X.4I6)

CONTENTS...IMPLICATIONS, IF ANYCOLUMNS

1-2 40

7-12 EDIT FLAG FOR POINTWISE INHOMOGENEOUS SOURCE0, NO EDITS (DEFAULT).1, PRINT EDITS.2, WRITE EDITS TO AUXILIARY OUTPUT FILE.3, WRITE EDITS TO BOTH PRINT AND AUXILIARY OUTPUT

FILE.

13-18 RTFL \ FILE VERSION NUMBER FOR A SYNTHESIS TRIALFUNC.ION SOURCE.

S(X,Y,Z,G)-D(X,Y,Z,G)*FLUX(X,Y,Z,G)WHERE D lr ' DIFFUSION COEFFICIENT AND FLUX IS A FLUX(OR ADJO:.,i f'LUX) FROM AN INPUT RTFLUX (OR ATFLUX)FILE. USE A NEGATIVE VALUE FOR ATFLUX. SET TO ZEROWHEN ANOTHER TYPE OF SOURCE IS REQUIRED.

19-24 VERSION NUMBER OF GEODST FILE SPECIFYING COMPOSITIONDISTRIBUTION REQUIRED FOR A SYNTHESIS TRIAL FUNCTIONSOURCE. 0 OR 1 IMPLIES THE GEOMETRY DEFINED BY THECURRENT A.NIP3 DATASET. THIS PARAMETER IS USED ONLYWHEN THE FLUX FILE VERSION IN COLS. 13-18 IS .GE. 1.

25-30 WORD LENGTH PARAMETER FOR THE FIXSRC FILE SOURCEDISTRIBUTION. ON SINGLE-WORD-LENGTH MACHINES(E.G. CDC) THIS INPUT FIELD IS IGNORED. ON DOUBLE-WORD-LENGTH MACHINES A VALUE OF 1 WILL PRODUCE ASHORT-WORD (I.E. RF.AL*4 ) FILE, A VALUE OF 2 WILLPRODUCE A DOUBLE-WORD (I.E. RF.AL*8) FILE. THK DIF3DCODE REQUIRF.S A DOUBLE-WORD FILE ON DOUBLE-WORD-

cnencc—

cCRCRcCL

cCDCDencCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNC

CRC

CLCCDCD

LENGTH MACINKS. (DEFAULT - 2 ON UOUBLE-WORD-LENCTHMACHINES)

NATURAL DECAY INHOMOGENEOUS SOURCE SPECIFICATIONS(TYPE 4!)

FORMAT (I2,4X,2(A6,E12.5,A6))


1-2 41

7-12 ISOTOPE LABEL

13-24 DECAY CONSTANT

25-30 SPECTRUM LABEL OF SPECTRUM TO BE USED WITH THISISOTOPE (SEE CARD TYPE 42)

11-36 ISOTOPE LABEL

37-48 DECAY CONSTANT

49-54 SPECTRUM LABEL OF SPECTRUM TO BE USED WITH THISISOTOPE (SEE CARD TYPE 42)

WHEN THERE ARE TYPE 41 CARDS A FIXSRC FILE WILL BECREATED CONTAINING THE DISTRIBUTED SOURCE

S(X,Y,Z,G) - SUM OVER ISOTOPES (I) OFSCHI;G,I)*DC(I)*ATND(X,Y,Z,I)

WHERE SCHI IS AN ISOTOPE SOURCE SPECTRUM (SEE THE TYPE42 CARDS), DC IS THE DECAY CONSTANT AND ATND IS THEISOTOPE NUMBER DENSITY.

AS MANY TYPE 41 CARDS SHOULD BE PROVIDED AS ARENECESSARY TO SPECIFY ALL ISOTOPES REQUIRED.

WHEN THE SPECTRUM LABEL IS BLANK THE SOURCE WILL BECOMPUTED WITH THE SPECTRUM EQUAL TO 1.(1 IN ALL GROUPS.

Cd

SOURCE SPECTRUM DATA (TYPE 4 2 )

FORMAT ( I 2 , 4 X , A 6 , 5 E 1 2 . 5 )

COLUMNS CONTENTS. . . IMPLICATIONS, I F ANY

CDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCC—

C —CRCCLCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

1-2 42

7-12 SPECTRUM LABEL

13-24 GROUP MULTIPLIER (SPECTRUM), FIRST CROUP.

25-36 CROUP MULTIPLIER (SPECTRUM), NEXT GROUP

37-48 GROUP MULTIPLIER (SPECTRUM), NEXT GROUP.



AS MANY TYPE 42 CARDS, FIVE ENERGY GROUPS PER CARD,SHOULD BE PROVIDED AS ARE NECESSARY TO SPECIFY ALL THESPECTRA NEEDED FOR THE NATURAL DECAY SOURCECALCULATION. THE FIRST TYPE 42 CARD MUST HAVE ANON-BLANK SPECTRUM LABEL. A REPEATED SPECTRUM LABELIMPLIES A CONTINUATION OF THE LAST CARD WITH THE SAMELABEL. A BLANK SPECTRUM LABEL IMPLIES A CONTINUATIONOF THE SPECTRUM ON THE PREVIOUS TYPE 42 CARD.

WHEN THE NUMBER OF DATA FOR A PARTICULAR SPECTRUM ISLESS THAN THE TOTAL NUMBER OF ENERGY GROUPS, THEREMAINING ELEMENTS OF THE SPECTRUM ARE SET TO ZERO.WHEN THE NUMBER OF DATA IS GREATER THAN THE NUMBEROF GROUPS THE SURPLUS ELEMENTS ARE IGNORED.

GRAPHICS OUTPUT CONTROL (TYPE 43)

FORMAT (I2,4X,I6,3E12.4,3I6)


1-2 43

7-12 GRAPHICS OUTPUT SENTINEL FOR MAP0...NO GRAPHICS (DEFAULT)1...GENERATE MAP

13-24 HEIGHT OF GRAPHICS OUTPUT FIELD (DEFAULT-11.0 INCHES)

25-36 WIDTH OF GRAPHICS OUTPUT FIELD (DEFAULT-11.0 INCHKS)

37-48 FOR TRIANGULAR AND HEXAGONAL GEOMETRIES - THIS FIELDCONTAINS THE FLAT-TO-FLAT DISTANCE ACROSS EACHHEXAGON, IN INCHES (DEFAULT - 0.5 INCHES)

FOR ORTHOGONAL GEOMETRIES - THIS FIELD CONTAINS THE

CDCDCCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCNC

CCRCCI.CCDCDCDCD

MINIMUM REDUCTION ALLOWED FOR LABELS (DEFAULTSEE THE NOTE BELOW.

0.5). -

49-54

55-60

61-66

PRINTER PLOTTER SENTINEL - HEXAGONAL MAP ONLY1... FLAT-TO-FLAT HEXAGON DIMENSION - 8 POWS2...FLAT-TO-FLAT HEXAGON DIMENSION - 6 AOWS (DEFAULT)

MAXIMUM NO. OF ROWS IN PRINTER-PLOTTER FIELD -HEXAGONAL MAP ONLY (DEFAULT - 48)

.^XIMUM NO. OF PRINT COLUMNS IN PRINTER-PLOTTER FIELD- HEXAGONAL MAP ONLY (DEFAULT -130)

THE GRAPHICS OPTION MAY NOT BE AVAILABLE IN ALLVERSIONS OF THE INPUT PROCESSOR GNIP4C.

THIS CARD CONTROLS THE FORMAT OF THE PRINTER-PLOTTEROUTPUT FOR HEXAGONAL MAPS BUT DOES NOT ACTUALLYTRIGGER THE PRINTER MAP. THAT T<! DONE BY A SENTINELON THE TYPE 02 CARD. THIS CARD HAS NO EFFECT ON THEPRINTER-PLOTTER MAP OF ORTHOGONAL GEOMETRY MODELS.

FOR TRIANGULAR AND HEXAGONAL GEOMETRIES THE SCALEOF THE PLOT IS DETERMINED BY THE FLAT-TO-FLAT DISTANCEIN COLS. 37-48. THE SIZE OF THE GRAPHICS PAGE IS SETBY THE DATA IN COLS. 13-36. THE CODE GENERATES ASMANY PAGES OF GRAPHICS OUTPUT AS IT TAKES TO COVER THEENTIRE MAP. LABELS ARE CENTERED IN EACH HEXAGON, ANDTHE CHARACTER SIZE IS A FIXED FRACTION (1/8) OF THEFLAT-TO-FLAT DISTANCE.

FOR ORTHOGONAL GEOMETRIES THE SCALE OF THE PLOT ISSET BY THE CODE SO THAT THE ENTIRE MAP IS FORCEDTO FIT IN A SINGLE GRAPHICS PAGE. THE MAXIMUMSIZE OF THE GRAPHICS PAGE IS SET BY THE DATA INCOLS. 13-36. LABELS WITH 0.1 INCH CHARACTER HEIGHTARE PLACE IN REGIONS AS LONG AS THERE IS ROOM. IF THEREGION IS TOO SMALL, THE LABEL IS REDUCED IN SIZE. IFTO FIT IN THE REGION THE LABEL SIZE MUST BE REDUCEDBY A FACTOR SMALLER THAN THE NUMBER IN COLS. 37-48NO LABEL IS DRAWN. WHEN THE NUMBER IN COLS. 37-48IS GREATER THAN 1.0 NO LABELS ARE DRAWN.

03m

J>

C3

ASSIGNMENT OF REGIONS TO CONTROL ROD BANKS (TYPE 44)

FORMAT (12 ,4X, 11A6 )


1-2 44

Appendix C

DIF3D CCCC BINARY INTERFACE FILE DESCRIPTIONS

C.I ISOTXS

c***********************************************************************ccCFCECCNCNCNCNCC***********************************************************,***********

REVISED 11/30/76

ISOTXS-IV

MICROSCOPIC GROUP NEUTRON CROSS SECTIONS

THIS FILE PROVIDES A BASIC BROAD GROUP

LIBRARY, ORDERED BY ISOTOPE

FORMATS GIVEN ARE FOR FILE EXCHANGE PURPOSES

ONLY.

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

CS

cc—c~CR

cCL

ccwcCBCBCCD

FILE STRUCTURE

RECORD TYPE PRESENT IF

FILE IDENTIFICATION

FILE CONTROL

FILE DATA

FILE-HIDE CHI DATA

ALWAYS

ALWAYS

ALWAYS

ICHIST.CT.1

*•***********(REPEAT FOR ALL ISOTOPES)

* ISOTOPE CONTROL AND GROUP

* INDEPENDENT DATA ALWAYS

* PRINCIPAL CROSS SECTIONS ALWAYS

* ISOTOPE CHI DATA ICHI.GT.l

* **********(REPEAT TO NSCMAX SCATTERING BLOCKS)

* * *******(REPEAT FROM 1 TO NSBLOK)

* * * SCATTERING SUB-BLOCK LORD(N).GT.O*************

FILE IDENTIFICATION

HNAME,(HUSE(I),I-1,2),IVERS

I+l*MUi.T-NUMBER OF WORDS

FORMAT(||H (IV ISOTXS , III*l2Ah,lll*.Ih)

CD

CI)enCll

enccc

CK

cci.cCWcCBrCI)

enena>enenenenCI)CI)CDenenenr

lll'SKd.' linU.KRITII USER IDEV" IFICATION fA6)

1VKXS FILE VERSION NIJMBKRMULT DOUBLE PRECISION PARAMEO.K

1- Aft WORO IS SINKLE WORD

2- Ah WORD IS ntlllBLF. PRECISION WORD

FILE CONTROL ( ID RECORD)

NfiR0U!',NISO,MAXUP,MAXDN,MAXORn, ICHIST.NSCMAX,NSBLOK

H-NI'MBER OF WORDS

FORMAT(4II ID ,

SCROIIPNISdMAXUP

MAXflNMAXORD

ICIIIST

NSCMAXNSBI.OK

N1IMBKR OF F.NKRCY CROUPS IN FILENIIHBF.R OF ISOTOPES IN FILEMAXIMUM NUMBER OF UPSCATTEK CROUPSMAXIMUM NUMBER OF DOWN^CATTER CROUPSMAXIMUM SCATTERINH ORDER (MAXIMUM VALUE OF

LEGENDRF. EXPANSION INDEX USED IN FILE).FILE-WIDE FISSION SPECTRUM FI.AC

ICHIST.F.O.n, NO FILE-WIDE SPECTRUMICHIST.EO.l, FILE-WIDK CHI VECTORICHIST.CT.1, FILE-WIDE CHI MATRIX

MAXIMUM NUMBER OF BLOCKS OF SCATTERING DATASUBBLOCKINi; CONTROL FOR SCATTER MATRICES. THE

SCATTERING DATA ARE SUBBLOCKEI) INTO NSBI.ilK•rXORDS(SUBBLOCKS) PKR SCATTERING BLOCK.

HNAMK HOLLERITH FILE NAME - ISOTXS - (Afi)

eCKe

ei.ei.ei.e

rweweCHCHen

CBCB

c

en

en

FII.F DATA (21) RECORD)

.l-l,!2),(HTSONM(I),I-I,NISO),

l(ni!(.l)...I-l ,NGROUP),(VEI,(.I),.I-1 .SCHIIUP),

3(KMAX( I),.1-1 ,NCROlip),EMIN',(I.0CA(I),I-l ,N1SO)

(NISn*r2)*HIM.T+l*NISO• N(;kO|l|>«(2 + ICHIST»(2/(ICHIST+l )))-NUMBFR OF WORDS

Fl)RMAT(4II 21) , 111* , II Ah. 1H*/ IISETID.III SdNMl l l l * , A h , I H » , 9 < I X , A h ) / ( I O ( I X . A h ) ) )

FliRMAT( h F I 2 . S ) CHI (PRESENT IF ICIIIST.Kd. I )FORMAT ( h E ^ . S ) VKL.KMAX .FMI,,,

HSETIIl(l)IIISONM(l)

HOLLERITH IDENTIFICATION (>F FII.F (Ah)HOLLERITH ISOTOPE LABEL FOR ISOTOPE I (Ah)

CDCDCDCDCDCDCC —C —CRCCCCCLCCWCCBCBCCDCDCDCDCDC

CRCCLCLCLCLCLCCWCCBCBCCDCDCDCDCDCDCDCDCDCDCDCDCD

CHT(J) FILE-WIDE FISSION SPECTRUM(PRESENT IF ICHIST.EQ.l)VEL(J) MEAN NF.UTRON VELOCITY IN GROUP J (CM/SEC)EMAX(J) MAXIMUM ENERGY BOUND OF CROUP J (EV)EMIN MINIMUM ENERGY BOUND OF SET (EV)LOCA(I) NUMBER OF RECORDS TO BE SKIPPED TO READ DATA FOR

ISOTOPE I. LOCA(1)-0

FILE-WIDE CHI DATA (3D RECORD)

PRESENT IF ICHIST.GT.I

((CHI(K,J),K-1,ICHIST),J-1,NGROUP),(ISSPEC(I),I-1,NGROUP)

NGROUP.*(ICHIST+1)-NUMBER OF WORDS

FORMAT(4H 3D , 5E12.5/(6E12.5)) CHIF0RMATO2I6) ISSPEC

CHI(K.J) FRACTION OF NEUTRONS EMITTED INTO GROUP J AS ARESULT OF FISSION IN ANY GROUP,USING SPECTRUM K

ISSPEC(I) ISSPEC(I)-K IMPLIES THAT SPECTRUM K IS USEDTO CALCULATE EMISSION SPECTRUM FROM FISSIONIN GROUP I

ISOTOPE CONTROL AND GROUP INDEPENDENT DATA (4D RECORD)

!IABSIO,HIDENT,HMAT,AMASS,EFISS.ECAPT,TEMP,SIGPOT.ADENS.KBR.ICHI,!IFIS,IALF,INP,IN2N,IND,INT,LTOT,LTRN,ISTRPD,2(IDSCT(N),N-1,NSCMAX),(LORD(N),N-1.NSCMAX),3((JBAND(J,N),J-1,NGROUP),N-1,NSCMAX),4((IJJ(J,N),J-1,NGROUP),N-1.NSCMAX)

3*MULT+17+NSCMAX*(2*NGROUP+2)«NUMBER OF WORDS

,3(lX,Ah)/ 6E12.5/FORMAT(4H1(1216))

HABSID

HIDENT

HMATAMASSEFISS "ECAPTTEMPSICPOT

ADENS

HOLLERITH ABSOLUTE ISOTOPE LABEL - SAME FOR ALLVERSIONS OF THE SAME ISOTOPE IN FILE (A6)-

IDENTIFIER OF LIBRARY FROM WHICH BASIC DATACAME(E.G. ENDF/B) (A6)

ISOTOPE IDENTIFICATION (E.G. ENDF/B MAT NO.) (A6) -GRAM ATOMIC WEIGHTTOTAL THERMAL ENERGY YIELD/FISSION (W.SEC/FTSS)TOTAL THERMAL ENERGY YIELD/CAPTURE (W.SEC/CAPT)ISOTOPE TEMPEP.ATURE (DEGREES KELVIN)AVERAGE EFFECTIVE POTENTIAL SCATTERING IN

RESONANCE RANGE (BARNS/ATOM)DENSITY OF ISOTOPE IN MIXTURE IN WHICH ISOTOPE

CROSS SECTIONS WERE GENERATED (A/BARN-CM)-

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDcnCDCDCDcnCDCDCDCDCDCDCDCDCRCDCDCDCDCDCDCDCDCD

KBR

ICHI

IFIS

IALF

INP

IN2N

IND

INT

LTOT

I.TRN

ISTRPD

IDSCT(N)

L(1RD(N)

ISOTOPE CLASSIFICATIONO-UNDEFINED1-FISSILE2-FERTILE3-OTHER ACTINIDE4-FISSION PRODUCT5-STRUCTURE6-COOLANT7-CONTROL

ISOTOPE FISSION SPECTRUM FLAGICHI.EQ.O, USE FILE-WIDE CHIICHI.EQ.1, ISOTOPE CHI VECTORICHI.GT.l, ISOTOPE CHI MATRIX

(N.F) CROSS SECTION FLAGIFIS-O, NO FISSION DATA IN PRINCIPAL CROSS

SECTION RECORD-1, FISSION DATA PRESENT IN PRINCIPAL

CROSS SECTION RECORD(N,ALPHA) CROSS SECTION FLAC

SAME OPTIONS AS IFIS(N.P) CROSS SECTION FLAG

SAME OPTIONS AS IFIS(N.2N) CROSS SECTION FLAG

SAME OPTIONS AS IFIS(N,D) CROSS SECTION FLAG

SAME OPTIONS AS IFIS(N.T) CROSS SECTION FLAG

SAME OPTIONS AS IFISNUMBER OF MOMENTS OF TOTAL CROSS SECTION PROVIDED

IN PRINCIPAL CROSS SECTIONS RECORDNUMBER OF MOMENTS OF TRANSPORT CROSS SECTION

PROVIDED IN PRINCIPAL CROSS SECTIONS RECORDNUMBER OF COORDINATE DIRECTIONS FOR WHICH

COORDINATE DEPENDENT TRANSPORT CROSS SECTIONSARE GIVEN. IF ISTRPD-0, NO COORDINATE DEPENDENTTRANSPORT CROSS SECTIONS ARE GIVEN.

SCATTERING MATRIX TYPE IDENTIFICATION FCXSCATTERING BLOCK N. SIGNIFICANT ONLY TFLORD(N).GT.OIDSCT(N)-nOO + NN, TOTAL SCATTERING, (SUM OF .

ELASTIC,INELASTIC, AND N.2N SCATTERINGMATRIX TERMS).

-100 + NN, ELASTIC SCATTERING-200 + NN, INELASTIC SCATTERING-300 + NN, (N,2N) SCATTERING, SEENOTE BELOW

WH'-:RF. NN IS THE LEGENDRE EXPANSION INDEX OF THEFIRST MATRIX IN BLOCK N

NUMBER OF SCATTERING ORDERS IN BLOCK N. IFL--'O(N)-0, THIS BLOCK IS NOT PRESENT FOR THISI.S ."OPE. IF NN IS THE VALUE TAKKN FROMIDSCT(N), THEN THE MATRICES IN THIS BLOCKHAVE LEGENDRE EXPANSION INDICES OF NN.NN+1,NN+2,...,NN+LORD(N)-1

NJ

enCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCNCNCNCNCN

7-12

13-18

19-24

25-10

31-36

37-42

43-48

49-54

55-60

61-66

67-72

CONTROL ROD BANK LABEL (REPEATED ON ADDITIONALTYPE 44 CARDS IF NECESSARY).

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVF.ABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVEABLE TORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE HOVEABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVEABLE PORTION OF THE ROD(S)THE SPECIFIED CONTROL ROD BANK.

IN

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVEABLR PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVEABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING RECION(S)AT THE TIP OF THE MOVEABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING RECION(S)AT THE TIP OF THE MOVEABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVF.ABLE PORTION OF THE ROD(S) INTHE SPECIFIED CONTROL ROD BANK.

REGION LABEL OR AREA LABEL DEFINING REGION(S)AT THE TIP OF THE MOVEABLE PORTION OF THE ROO(S) INTHE SPECIFIED CONTROL ROD BANK.

ALL REGIONS IN A ROD CHANNEL ABOVE THE ROD TIPMOVE TOGETHER. ALL REGIONS BELOW THE TIP ARESTATIONARY, AND ARE REPLACED BY ROD REGIONS AS THEROD MOVES DOWN. THE TOPMOST REGION IN THE RODEXPANDS AS THE ROD MOVES DOWN FROM ITS INITIALPOSITION. THE RECION JUST BELOW THE INITIAL ROD-TIPPOSITION EXPANDS AS THE ROD MOVES UP FROM ITSORIGINAL POSITION.

THE LOWER BOUNDARY OF ALL ROD-TIP REGIONS WHICH DEFINERODS ASSIGNED TO A PARTICULAR CONTROL ROD BANK MUST

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

CN

a>CN

CN

CN

CN

CN

CN

CN

CN

CN

CM

CN

CN

CN

CN

CN

CN

CN

C.

r—

BK AT TMK SAME AV1AL POSITION. "AXIAI." RF.FEKS TO THK

Z-IMMKNSION IN R/., XYZ, AND IIKX-Z, AND TO THK Y

DIMENSION IN XY. THUS FOR THK (R-Z E.G. ) UEUMF.TRY

PICTURED BELOW,

THE FOLLOWING TYPE 44 CARDS (GIVEN IN FREK FORMAT

STYLE INPUT) WOULD RF.SUL'f IN A FATAL ERROR

44 BANKI CR12 CP.22

WHEREAS

44 BANKI CR12 CR23

WOULD BE ACCEPTABLE. ALSO, A ROD BANK MAY NOT BK

SPECIFIED USING MORE THAN ONE RECION IS A PARTICULAR

VERTICAL CHANNEL. THUS

44 BANKI CK22 CR23

WOULD LEAD TO A FATAL INPUT ERROR.

MITE THAT SINCE IT MUST BF. ASSUMED THAT \ CONTROL ROD -

BANK WILL BE MOVED DURING THE COURSE OF A PROBLEM,

AT LEAST ONE REGION MUST BF. DEFINED BKI.HW KACH KKG10N -

SPECIFIED IN COLS. 13-72. THI'S. THE FOLLOWING TYPE

44 CARD WOULD SOT BK ACCEPTABLE FOR THK GEOMETRY GIVKN -

ABOVE

44 BANKI CI

AN AKKA LABEL IN COLS. 11-72 IMPLIES ALL THK KKCIDNS

ASSIGNED TO THAT AKKA. AREAS ARE DEFINED ON THK

TYPE 07 CARD OF DATASET A.NIP3.

THE FIRST BLANK REGION LABEL ENCOUNTERED TERMINATES

READING OF THK DATA OH THAT PARTICULAR TYI'h 44 CARD.

NOTF THAT A BLANK CONTROL ROD BANK LABEL IS ACCF.PTAB1.F..-

00

I

CEOF

CDCDCDCDCDCDCDCDCDCCNCNCNCNCNCMCc—c—CRCCLCLCLCLCLCLCLCCWCWCCBCo>CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

JBAND(J.N) NUMBER OF GROUPS THAT SCATTER INTO GROUP J,INCLUDING SELF-SCATTER, IN SCATTERING BLOCK N.IF JBAND(J,N)-0, NO SCATTER DATA IS PRESENT INBLOCK N

IJJ(J.N) POSITION OF IN-GROUP SCATTERING CROSS SECTION INSCATTERING DATA FOR GROUP J, SCATTERING BLOCKN.COUNTED FROM THF. FIRST WORD OF GROUP J DATA.IF JBAND(J,N).NE.O THEN IJJ(J.N) MUST SATISFYTHE RELATION 1.LE.IJJ(J,N).LE.JBAND(J,N)

NOTE- FOR N.2N SCATTER, THE MATRIX CONTAINS TERMS,SCAT(J TO G), WHICH ARE EMISSSION (PRODUCTION)-BASED, I.E,, ARE DEFINED SUCH THAT MACROSCOPICSCAT(J TO G) TIMES THE FLUX IN GROUP J GIVESTHF. RATE OF EMISSION (PRODUCTION) OF NEUTRONSINTO GROUP G.

PRINCIPAL CROSS SECTIONS (5D RECORD)

((STRPL(J.L).J-l,NGROUP),L-I,LTRN),I((STOTPL(J,L),J-1,NGROUP),L-1,LTOT),(SNGAM(J),J-l.NGROUP),2(SFIS(J),J-1,NGROUP),(SNUTOT(J),J-1,NGROUP),3(CHISO(J),J-I,NGROUP),(SNALF(J).J-l,NGROUP),4(SNP(J),J-1,NGROUP).(SN2N(J),J-1.NGROUP),5(SND(J),J-1,NCROUP),(SNT(J),J-1,NGROUP)6((STRPD(J,I),J-l,NGROUP),I-l.ISTRPD)

(1+LTRN+LTOT+IALF+INP+IN2N+IND+INT+ISTRPD+2*IFIS+ICHl*(2/(ICHI+l)))*NGROUP=NUKBER OF WORDS

FORMATfAH 5D , 5E12.5/(6EI2.5)) LENGTH OF LIST AS ABOVE

STRPL(J.L) PL WEIGHTED TRANSPORT CROSS SECTIONTHE FIRST ELEMENT OF ARRAY STRPL IS THECURRENT (PI) WEIGHTED TRANSPORT CROSS SECTIONTHE LEGENDRE EXPANSION COEFFICIENT FACTOR (2L+1)-IS NOT INCLUDED IN STRPL(J.L).

STOTPL(J.L) PL WEIGHTED TOTAL CROSS SECTIONTHE FIRST ELEMENT OF ARRAY STOTPL IS THEFLUX (PO) WEIGHTED TOTAL CROS.^ SECTIONTHE LEGENDRE EXPANSION COEFFICIENT FACTOR (2L+1)-IS NOT INCLUDED IN STOTPL(J.L).

SNGAM(J) (N,GAMMA)SFIS(J) (N,F) (PRESENT IF IFIS.CT.O)SNUTOT(J) TOTAL NEUTRON YIELD/FISSION (PRESENT IK IFIS.GT.O)-CHISO(J) ISOTOPE CHI (PRESENT IF ICHI.EQ.l)SNALF(J) (N,ALPHA) (PRESENT IF IALF.GT.O)SNP(J) (N.P) (PRESENT IF INP.GT.O)SN2N(J) (N,2N) (PRESENT IF IN2N.GT.O) SF.K

NOTE BELOWSND(J) (N,D) (PRESENT IF IND.GT.O)SNT(J) (N,T) (PRESENT IF INT.GT.O)

CDCDCCNCNCNCNCNCNCNCCCCRCCCCCLCCWCCBCBCCDCDCDCDCDCC

CCRCCCCCLCCCCCCCCCCCcCCCCcCWcCBcCDCD

STRPD(J.I) COORDINATE DIRECTION I TRANSPORT CROSS SECTION(PRESENT IF ISTRPD.GT.O)

NOTE - THE PRINCIPAL N.2N CROSS SECTION SN2N(J)IS DEFINED AS THE N.2N REACTION CROSS SECTION,I.E., SUCH THAT MACROSCOPIC SN2N(J) TIMES THEFLUX IN GROUP J GIVES THE RATE AT WHICH N,2NREACTIONS OCCUR IN GROUP J. THUS, FOR N.2HSCATTERING, SN2N(J) - 0.5*(SUM OF SCAT(J TO G)SUMMED OVER ALL G ) .

ISOTOPE CHI DATA (6D RECORD)

PRESENT IF ICHI.GT.l

((CHIISO(K,J),K-1,ICHI),J-1,NGROUP),(ISOPEC(I) ,1-1 ,NGROUP)

NGROUP*(ICHI+1)-NUMBER OF WORDS

FORMAT(4H 5D , 5E12.5/(6E12.5)) CHIISOFORMATU2I6) ISOPEC

CHIISO(K.J) FRACTION OF NEUTRONS EMITTED INTO GROUP J AS ARESULT OF FISSION IN ANY GROUP,USING SPECTRUM K

ISOPEC(I) ISOPEC(I)-K IMPLIES THAT SPECTRUM K IS USEDTO CALCULATE EMISSION SPECTRUM FROM FISSIONIN GROUP I

O

SCATTERING SUB-BLOCK (7D RECORD)

PRESENT IF LORD(N).GT.O

((SCAT(K,L),K-l,KMAX),L-l,LORDN)

KHAX-SUM OVER J OF JBAND(J.N) WITHIN THE J-GROUP RANGE OF THISSUB-BLOCK. IF M IS THE INDEX OF THE SUB-BLOCK, THE J-GROUPRANGE CONTAINED WITHIN THIS SUB-BLOCK ISJL-(M-1)*((NGROUP-1)/NSBLOK+1)+1 TO JU-MINO(NGROUP,JUP),WHERE JUP-M*((NGROUP-1)/NSBI.OK +1).

LORDN-LORD(N)

N IS THE INDEX FOR THE LOOP OVER NSCMAX (SEE FILE STRUCTURE)

KMAX*LORDN-NUMBER OF WORDS

FORMAT(AH 7D , 5E12.5/(6E12.5))

SCAT(K.L) SCATTERING MATRIX OF SCATTERING ORDER L, FORREACTION TYPE IDENTIFIED BY IDSCT(N) FOR THIS

BLOCK. .'<?AND(J,N) VALUES FOR SCATTERING INTOGROUP J ' RF. STORED AT LOCATIONS K-SUM FROM 1TO (J-, j OF JBAND(J.N) PLUS 1 TO K-l+JBAND(J,N).-THE SUM IS ZERO WHEN J-l. J-TO-J SCATTER ISTHE i.JJv'J,N)-TH ENTRY IN THE RANGE JBAND(J.N). -VALUES ARE STORED IN THE ORDER (J+JUP),(J+JUP-1),...,(J+l),J,(J-t),...,(J-JDN),WHERE JUP-IJJ(J,N)-1 AND JDN-JBAND(J,N)-IJJ(J,N)-

CDCDCDCDCDCDCDCDCC-CEOF

C.2 CEODST

C***********************************************************************

C REVISED 12/30/76CCF GEODST - IVC

CE GEOMETRY DESCRIPTIONCC***********************************************************************

CRCCLCCWCCDCDCDCDCDCDCC—C~CRCCLCLCLCCWCCDCDCDCDCDCD

FILE IDENTIFICATION (OV RECORD)


1+3*MULT

HNAMEHUSEIVERSMULT

HOLLERITH FILE NAME - GEODST - (A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER

1- A6 WORD IS SINGLE WORD2- A6 WORD IS DOUBLE PRECISION WOF..,

FILE SPECIFICATIONS (ID RECORD)

IC;OM,NZ0NE,NREC,N7.CL,NCINTI,NCINTJ,NCINTK.NINTI,NINTJ,NINTK.IMB1,-IMB2, JMB1 , JMB2 ,KMB1 ,KMB2 , NBS, NBCS, NIBCS, NZWBB, NTRIAG, NRASS , NTHI'T, -(NGOP(I),1-1,4)

27

IGOM GEOMETRY 0- POINT (FUNDAMENTAL MODE)1- SLAB2- CYLINDER3- SPHERE6- X-Y7- R-Z

COCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

cnCDCDCCCCCCCCCCCCCCC

cCDCDCD

N7.0NE

NREGNZCLNCINTINCINTJ

NCINTK

NINTININTJ

NINTK

IMB1

IMB2.IMB1.IMR2

8- THETA-R9- UNIFORM TRIANGULAR10- HEXAGONAL (1 MESH POINT IN EACH

HEXAGONAL ELEMENT)11- R-THF.TA12- R-THETA-Z13- R-THETA-ALPHA14- X-Y-Z15- THETA-R-Z16- THETA-R-ALPHA17- UNIFORM TRIANGULAR-Z18- HEXAGON-Z (MESH POINTS AS IN 10 -

ABOVE)NUMBER OF ZONES (EACH HOMOCENEOUS IN NEUTRONICS-PROBLEM - A ZONE CONTAINS ONE OR MORE REGIONS) -NUMBER OF REGIONSNUMBER OF ZONE CLASSIFICATIONS (EDIT PURPOSES) -NUMBER OF FIRST DIMENSION COARSE MESH INTERVALS-NUMBER OF SECOND DIMENSION COARSE MESH

INTERVALS. NCINTJ.EQ.l FOR ONE DIMENSIONAL -CASE.

NUMBER OF THIRD DIMENSION COARSE MESH INTERVALS-NCINTK.EQ.l FOR ONE AND TWO DIMENSIONALCASES.

NUMBER OF FIRST DIMENSION FINE MESH INTERVALS -NUMBER OF SECOND DIMENSION FINE MESH INTERVALS -

NINTJ.EQ.l FOR ONK DIMENSIONAL CASE.NUMBER OF THIRD DIMENSION FINE MESH INTERVALS -

NINTK.EQ.l FOR CNE AND TWO DIMENSION CASES.-FIRST BOUNDARY ON FIRST DIMENSION

0 - ZERO FLUX (DIFFUSION)1 - REFLECTED2 - EXTRAPOLATED (DIFFUSION - DEL PHI/PHI -

- -C/D WHERE C IS GIVEN AS BNDC BELOW -AND D IS THE CROUP DIFFUSION CONSTANT, -TRANSPORT - NO RETURN).

3 - REPEATING (PERIODIC) WITH OPPOSITE FACE-4 - REPEATING (PERIODIC) WITH NEXT ADJACKNT-

FACE.5 - INVERTED REPEATING ALONG THIS FACE.

(180 DEGREE ROTATION)6 - ISOTROPIC RETURN (TRANSPORT)

NOTE FOR REPEATING CONDITIONS (3,4,")) - LKT II DENOTE FIRST-BOUNDARY ON FIRST DIMENSION, 12 THE SECOND BOUNDARY ON THE -FIRST DIMENSION, .11 THE FIRST BOUNDARY ON THE SECONDDIMENSION, ETC. THEN THESE REPEATING BOUNDARY CONDITIONSONLY APPLY TO BOUNDARIES I1,I2,J1, AND .12. GOING IN ORDER -OF II,.11,12,J2, THE FIRST BOUNDARY WHICH IS INVOLVEDCARRIES THK DESIGNATOR DEFINING THE RF.PF.ATING CONDITION.

LAST BOUNDARY ON FIRST DIMENSIONFIRST BOUNDARY ON SECOND DIMENSIONLAST BOUNDARY ON SECOND DIMENSION

O

CI)CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCI)CDCDCD

KMB1KMB2NBS

NBCS

NIBCS

NZWB8NTRIAG

FIRST BOUNDARY ON THIRD DIMENSION -LAST BOUNDARY ON THIRD DIMF.NSION -NUMBER OF BUCKLING SPECIFICATIONS -

0 - NONE "1 - SINGLE VALUE APPLIES EVERYWHERE -.EQ.NZONE- ZONE DEPENDENT -M*NZONE - DATA IS GIVEN OVER ALL ZONES FOR -

THE FIRST ENERGY GROUP, THEN FOR THF -NEXT GROUP, TO END OF LIST. IF -M.LT.NGROUP THEN THE M-TH GROUP DATA -APPLIES TO ATX ADDITIONAL GROUPS. -(2.LE.M.LE.NGROUP) -

NUMBER OF CONSTANTS FOR EXTERNAL BOUNDARIES -0 - NONE "1 - SINGLE VALUE USED EVERYWHERE -6 - INDIVIDUAL VALUE GIVEN FOR EACH -

EXTERNAL BOUNDARY. THE ORDERING OF THE -VALUES IS THE SAME AS THE ORDERING OF -THE BOUNDARY CONDITIONS. -

6*M - SIX VALUES GIVEN FOR FIRST ENERGY -GROUP (ORDERED AS DESCRIBED ABOVE), -THEN 6 FOR THE NEXT GROUP, TO END OF -LIST. (2.LE.M.LE.NGROUP). -IF M.LT.NGROUP THEN THE M-TH GROUP DATA-APPLIES TO ALL REMAINING GROUPS. -

NUMBER OF CONSTANTS FOR INTERNAL BOUNDARIES -0 - NONE -1 - SINGLE VALUE USED EVERYWHERE -.GT.l - VALUES ARE GIVEN BY ENERGY GROUP -WITH NON-BLACK CONDITION INDICATED BY -ZERO ENTRY - LAST VALUE APPLIES TO -ADDITIONAL GROUPS -

NUMBER OF ZONES WHICH ARE BLACK ABSORBERS -TRIANGULAR/HEXAGONAL GEOMETRY OPTION -

0 - REGION OF SOLUTION IS A RHOMBUS IN -WHICH THE 1ST AND 2ND DIMENSION AXES -INTERSECT AT AN ANGLE OF 120 DEGREES. -

1 - REGION OF SOLUTION IS A RHOMBUS IN -WHICH THE 1ST AND 2ND DIMENSION AXKS -INTERSECT AT AN ANCLE OF 60 DEGREES. -

2 - REGION 0? SOLUTION IS A RECTANGLE. THE-BOUNDARIES II AND 12 BISECT MF..-.H -TRIANGLES. SEE NTHPT BELOW. -(ICOM-9,17 ONLY) -

3 - REGION OF SOLUTION IS AN EQUILATERAL, -60 DEGREE TRIANGLE. (ICOM-9,17 ONLY) -

4 - REGION OF SOLUTION IS A 30-60 DEGREE -RIGHT TRIANGLE IN WHICH THE 1ST AND 2ND-DIMENSION AXES INTERSECT AT THE 30 -DEGREE ANGLE. (IGOM-9,17 ONLY) -

5 - REGION OF SOLUTION IS A RHOMBUS IN -WHICH THE 1ST AND 2ND DIMENSION AXES -INTERSECT AT AN ANGLE OF 30 DEGREES. -(IGOM-9,17 ONLY) -

CDCDCDCDCDCDCDCDCi)CDCDCDCCCCRCRCCCCCLCCWCCDCDCDCDCDCCCCCCC—C-CRCRCCCCCLCL

NRASS

NTHPT

NGOP

REGION ASSIGNMENTS0- TO COARSE MESH1- TO FINE MESH

ORIENTATION OF FIRST FINE MESH INTERVAL INTRIANGULAR GEOMETRIES. NTRIAG-2 ONLY.1- TRIANGLE(l.l) POINTS AWAY FROM FIRST

DIMENSION AXIS, I.E., NO INTERNAL MESHLINE INTERSECTS THE ORIGIN.

2- TRIANGLE(l.l) POINTS TOWARD THE FIRSTDIMENSION AXIS, I.E., AN INTERNAL MESHLINE INTERSECTS THE ORIGIN.

RESERVED

ONE DIMENSIONAL COARSE MESH INTERVAL BOUNDARIES AND FINEMESH INTERVALS (2D RECORD)

PRESENT IF IGOM.GT.O AND IG0M.LE.3

(XMESH(I),I-1,NCBNDI),(IFINTS(I),1-1.NCINTI)

NCBNDI*HULT+NCINTI

XMESHIFINTS

NCBNDI

COARSE MESH BOUNDARIES, FIRST DIMENSIONNUMBER OF EOUALLY SPACED FINE MESH INTERVALS

PER COARSE MESH INTERVAL, FIRST DIMENSION. -NCINTI+1, NUMBER OF FIRST DIMENSION COARSE MESH-

BOUNDARIES

nIs)

UNITS ARE CM FOR LINEAR DIMENSIONS AND RADIANS FOR ANGULARDIMENSIONS

TWO DIMENSIONAL COARSE MESH INTERVAL BOUNDARIES AND FINEMESH INTERVALS (3D RECORD)

PRESENT IF IGOM.GE.6 AND IGOM.LE.ll

(XMKSH(I).I-l , NCBNDI), (YMF.SI'.(J) ,J-1, NCBNDJ),1(IFINTS(I),I-1,NCINTI),(JFINTS(J),J-1.NCINTJ)

CW (NCBNDI+NCBNI)J)*MULT+NCINTI+NCINTJ

COARSE MESH BOUNDARIES, SECOND DIMF.NSIONNUMBER OF EOUALLY SPACED FINE MESH INTERVALS

PER COARSE MESH INTERVAL, SECOND DIMF.NSION.NCINTJ+1, NUMBER OF SECOND DIMENSION COARSE

MESH BOUNDARIES

FOR UNIFORM-TRIANGULAR-MESH GEOMETRY (ICOM - 9) THELENGTH (L) CF THE SIDE OF A MESH TRIANGLE MUST BE GIVENBY THE EXPRESSION

CI)CDCDCI)CI)CCCCCCC

YMESH.IFINTS

NCBNDJ

cccccccccccc—c—CRCRCCC

cCLCLCLCcwcCDCDCOCDCDCCCCCCCCCcccccccccc—c—CRccccCLCLCLCCWCCDCDCDCDCDCDCDC

L - 2.*(XMESH(2)-XMESH(1))/IFINTS(1) .FOR UNIFORM-HEXAGONAL-MESH GEOMETRY (ICOM - 10) THEFLAT-TO-FLAT DISTANCE (FTP) ACROSS A MESH HEXACON MUSTBE GIVEN BY THE EXPRESSION

FTF - (XMESH(2)-XMESH(1))/IFINTS(1)

THREE DIMENSIONAL COARSE MESH INTERVAL BOUNDARIES AND FINE -MESH INTERVALS (4D RECORD)

PRESENT IF ICOM.GE.12

(XMESH(I)il-l,NCBNDI),(YMESH(J),J-1.NCBNDJ),1(ZMESH(K),K«1,NCBNDK),(IFINTS(I),I-1.NCINTI),2(JFINTS(J),J-1.NCINTJ),(KFINTS(K),K-1.NCINTK)

(NCBNDI+NCBNDJ+NCBNDK)*MOLT+NCINTI+NCINTJ+NCINTK

ZMESH COARSE MESH BOUNDARIES, THIRD DIMENSIONKFINTS NUMBER OF EQUALLY SPACED FINE MESH INTERVALS

PER COARSE MESH INTERVAL, THIRD DIMENSION. -NCBNDK NCINTK+1, NUMBER OF THIRD DIMENSION COARSE MESH-

BOUNDARIES

FOR UNIFORM-TRIANGULAR-MESH GEOMETRY (IGOM - 17) THELENGTH (L) OF THE SIDE OF A MESH TRIANGLE MUST BE GIVENBY THE EXPRESSION

L - 2.*(XMESH(2)-XMESH(1))/IFINTS(1) .FOR UNIFORM-HEXAGONAL-MESH GEOMETRY (IGOM « 18) THEFLAT-TO-FLAT DISTANCE (FTF) ACROSS A MESH HEXAGON MUSTBE GIVEN BY THE EXPRESSION

FTF - (XMESH(2)-XMESH(1))/IFINTS(1)

GEOMETRY DAT/ (5D RECORD)

PRESENT IF IGOM.GT.O OR NBS.GT.O

(VOLR(N),N-I,NREG),(BSQ(N),N«1,NBS),(BNDC(N),N-1,NBCS),(BNCI(N).N-l,NIBCS),((NZHBB(N),N-1,NZWBB),(NZC(N),N-1,NZONE),(NZNR(N).N-l,NREC)

2*NREC+NBS+NBCS+NIBCS+NZWBB+NZONE

VOLRBSQBNDCBNCINZHBBNZCNZNR

REGION VOLUMES (CC)BUCKLING (B**2) VALUES (CM**-2)BOUNDARY CONSTANTS (DEL PHI/PHI —C/D)INTERNAL BLACK BOUNDARY CONSTANTSZONE NUMBERS WITH BLACK ABSORBER CONDITIONSZONE CLASSIFICATIONSZONE NUMBER ASSIGNED TO EACH REGION

CR REGION ASSIGNMENTS TO COARSE MESH INTERVALS (6D RECORD)CCC PRESENT IF IGOM.GT.O AND NRASS.EQ.OCCL ((MR(I,J),1-1.NCINTI),J-l.NCINTJ) NOTE STRUCTURE BELOWCCW NCINTI*NCINTJ

CCS DO 1 K-l.NCINTKCS 1 READ(N) "LIST AS ABOVE*CCD MR REGION NUMBERS ASSIGNED TO COARSE MESHCD INTERVALSC

CR REGION ASSIGNMENTS TO FINE MESH INTERVALS (7D RECORD)

CCC PRESENT IF IGOM.GT.O AND NRArS.EQ.lCCL ((MR(I.J).I-l .NINTD.J-1 ,NINTJ) NOTE STRUCTURE BELOWCCW NI(JTI*NINTJCCS DO 1 K - l , N I N T KCR 1 READ(N) *LIST AS ABOVE*CCD MR REGION NUMBERS ASSIGNED TO FINE MESH INTERVALS -C

CKOF

C.3 NDXSRF

(-•***************************************•**********************»******•*

C REVISED 11/30/76

CCF NDXSRF-IVCCE NUCLIDE DENSITY, DATA, CROSS SECTION REFERENCINGCC***********************************************************************

CR FILE IDENTIFICATIONCCL HNAME,(miSE(I),I-l,2),IVERSCCW 1+1*MULT-NUMBER OF WORDSCCD IINAMF. HOLLERITH FILE NAME - NDXSRF - ( A 6 )

u>

CDCDCDCDCDCC —C —CRCCLCCWCCDCDCDCDCDCDCC —c—ccCL

CL

CL

C

CW

C

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

CD

HUSE(I) HOLLERITH USER IDENTIFICATION (A6)

IVERS FILE VERSION NUMBER

MULT DOUBLE PRECISION PARAMETER

1- A6 WORD IS SINGLE WORD

2-A6 WORD IS DOUBLE PRECISION WORD

NOR(N.L)

SPECIFICATIONS

NON.NSN.NNS,NAN,NZONE,NSZ

6 -NUMBER OF WORDS

(ID RECORD)

NON

NSN

NNS

NAN

NZONE

NSZ

NUMBER OF NUCLIDES IN CROSS SECTION DATA

NUMBER OF NUCLIDE SETS IDENTIFIED

MAXIMUM NUMBER OF NUCLIDES IN ANY SET

NUMBER OF DIFFERENT NUCLIDES IN DATA

NUMBER OF ZONES

NUMBER OF SUBZONES (SUBASSEMBLIES)

NUCLIDE REFERENCING DATA (2D RECORD)

(HNNAME(N),N-1,NON),(HANAME(N),N-1,NON),(WPF(N),N-1,NON),(ATWT(J),J-1,NAN),(NCLN(N),N-1,NON),((NDXS(K,L),K-1,4),L-1,NSN),(<NOS(I,L),I-l,NNS),L-l,NSN),((NOR(N,L),N-l,NON),L-l.NSN)

NAN+2*NON*(1+MULT)+NSN*(4+NNS+NON)-NUMBER OF WORDS

HNNAME(N)

HANAME(N)

WPF(N)

ATWT(J)NCLN(N)

NDXS(K.L)

NOS(I.L)

UNIQUE REFERENCE NUCLIDE NAME, IN LIBRARY ORDER-

(A6) ALPHANUMERIC

ABSOLUTE NUCLIDE REFERENCE, IN LIBRARY ORDER

(A6) ALPHANUMERIC

RESERVED

ATOMIC WEIGHT

NUCLIDE CLASSIFICATION

1- FISSILE

2- FERTILE

3- OTHER ACTINIDE

4- FISSION PRODUCT

5- STRUCTURAL

6- COOLANT

7- CONTROL ROD

GREATER THAN 7, UNDEFINED

REFERENCE DATA FOR SET L

K - 1, NUMBER OF NUCLIDES IN SET

K - 2, RESERVED

K » 3, RESERVED

K • 4, RESERVED

ORDER NUMBER OF NUCLIDE IN CROSS SECTION DATA -

(IN HNNAME LIST) OF NUCLIDE ORDERED I TN

SET L

(VOLZ(N).N-l,NZONE),(VFPA(N).N-l,NZONE),(VLSA(M),M»1,NSZ),

(NSPA(N).N-l,NZONE),(NSSA(M),M-l,NSZ),(NZSZ(M),M-1,NSZ)

3*(NZONE+NSZ)-NUMBER OF WORDS

CD

CD

C.

C-

C

CR

C

CL

CL

C

CW

C

CD

CD

CD

CD

CD

CD

CD

C

C

C

C

C

C

cc

CFOF

C.4 ZNATDN

ORDER NUMBER OF NUCLIDE IN SET L GIVEN ORDF.R

NUMBER N IN CROSS SECTION DATA

NUCLIDE CONCENTRATION ASSICNM+-T DATA (3D RECORD

VOLZ(N)

VFPA(N)

VLSA(M)

NSPA(N)

NSSA(M)

NZSZ(M)

VOLUMES OF ZONES, CC

VOLUME FRACTIONS FOR PRIMARY ZONE ASSIGNMENTS

VOLUMES OF SUBZONES

NUCLIDE SET REFERENCE, PRIMARY ZONE ASSIGNMENT

(MAY BE ZERO ONLY IF THERE ARE SUBZONES)

NUCLIDE SET REFERENCE ASSIGNMENT TO SUBZONES

ZONE CONTAINING SUBZONE

NOTE THAT TO CALCULATE MACROSCOPIC CROSS SECTIONS FOR A ZONE,

IT IS NECESSARY TO CONSIDER THE CONCENTRATION OF EACH NUCLIDE

IN THE PRIMARY SET ASSIGNMENT (UNLESS A ZERO IN NSPA INDICATES

THERE ARE NONE) TIMES THE VOLUME FRACTION, AND THE CONCENTRATION

OF EACH NUCLIDE IN F.ACH SUBZONE ASSIGNED TO THE ZONE TIMES THE

RATIO OF THE SUBZONE VOLUME TO THE ZONE VOLUME.

************************************

REVISED 11/30/76

£*************

C,

cCF ZNATDN-IV

C

CK ZONE ATOMIC DENSITIES (OF NUCLIDES)

CC***********************************************************************

c—CR

C

CL

C

CW

C

crenCD

CD

FILE IDENTIFICATION

HNAME,(HUSE(I),1-1,2),IVERS

I+3*MULT-NUMBER OF WORDS

HNAMK

HIISF.( I )IVKRSMULT

HOLLERITH FILE NAME - ZNATDN -(Aβ)

HOLLERITH USER IDENTIFICATION (Afi)

FILE VERSION NUMBER

DOUBLE PRECISION PARAMETER

CD 1- A6 WORD IS SINGLE WORD

CDCC—C—CRCCLCCWCCDCDCDCDCDCCCCRCCLCcwcccCC 1ccccccCDCDCDC

c

2- A6 WORD IS DOUBLE PRECISION WORD

SPECIFICATIONS

TIME,NCY,NTZSZ,NNS,NBLKAD

5-NUMBER OF WORDS

(ID RECORD)

TIMENCYNTZSZNNSNBLKAD

REFERENCE REAL TIME, DAYSREFERENCE CYCLE NUMBERNUMBER OF ZONES PLUS NUMBER OF SUBZONESMAXIMUM NUMBER OF NUCLIDES IN ANY SETNUMBER OF BLOCKS OF ATOM DENSITY DATA

ZONE ATOMIC DENSITIES (OF NUCLIDES) (2D RECORD)

((ADEN(N,J),N-1,NNS),J-JL,JU) SEE STRUCTURE BELOW

NNS*(JL - JU + 1) - NUMBER OF WORDS

DO 1 M-l.NBLKADREAD(N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-(M-1 )*((NTZSZ-1 )/NBL ~H-1 )+lAND JU-MINO(NTZSZ.JUP) WITH JUP-M*((NTZSZ-1)/NBLKAD 1)

ADEN(N.J) ATOMIC DENSITY OF NUCLIDE ORDERED N INASSOCIATED SET GIVEN IN ORDER FOR EACHFOLLOWED IN ORDER FOR EACH SUBZONE

VE

CEOF

C.5 FIXSRC

C***********************************************************************

C REVISED t1/30/76CCF FIXSRC-IVCE DISTRIBUTED AND SURFACE FIXED SOURCESCC***********************************************************************

CR 'LE IDENTIFICATIONCCL HNAME,(HUSE(I),I-1,2),IVERSCCW 1+3*MULT»NUMBER OF WORDS

CCDCDCDCDCDCDCC

CRCCLCLCCWCCDCDCDCDCDCD

CDCDCDCDCDCDCDCDCDCDCDCDCDC

CCRCCCCCLCCWCCCCCDCDCC

HNAMEHUSE(I)IVERSMULT

HOLLERITH FILE NAME - FIXSRC - (A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER

1- A6 WORD IS SINGLE WORD2- A6 WORD IS DOUBLE PRECISION WORD

SPECIFICATIONS (ID RECORD)

ITYPE.NDIM.NGROUP NINTI.NINTJ.NINTK,IDISTa,NDCOMP,NSCOMP.NEDGI,NEDC J , NEDGK, NBLfX

13-NUMBER OF WORDS

ITYPE

NDIM

NGROUPNINTININTJNINTKIDISTS

NDCOMPNSCOMPNEDGINEDCJNEDCKNBLOK

TYPE SOURCE. 0-DIFFUSION1-SN

NUMBER OF DIMENSIONSNUMBER OF GROUPSNUMBER OF FIRST DIMENSION FINE MESH INTERVALSNUMBER OF SECOND DIMENSION FINE MESH INTERVALSNUMBER OF THIRD DIMENSION FINE MESH INTERVALSDISTRIBUTED SOURCE FLAG.

0- NO DISTRIBUTED SOURCE GIVEN.1- DISTRIBUTED SOURCE IS GIVEN.

NUMBER OF DISTRIBUTED SOURCE COMPONENTSNUMBER OF SURFACE SOURCE COMPONENTSNUMBER OF FIRST DIMENSION BOUNDARY SOURCESNUMBER OF SECOND DIMENSION BOUNDARY SOURCESNUMBER OF THIRD DIMENSION BOUNDARY SOURCESDATA BLOCKING FACTOR FOR DISTRIBUTED FIXED

SOURCES IN MULTI-DIMENSIONS. (2ND DIMENSIONVARIABLE IS BLOCKED INTO NBLOK BLOCKS,SEE 3D RECORD BELOW)

I

ONE-DIMENSIONAL DISTRIBUTED FIXED SOURCE (2D RECORD)

PRESENT IF NDIM.EQ.I AND IDISTS.NE.O

((QDIST(L,I),L-l,NDCOMP),I«l,NINTI) NOTE STRUCTURE BELOW

NDCOMP*NINTI-NUMBER OF WORDS

DO 1 J-l.NGROUP1 READ (N) *LIST AS ABOVE*

QDIST(L.I) DISTRIBUTED SOURCE BY COMPONENT, INTERVAL,AND GROUP

CRCCCCCLccwcccccccCCCCcCDc

MULTI-DIMENSIONAL DISTRIBUTED FIXED SOURCE (3D RECORD)

PRESENT IF NDIM.GE.2 AND IDISTS.NE.O

((QDIST(I,J),I-1,NINTI),J-JL,JU) SEE STRUCTURE BELOW

NINTI*{JU - JL + 1) - NUMBER OF WORDS

DO 1 N-l.NGROUPDO 1 L-l.NDCOMPDO 1 K-l.NINTKDO 1 M-l.NBLOK

1 READ (N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-1+(M-1)*((NINTJ-1)/NBLOK +1) -AND JU-MINO(NINTJ,JUP) WHERE JUP-M*((NINTJ-1)/NBLOK +1)

QDIST(I.J) DISTRIBUTED SOURCE AS DEFINED ABOVE

c—CRcCCcCLccwccccCDCDCDCDCDCDCDCD

FIRST DIMENSION SURFACE SOURCE POINTERS (4D RECORD)

PRESENT IF NEDGI.NE.O

((ISPTRI(I,J),I-1,NBDRYI),J-1,NINTJ)- NOTE STRUCTURE BELOW

NBDRYI*NINTJ-NUMBER OF WORDS

DO 1 K-l.NINTK1 READ (N) *LIST AS ABOVE*

ISPTRI(I.J) ISPTRI(I.J) DENOTES THE INTERCEPT OF CHANNELJ,K WITH MESH BOUNDARY PLANE I. IF ISPTRI(I.J)--0, NO SURFACE SOURCE IS PRESENT AT THEINTERCEPT. IF ISPTRKl ,J)-M, THE MTH SURFACE -SOURCE SPECIFIED IN THE NEXT RECORD BELOW ISPRESENT AT THE INTERCEPT.

NBDRYI -NINTI+l, NUMBER OF FIRST DIMENSION FINE MESH -BOUNDARIES

c—CRCCCCCLCCWCCDCDC

FIRST DIMENSION SURFACE SOURCES (5D RECORD)

PRESENT IF NEDGI.NE.O

(((OSURFI(M.L.N), M-l ,NEDGI),L-1,NSCOMP), N-l.NGROUP)

NEDGI*NGROUP*NSC0MP-NUMBER OF WORDS

C —

CRCCCCLCCWCCCcCDCDCDCDCDCDCDCDC

QSURFI(M,L,N) FIRST DIMENSION BOUNDARY SOURCES BY BOUNDARY,COMPONENT, AND GROUP.

CRCCCCCLCCWcCDCDC

c-CRCCCCCLCCWCCCCCDCDCDCDCDCD

SECOND DIMENSION SURFACE SOURCE POINTERS (6D RECORD)

PRESENT IF NDIM.GE.2 AND NEDGJ.NE.O

((ISPTRJ(I,J),I-1,NINTI),J-1,NBDRYJ) NOTE STRUCTURE BELOW

NINTI*NBDRYJ-NUM8ER OF WORDS

DO 1 K-l,NINTK1 READ (N) *LIST AS ABOVE*

ISPTRJ(I.J) ISPTRJ(I-J) DENOTES THE INTERCEPT OF CHANNELI,K WITH MESH BOUNDARY PLANE J. IF ISPTRJ(I.J)--0, NO SURFACE SOURCE IS PRESENT AT THEINTERCEPT. IF ISPTRJ(I,J)-M, THE MTH SURFACE -SOURCE SPECIFIED IN THE NEXT RECORD BELOW IS -PRESENT AT THE INTERCEPT.

NBDRYJ -NINTJ+1, NUMBER OF SECOND DIMENSION FINE HEiH -BOUNDARIES

SECOND DIMENSION SURFACE SOURCES (7D RECORD)

PRESENT IF NDIM.GE.2 AND NEDGJ.NE.O

(((QSURFJ(M,L,N),M-1,NEDGJ),L-1,NSCOMP),N-1,NGROUP)

NF.DGJ*NGROUP*NSCOMP-NUMBER OF WORDS

OSURFJ(M,L,N) SECOND DIMENSION BOUNDARY SOURCES BY BOUNDARYCOMPONENT, AND GROUP

THIRD DIMENSION SURFACE SOURCE POINTERS (8D RECORD)

PRESENT IF NDIM.EQ.3 AND NEDT.K.NE.O

((ISPTRK(I,J),I»1,NINTI),J-1,NINTJ) NOTE STRUCTURE BF.LOW

NINTIflNINTJ-NUMBER OF WORDS

DO 1 K«!.NBDRYK1 READ (N) *LIST AS ABOVE*

ISPTRK(I.J) ISPTRK(I.J) DENOTES THE INTERCEPT OF CHANNELI.J WITH MESH BOUNDARY PLANE K. IF ISPTRK(I.J)--0, NO SURFACE SOURCE IS PRESENT AT THEINTERCEPT. IF ISPTRK(I,J)-M, THE MTH SURFACE -SOURCE SPECIFIED IN THE NEXT RECORD BELOW ISPRESENT AT THE INTERCEPT.

CDCDCC —C-CRCCCCCLCCWCCDCDCC —

NBDRYK "NINTK+1, NUMBER OF THIRD DIMENSION FINE MESHBOUNDARIF.S

THIRD DIMENSION SURFACE SOURCES (9D RECORD)

PRESENT IF NDIM.EQ.3 AND NEDCK.NE.O

(((QSURFK(M,L,N),M-1.NEDGK),L«1.NSCOMP) ,N-1,NGROUP)

NEDGK*NGROUP*NSCOMP-NUMBER OF WORDS

QSURFK(M,L,N) THIRD DIMENSION BOUNDARY SOURCES BY BOUNDARY,COMPONENT, AND GROUP

CEOF

C.6 RTFLUX

C * * * ! ) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C RF.VISED 1 1 / 3 0 / 7 6CCF RTFLUX-IVCE REGULAR TOTAL FLUXESCC***********************************************************************CD ORDER OF GROUPS IS ACCORDING TO DECREASINGrD ENERGY. NOTE THAT DOUBLE PRECISION FLUXES ARECD GIVEN WHEN MULT-2

FILE IDENTIFICATION


1+3*MULT-NUMBER OF WORDS

HNAMKHUSF.(I)IVERSMULT

HOLLERITH FILE NAMF. - RTFLUX - (Aft)HOLLERITH USER IDENTIFICATION (Aft)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER


CCR SPECIFICATIONS (ID RECORD)CCI, NDIM, NGROUP, NINTI,NINTJ,NINTK,ITER,EFFK, POWER, NBI.OKCCM 9 -NUMBER OF WORDS

CCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDC

CCRCCCCCLCCWccccCCCC

cCDCDCC

c—CRCCC

- CCLCCW_C*"CCCCCCCCC

c

NDIMNGROUPNINTININTJNINTK

ITER

F.FFKPOWERNBLOK

NUMBER OF DIM! ?JSIONSNUMBER OF ENERGY GROUPSNUMBER OF FIRST DIMENSION FINE MESH INTERVALS -NUMBER OF SECOND DIMENSION FINE MESH INTERVALS -NUMBER OF THIRD DIMENSION FINE MESH INTERVALS. -NINTK.fc/). 1 IF NDIM.LE.2OUTER ITERATION NUMBER AT WHICH FLUX WASWRITTENEFFECTIVE MULTIPLICATION FACTORPOWER IN WATTS TO WHICH FLUX IS NORMALIZEDDATA BLOCKING FACTOR

IF NDIM.EC.1 THE GROUP VARIABLE IS BLOCKED -INTO NBLOK BLOCKS (SEE 2D RECORD BELOW) -

IF NDIM.CE.2 THE 2ND DIMENSION VARIABLE IS -BLOCKED INTO NBLOK BLOCKS (SEE 30 RECORD)-

ONE DIMENSIONAL REGULAR TOTAL FLUX (2D RECORD)

PRESENT IF NDIM.EQ.l

((FREG(I,J),I-1,NINTI),J-JL,JU) SEE STRUCTURE BELOW

NINTI*(JU - JL + 1)*MULT - NUMBER OF WORDS

DO 1 M-l,NBLOKI READ(N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-(M-1)*((NGROUP-1)/NBLOK+l)+lAND JU-MINO(NGROUP.JUP) WHERE JUP-M*((NGROUP-I)/NBLOK +1)

FREG(I.J) ONE DIMENSIONAL REGULAR TOTAL FLUX BY INTERVALAND GROUP.

r>

I

MULTI-DIMENSIONAL REGULAR TOTAL FLUX (3D RECORD)

PRESENT IF NDIM.GE.2

((FREG(I,J),I-1,NINTI),J-JL,JU) SEE STRUCTURE BELOW

NINTIMJU - JL + 1)*MULT - NUMBER Or WORDS

1X1 1 L-l .NGROUPDO 1 K-l,NINTKDO 1 M-1,NBLOK

1 READ(N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-(M-1)*((NINTJ-1)/NBLOK +1 )+lAND Jll-MINO(NINTJ.JUP) WHERE JUP-M*((NINTJ-1)/NBLOK +1)

CRCRCCCCCLCCWCCDCDCDCC —

NUCLIDES FOR PROPORTIONAL SEARCH AND SPECIAL SEARCH(4D RECORD)

PRESENT IF ISRCH.EQ.7

(NSHZ1(I),I-1,NSETS),(NSHZ2(I),I-1,NS£TS),((HNNAMS(N,I),N-I.NISOSR),1-1.NSETS),(HNSHN(J),J-1,10)

2*NSETS+MULT*(NISOSR*NSE7S+10)-NUMRER OF WORDS

C —CRCRCCCCCLCLCCWCCDCDCDCDCDCDCDCDCDCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

COARSE MESH MODIFIERS FOR DIMENSION SEARCH(3D RECORD)


(SRHDI(I),W,NCINTI),(SRHDj(J),J-l,NCINTJ),(SRHDK(K),K-l,NCINTK)-

NCINTI+NCINTJ-=-NCINTK-NUMBER OF WORDS

SRHDI(I)SRHDJ(J)SRHDK(K)

FIRST DIMENSION COARSE MESH MODIFIERSSECOND DIMENSION COARSE MESH MODIFIERSTHIRD DIMENSION COARSE MESH MODIFIERS

NSHZl(I)

NSHZ2(I)HNNAMS(N.I)

HNSHN(J) *N.A.*

*MOD*

FIRST NUMBER OF A CONSECUTIVE SET OF ZONESIF ISZOP.EQ.O, OR OF A CONSECUTIVE SET OF •SUBZONES IF ISZOP.EQ.l

LAST NUMBER OF A SET OF ZONES OR SUBZONESREFERENCE NAMES OF NUCLIDES WHOSE

CONCENTRATIONS ARE TO BE ADJUSTEDPROPORTIONATELY IN ABOVE ZONES (Afi)

SEARCH NUCLIDE REFERENCE USED AS NOTED BELOW(A6)

HNNAMS CONCENTRATIONS ADJUSTED ACCORDING TOC2 - C1*EI AND HNSHN CONCENTRATIONS ADJUSTEDACCORDING TO C2 -CI + Cl*(1.0-EI)*CMOD WHERE

EI IS THE EIGENVALUE,CI IS THE INITIAL CONCENTRATION, ANDC2 IS THE FINAL OR INTERMEDIATE VALUE OF

THE CONCENTRATION

THE ANL SEARCH IMPLEMENTATION REQUIRES THATCONCENTRATIONS BE MODIFIED FOR ALL NUCLIDES(NISOSR-NNS) PRESENT IN THE SUBZONES SPECIFIEDABOVE. THESE ARE TERMED *MODIFIER* SUBZONKS.DIRF.CT MODIFICATION OF ZONE NUCLIDES IS NOTPERMITTED. CONSEQUENTLY, NISOSR MUST EQUAL

CCCCCCCC

CC-

CCRCRCRCCCCCLCLCLCCWCCDCDCDCDCDCDCDCCCCCCCCC

CR *NKW*CRCCCCCLCCWCCDCDCC —

CEOF

NNS, THE MAXIMUM NUMBER OF NUCLIDES 1:1 ANYNUCLIDE SET, HENCE IN ANY SUBZONE. SUBZONKTO ZONE ASSIGNMENTS ARE INDICATED IN THE NZSZARRAY GIVEN -*N RECORD 3D OF DATA SET NDXSRF.

*N.A.* NUCLIDES FOR SEARCH INVOLVING WEIGHTED EIGENVALUEADJUSTMENTS TO INITIAL CONCENTRATIONS

(5D RECORD)


(NSHZ1(I),I-1,NSETS),(NSHZ2(I),I-1,NSETS),((HNNAMS(N,I),N-1,NISOSR),1-1,NSETS),((CHZDN(N,I),N-1,NISOSR),I-1,NSETS)

NSETS*(2+NISOSR*(1+MULT))-NUMBER OF WORDS

USHZl(I)

NSHZ2U)HNNAMS(N,I)

CHZDN(N.I)

FIRST NUMBER OF A CONSECUTIVE SET OF ZONESIF ISZOP.EQ.O, OR OF A CONSECUTIVE SET OFSUBZONES IF ISZOP.EQ.l

LAST NUMBER OF A SET OF ZONES OR SUBZONESREFERENCE NAMES OF NUCLIDES WHOSE

CONCENTRATIONS ARE TO BE ADJUSTED (A6)CONCENTRATION MODIFIERS

CONCENTRATIONS ADJUSTED ACCORDING TOC2 - C1+EI*CHZDN WHERE EI, CI, AND C2 AREAS DEFINED UNDER ISRCH .EQ. 7

BUCKLING MODIFIERS FOR CRITICALITY SEARCH(6D RECORP)


(BKI.MOD(I),I-! .NZONE)

NZONE*MULT-NUMBER OF WORDS

BKLMOD(I) BUCKLING MODIFIER FOR ZONE INZONE NRCH(2), THE NUMBER OF ZONES

CD FRF.G(I.J)COCC-CEOR

MULTI-DIMENSIONAL REGULAR TOTAL FLUXBY INTERVAL AND GROUP.

C.7 SEARCH

REVISED 03/09/81

SEARCH -IV (AflL)

CRITICAI.ITY SEARCH FILE

THIS VERSION OF THE SEARCH FILE INDICATES THE SEARCHOPTIONS CURRENTLY IMPLEMENTED IN THE CRITICALITV SEARCHOPTION AT ARGPNNE NATIONAL LABORATORY. EXISTING OPTIONSWHICH DO NOT APPLY ARE INDICATED BY *N.A.*. NEW OPTIONSARE INDICATED BY *NEW*. MODIFICATIONS ARE INDICATED BY*MOD* OR BY A STRING OF CHARACTERS DELIMITED BY ASTERISKS.THIS RESTRICTED SUBSET OF THE SEARCH FILE OPTIONS ISCOMPATIBLE WITH THE ORIGINAL SEARCH FILE (WITH THEEXCEPTION OF THE BUCKLING MODIFIERS RECORD WHICH DID NOTPREVIOUSLY EXIST).

C —CSCSCSCSCSCSCSCSCSCSCSCSCSCSCSCScc-c-CRcCL

FILE STRUCTURE


FILE IDENTIFICATION*******(REPEAT UNTIL NSHID.LT.O)

*NEW*

INDIVIDUAL DATASET IDENTIFIERFILE SPECIFICATIONSCOARSE MESH MODIFIERSNUCLIDES FOR PROPORTIONAL SEARCHNUCLIDES FOR SEARCH INVOLVINGWEIGHTED EIGENVALUE ADJUSTMENTSTO INITIAL CONCENTRATIONSCOMPOSITION DEPENDENT BUCKLINGMODIFIERS

ALWAYS

ALWAYSNSHID.GT.ONSHID.GT.O,ISRCH-5NSHID.GT.O, ISRCIW

NSHID.CT.O.ISRCH-9

NSHID.GT.O,ISRCH-I

FILE IDENTIFICATION

HNAMK,(HtISK(I),I-l,2),IVERS

CcwcCD.:DCDCDCDCDCC

C———CRCCLCCWCCOCDCDCDCDCDCDCDCDCDCC


HNAMEHIJSE(I)IVERSMULT

HOLLERITH FILE NAME - SEARCH - (A6)HOLLERITH USER IDENTIFICATION (Af>)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER


C —CRCCLCLCLCCWcC!)CDCDCDCD

enCDCDCDCDCDCDCD

INDIVIDUAL DATA SET IDENTIFIER (ID RECORD)

NSHID,NREC,(NSP(i),I-l,8),(SP(I),I-l,10)

20-NUMBER OF WORDS

NSHID

NREC

NSP(I)SP(1)SP(2)

SP(I)

*MOD**MOD*

*MOD*

POSITIVE INTEGER IDENTIFYING A SET OF SEARCHDATA. THIS AND FOLLOWING RF.CORDS REPEATEDUNTIL NEGATIVE NSHID TERMINATES FILE

NUMBER OF RECORDS TO SKIP TO POSITION ON NEXTINDIVIDUAL DATA SET IDENTIFIER RECORD

RESERVEDAVERAGE TIME IN SECONDS/SEARCH PASSTIME rJEMAINING AT THE START OF THE PREVIOUSSEARCH PASS.RESERVED

O

FILE SPECIFICATIONS (2D RECORD)

EFFK,DKEFF,EPSK,EPSEI,CMOD.(SRCH(I),I-1,5),ISRCH,ISZOP,NMAXNP,NCINTI,NCINTJ,NCINTK,NISOSR,NSETS,NEIRNG,ITEND,ICEND,

40-NUMBER OF WORDS

KFFK DESIRED MULTIPLICATION FACTORDKEFF USER SPECIFIED MULTIPLICATION FACTOR SLOPEEPSK CONVERGENCE CRITERION TO BE MET BY KFFKEPSEI *N.A.* CONVERGENCE CRITERION TO BE MET BY PRIMARY

VARIABLECMOD *MOD* MODIFIER APPLIED TO ALPHA (ISRCH=-2) OR

MODIFIER APPLIED TO NUCLIDE CONCENTRATIONSVARIED SPECIALLY (ISRCH-7 BF.LOW) .MAY BE.LT.O

SRCH(l) *EI(1)» PREVIOUS PASS-1 SEARCH PARAMETER (EI)SRCH(2) *EI(2)* PREVIOUS PASS SEARCH PARAMETER (EI)SRCHO) *EI(3)* MOST RECENT SEARCH PARAMETER (EI)SRC1K4) *EIMIN* USER SPECIFIED LOWER BOUND FOR SEARCH PARAMETER-

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDcnCDCDCDCDCDCDCDCDCDCDCDCDCDCDCI)CI)CDCD

SRCHO)

ISRCH

ISZOP

NMAXNP

NCINTINCINTJ

NCINTKNISOSR

NSETS

NEIRNG

ITEND

ICEND

NRCH(1>NRCH(2)NRCH(3)

*BIMAX*

*N.A.*

*N.A.*

*GT 0**0NLY*

*-NNS**0NLY*

*M0D*

*N.A.*

*N.A.*

*N.A.*

*N.A.»

*NPAFS**N7.0NE*•IE0TP*

USER SPECIFIED UPPER BOUND FOR SEARCH PARAMKTER-

(EI)TYPE OF SEARCH

0- NOT DEFIMED1- BUCKLING SEARCH2- ALPHA SEARCH5- DIMENSION SEARCH7- NUCLIDE CONCENTRATION SEARCH BY

PROPORTIONAL ADJUSTMENTS OF SELECTEDINITIAL CONCENTRATIONS

9- NUCLIDE CONCENTRATION SEARCH BY ADDING -WEIGHTED EIGENVALUE ADJUSTMENTSTO SELECTED INITIAL CONCENTRATIONS

SUBZONE OPTION FOR ir "XH - 7 OR 90- SEARCH DATA IS BY ZONE1- SEARCH DATA IS BY SUBZONE

MAXIMUM NUMBER OF NEUTRONICS PROBLEMS OR TRIAL -EIGENVALUES ALLOWED IN A SEARCH. A ZEROHERE SPECIFIES A DIRECT SEARCH.

NUMBER OF FIRST DIMENSION COARSE MESH INTERVALS-NUMBER OF SECOND DIMENSION COARSE MESH

INTERVALSNUMBER OF THIRD DIMENSION COARSE MESH INTERVALS-NUMBER OF ISOTOPES OR NUCLIDES INVOLVED IN

CONCENTRATION SEARCH (ISRCH - 7 OR 9)NUMBER OF SPECIFICATION SETS IN CONCENTRATION -

.SEARCH (ISRCH - 7 OR 9)EIGENVALUE (EI) RANGE RESTRICTIONS. SEARCH

TERMINATED IF SPECIFIED RANGE IS VIOLATED. --1 EI.LT.O0- NO RESTRICTION ON EI1- EI.GT.EIMIN AND EI.LT.EIMAX2- ET.GT.l

TERMINATION OPTION ON ITERATIVE PROCESS. SEARCH-IS LIMITED BY NMAXNP,NUMBER OF OUTERITERATIONS,OR OTHER PARAMETER,THEN0- NO RESTRAINT1- TERMINATE IF CONVERGENCE CRITERIA ARE

NOT MET2- IF CONVERGENCE CRITERIA ARE NOT MET,

TERMINATE ONLY IF PROBLEM IS NOTCONVERGING.

TERMINATION OPTIONS ON NUCLIDE CONCENTRATIONS -0- TERMINATE IF ANY NUCLIDE CONCENTRATION -

BECOMES NEGATIVE AT ANY STAGE OF THECALCULATION

1- TERMINATE IF ANY NUCLIDE CONCENTRATION -IS NEGATIVE AT THE END OF THE SEARCH

2- ALLOW NEGATIVE NUCLIDE CONCENTRATIONSSEARCH PASS NUMBER, INITIALLY 0NUMBER OF ZONES (ISRCH - 1)SEARCH PARAMETER EDIT OPTIONTWO DIGIT NUMBER (IF) WHERE

CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

n>CDCDCDCDCDCDCDCDCDCDCDCDCDCDCPCDCDCC

NRCH(4) *IEDTQ*

NRCH(5) *IBOUND*

I CONTROLS INTERMEDIATE PASS PARAMETER EDITSF CONTROLS F.NAL PASS PARAMETER EDITS

THE INTEGERS I AND F ARE ASSIGNED ONE OF THEFOLLOWING VALUESO...NOEDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILESEARCH QUANTITY EDIT OPTIONTWO DIGIT NUMBER (IF) WHERE

I CONTROLS INTERMEDIATE PASS QUANTITY EDITSF CONTROLS FINAL PASS QUANTITY EDITS

THE INTEGERS I AND F ARE ASSIGNED ONE OF THEFOLLOWING VALUES0...NOEDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILESEARCH PARAMETER iJANGE SENTINEL0...RANGE NOT EXCEEDEDN...RANGE EXCEEDED N TIMES

NRCH(6) *IHIST(1)*PREVIOUS PASS-1 (N) AND METHOD (M) -10N+MNRCH(7) *IHIST(2)*PREVI0US PASS (N) AND METHOD (M) -10N+MNRCH(8) *IHIST(3)*PRESENT PASS (N) AND METHOD (M)-10N+MNRCH(9) *IC0NV* SEARCH TERMINATION SENTINEL

0...INITIALIZED VALUE1...SEARCH CONVERGED2...SEARCH TERMINATED, MAXIMUM SEARCH PASSES

ACHIEVED3...POOR CHOICE OF SEARCH PARAMETERSA...INSUFFICIENT TIME FOR NEXT SEARCH PASS5...NEUTRONICS TERMINATED FOR INSUFFICIENT TIME-6...RESTART, PREVIOUS TERMINATION CONDITION

UNKNOWNRESERVED

SRCH1(1)*KEFF(1)* PREVIOUS PASS-1 MU .TIPLICATION FACTORSRCH1(2)*KEFF(2)* PREVIOUS PASS MULTIPLICATION FACTORSRCH1(3)*KEFF(3)* MOST RECENT MULTIPLICATION FACTORSRCH1(4)*DXNM2* PREVIOUS PASS-1 DX

PREVIOUS PASS DXMOST RECENT DXPREVIOUS PASS-1 K-EFFECTIVE CHANGEPREVIOUS PASS K-EFFECTIVE CHANGEMOST RECENT K-EFFECTIVE CHANGE

N3

NRCH(IO)

SRCH1(5)*DXNMI*SRCH1(6)*DXNTH*SRCH1(7)*DKNM2*SRCH1(8)*DKNM1*SRCH1(9)*DKNTH*

C.fi ATFLUX

c414*****4****t****************4**************************A*************

C REVISED 11/30/76

C

CF ATFLUX-IVCE ADJOINT TOTAL FLUXESCC***********************************************************************CDCDCD

CRCCLCcwcCDCDCDCDCDCDCC

CRCCLCCWCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCC-CRC

ORDER OF GROUPS IS ACCORDING TO INCREASINGENERGY. NOTE THAT DOUBLE PRECISIONFLUXES ARE GIVEN WHEN MULT.EQ.2

FILE IDENTIFICATION




HOLLERITH FILE NAME - ATFLUX - (A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER



NDIM,NGROUP,NINTI,NINTJ,NINTK,ITER,EFFK,AnUM,NBLOK

9 -NUMBER OF WORDS

NDIMNGROUPNINTININTJNINTK

ITER

EFFKATOMNBLOK

NUMBER OF DIMENSIONSNUMBER OF ENERGY GROUPSNUMBER OF FIRST DIMENSION FINE MESH INTERVALS -NUMBER OF SECOND DIMENSION FINF. MESH INTERVALS -NUMBER OF THIRD DIMENSION FINE MESH INTERVALS. -NINTK.EO.l IF NDIM.LE.2OUTER ITERATION NUMBER AT WHICH FLUX WASWRITTENEFFECTIVE MULTIPLICATION FACTORRESERVEDDATA BLOCKING FACTOR

IF NDIM.EO.l THE GROUP VARIABLE IS BLOCKED -INTO NBLOK BLOCK? (SEE 2D RECORD BELOW) -

IF NDIM.GE.2 THE 2ND DIMENSION VARIABLE IS -BLOCKED INTO NBLOK BLOCKS (SEE 3D RECORD)-

ONE DIMENSIONAL ADJOINT TOTAL FLUX (2D RECORD)

CCCCLCCWccC 1

cCCCCcCDcncccCRcCCcCLcCWccccC 1

cCCCC

cCDCDccCKOF

PRESENT IF NDIM.E0.1

((FADJ(I,J),I-1,NINTI),J-JL,JU) SEE STRUCTURE BELOW

NINTI*(JU - JL + l)*Ml'LT - NUMBER OF WORDS

DO 1 M-l,NBLOKREAD(N) *LIST AS ABOVE*

WIT'< M AS THE BLOCK INDEX, JL-(M-1 )*( (NGROUP-1 )/NBLOK+l )+lAND JU-MINO(NGROUP,JUP) WHERE JUP-M*((NGROUP-1)/NBLOK+l )

FADJ(I.J) ONE DIMENSIONAL ADJOINT TOTAL FLUX BY INTERVALAND GROUP.

MULTI-DIMENSIONAL ADJOINT TOTAL FLUX (3D RECORD)

PRESENT IF NDIM.GE.2

((FADJ(I,J),I-1,NINTI)J-JL,JU) SEE STRUCTURE BELOW

NINTI*(JU - JL + 1)*MULT - NUMBER OF WORDS

DO 1 L-l,NGROUP

DO I K=l,NINTKDO 1 M-l,NBLOKREAD(N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-(M-1 )*( (NINTJ-1 )/NBLOK +D+1AND JU-MINO(NINTJ.JUP) WHERE JUP-M*((NINTJ-1)/NBLOK +1)

CO

FADJ(I.J) MULTI-DIMENSIONAL ADJOINT TOTAL FLUXBY INTERVAL AND GROUP.

C.9 RZFLUX

C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *C REVISED 1 1 / 3 0 / 7 6CCF R7.FLUX-IVCCE REGULAR ZONE FLUX BY CROUP, AVERAGED OVER EACH ZONECCM*********************************************************************

c-CRC ~~CLCCWCCDCDCDCDCDCDCCC —CRCCLCLCCWCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

FILE IDENTIFICATION

HNAME,(HUSE(I),I«1,2),IVERS


HNAHEHIISE(I)IVERSMULT

HOLLERITH FILE NAME - RZFLUX - (A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER



TIME,P0WER,VOL,EFFK,EIVS,DKDS,TNL,TNA,TNSL,TNBL,TNBAL,TNCRA.I(X(I),I-I,3),NBLOK,ITPS,NZONE,NGROUP,NCY

20-NUMBER OF WORDS

TIMEPOWER

VOLEFFKEIVSDKDSTNLTNATNSLTNBLTNBALTNCRAX(I),1-1,3NBLOK

ITPS

REFERENCE REAL TIME, DAYSPOWER LEVEL FOR ACTUAL NEUTRONICS PROBLEM,WATTS-

THERMALVOLUME OVER WHICH POWER WAS DETERMINED, CCMULTIPLICATION FACTOREIGENVALUE OF SEARCH OF SEARCH PROBLEMDERIVATIVE OF SEARCH PROBLEMTOTAL NEUTRON LOSSESTOTAL NEUTRON ABSORPTIONSTOTAL NEUTRON SURFACE LEAKAGETOTAL NEUTRON BUCKLING LOSSTOTAL NEUTRON BLACK ABSORBER LOSSTOTAL NEUTRON CONTROL ROD ABSORPTIONSRESERVEDDATA BLOCKING FACTOR. THE GEOMETRIC ZONE

VARIABLE IS BLOCKED INTO NBLOK BLOCKS.ITERATIVE PROCESS STATE

-0, NO ITERATIONS DONK-I, CONVERGENCE SATISFIED-2, NOT CONVERGED, BUT CONVERGING•3, NOT CONVERGED, NOT CONVERGING

CI)CI)CDCCCCRCCI.

cCWccC I

cCCCC

cCDCDCCCEOF

N7.0NENGROUPNCY

NUMBER OF GEOMETRIC ZONESNUMBER OF NEUTRON ENERGY GROUPSREFERENCE COUNT (CYCLE NUMBER)

FLUX VALUES (20 RECORD)

((7.0F(K,.I),K-l.NGROUP),J-JL.JU)

NGRO1IP*(JU-JL+1) - NUMBER OF WORDS

-SEE STRUCTURE BELOW

DO 1 M-l .NBLOKRF.AD(N) *LIST AS ABOVE*

WITH M AS THE BLOCK INDEX, JL-(M-1)*((NZONE-1)/NBLOK +1)+lAND JU-MINO(NZONE.JUP) WHERE JUP-M*((NZONE-1)/NBLOK +1)

ZGF(K.J) REGULAR ZONE FLUX BY GROUP, AVERAGED OVER ZONENEUTRONS/SEC-CM**2

Appendix D

DIF3D CODE-DEPENDENT BINARY INTERFACE FILE DESCRIPTIONS

D.I COMPXS

C***********************************************************************

C

C PREPARED 3/7/78 AT ANLC LAST REVISED 12/5/80CCF COHPXSCE MACROSCOPIC COMPOSITION CROSS SECTIONSC

c***********************************************************************

c-cscscscscscscscscscscscscscscscscc~

CDCDCDCDCI)CDCDCDCDCDCDCDCDCD

FTLE STRUCTURE


SPECIFICATIONS ALWAYSCOMPOSITION INDEPENDENT DATA ALWAYS

********* (REPEAT FOR ALL COMPOSITIONS)* COMPOSITION SPECIFICATIONS ALWAYS* ****** (REPEAT FOR ALL ENERCY GROUPS* * IN THE ORDER OF DECREASING* * ENERGY)* * COMPOSITION MACROSCOPIC GROUP ALWAYS* * CROSS SECTIONS*********

FISSION POWER CONVERSION FACTORS ALWAYS

NGR01IPICHI

NUP(I)

NDN(I)

NUMBER OF ENERGY GROUPS.PROMPT FISSION SPECTRUM FLAG FOR THISCOMPOSITION. ICHI — 1 IF COMPOSITION USES THESET-WIDE PROMPT CHI GIVEN IN SET CHI RECORD(BELOW). ICHI-0 IF COMPOSITION IS NOTFISSIONABLE. ICHI-1 FOR COMPOSITION PROMPT CHIVECTOR. TCHI-NGROUP FOR COMPOSITION PROMPT CHIMATRIX.NUMBER OF GROUPS OF UPSCATTERING INTO GROUP IFROM LOWER ENERGY GROUPS FOR THE CURRENTCOMPOSITIONNUMBER OF GROUPS OF DOWNSCATTERING INTO GROUP IFROM HiGHFR ENERGY I.ROUPS FOR THE CURRENTCOMPOSITION

CDCDCDCDCDCDCD

CCRCCLCCWCcnCDcnCDCDCDCDCDCDC

ISCHI

NFAMMULT

PROMPT FISSION SPECTRUM FLAG. ISCHI-0 IFTHERE IS NO SET-WIDE PROMPT CHI. ISCHI-1THERE IS A SET-WIDE PROMPT CHI VECTOR.ISCHI»NGROUP IF THERE IS A SET-WIDE PROMPTCHI MATRIX.NUMBER OF DELAYED NEUTRON FAMILIES.2 FOR IBM MACHINES, 1 OTHERWISE.

IF

SPECIFICATIONS (TYPE I)

NCMP,NCROUP,ISCHI,NFCMP,MAXUP,MAXDN,NFAM,NDUM1,NDUM2,NDUM3

10

NCMPNFCMPMAXUP

MA:;DN

NDUM1NDUM2NDUM3

NUMBER OF COMPOSITIONS.;JUWBER OF FISSIONABLE COMPOSITIONS.MAXIMUM NUMBER OF GROUPS OF UPSCATTERING FORTHE SET.MAXIMUM NUMBER OF GROUPS OF DOWNSCATTERINGFOR THE SET.RESERVED.RESERVED.RESERVED.

•

I—"I

CCRCCCCCLCLCLCCWCCDCDCDCDCDCDCI)CDCD

COMPOSITION INDEPENDENT DATA (TYPE 2)

ALWAYS PRESENT

((CHI(I,J),I-1,ISCHI),J-1,NGROUP),(VEL(J),J-1,NGROUP),I(EMAX(J),.J-1 ,NGROUP),EMIN,((CHID(J,K),J-1 .NGROIIP) ,K-1 .NFAM),2(FLAM(K),K-1,NFAM),(NKF.\M(J),J-1 .NCMP)

MULT*(NGROIIP*(ISCi!I+2+NFAM)+l+NFAM)+NCMP

CHT

VELKMAXEMINCHID

PROMPT FISSION FRACTION INTO GROUP J FROMGROUP I. IF ISCHI-1, THE LIST REDUCES TO(CHI(J).J-l.NGROUP), WHERE CHI(J) IS THEFISSION FRACTION INTO GROUP J.MEAN NEUTRON VELOCITY IN GROUP J (CM/SEC).MAXIMUM ENERGY BOUND OF GROUP J (EV).MINIMUM ENERGY BOUND OF SET (EV).FRACTION OF DELAYED NEUTRONS EMITTED INTONEUTRON ENERGY GROUP J FROM PRECURSOR

CDCDCDCDCDCDCC —

FLAM

NKFAM

FAMILY K.DELAYED NEUTRON PRECURSOR DECAY CONSTANTFOR FAMILY K.NUMBER OF FAMILIES TO WHICH FISSION INCOMPOSITION J CONTRIBUTES DELAYED NEUTRONPRECURSORS.

CRCCCCCLCLCCCCcwcCDCDCC —

COMPOSITION SPECIFICATIONS (TYPE 3)

ALWAYS PRESENT

ICHI,(NUP(I),I-1,NGROUP),(NDN(I),I-1,NGROUP),1(NUMFAM(I),I-1,NKFAMI)

NKFAMI • NKFAM(K)

1+2*NGROUP+NKFAMI

NUMFAM FAMILY NUMBER OF THE I-TH YIELD VECTOR INARRAY SNUDEL(I)..

C-CRCCCCCLCLCLCCCCCCCCCWCWCWcCDCDCDCDCDCDCDCDCD

COMPOSITION MACROSCOPIC GROUP CROSS SECTIONS (TYPE 4)

ALWAYS PRESENT

XA,XTOT,XREM,XTR,XF,XNF,(CHI(I),I-1,ICHI),l(XSCATU(I),T«l,NUMUP),XSCATJ,(XSCATD(I),I-l,NUMDN),2PC,A!,B1,A2,B2,A3,B3,(SNUDEL(I),I-1,NKFAMI),XN2N

NUMUP - NUP FOR THE CURRENT GROUPNUMON - NDN FOR THE CURRENT GROUPNKFAMI - NKFAM(K)

M11LT*(15+ICHI+NUMUP+NUMDN+NKFAMI) IF ICHI.GT.OMUL"T*(1 5+NUMUP+NUMDN+NKFAMI) IF ICHI.EQ.-lrtULT*(13+NUMUP+NUMDN+NKFAMI) IF ICHI.F.Q.O

XA.XTOTXRF.M

XTRXF

XNF

ABSORPTION CROSS SECTION.TOTAL CROSS SECTION.REMOVAL CROSS SECTION, TOTAL CROSS SF.CTIONFOR REMOVING A NEUTRON FROM GROUP J DUE TO ALLPROCESSES.TRANSPORT CROSS SECTION.FISSION CROSS SECTION, PRESENT ONLY IFICHI.NE.O.TOTAL NUMBER OF NEUTRONS EMITTED PEk FISSION

CDCDCDCDCDCDCDCDCDCDCDCDCDCI)CDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

cnCD

cCNCNCNCNCNC

CHI

XSCATU

XSCAT.I

XSCATD

PC

Al

Bl

A2

B2

A3

B3

SNUDEL

XN2N

TIMES XF, PRESENT ONLY IF ICHI.NE.O.PROMPT FISSION FRACTION INTO GROUP J FROMGROUP I, PRESENT ONLY IF ICHI.GT.O. IF ICHI-1, -THE LIST REDUCES TO THE SINGLE NUMBER CHI,WHICH IS THE PROMPT FISSION FRACTION INTOGROUP J.TOTAL SCATTERING CROSS SECTION INTO GROUP JFROM GROUPS J+NUP(J),J+NUP(J)-1 ,... ,J+2,J+I,PRESENT ONLY IF NUP(J).GT.O.TOTAL SELF-SCATTERING CROSS SECTION FROMCROUP J TO GROUP J.TOTAL SCATTERING CROSS SECTION INTO CROUP JFROM GROUPS J-l,J-2,...,J-NDN(J), PRESENTONLY IF NDN(J).GT.O.PC TIMES THE GROUP J REGION INTEGRATEDFLUX FOR THE REGIONS CONTAINING THE CURRENTCOMPOSITION YIELDS THE POWER IN WATTS IN THOSE -REGIONS AND ENERGY GROUP J DUE TO FISSIONSAND NON-FISSION ABSORPTIONS.FIRST DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT MULTIPLIER.FIRST DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT ADDITIVE TERM.SECOND DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT MULTIPLIER.SECOND DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT ADDITIVE TERM.THIRD DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT MULTIPLIER.THIRD DIMENSION DIRECTIONAL DIFFUSIONCOEFFICIENT ADDITIVE TERM.NUMBER OF DELAYED NEUTRON PRECURSORS PRODUCED -IN FAMILY NUMBER NUMFAM(I) PER FISSIONIN GROUP J.N.2N REACTION CROSS SECTION

THE MACROSCOPIC XN2N(J) TIMES THE FLUX IN GROUP-J GIVES THE RATE AT WHICH N.2N REACTIONS OCCUR -IN GROUP J. THUS, FOR N,2N SCATTERING,XN2N(J)-0.5*(SUM OF SCAT(J TO G)) SUMMED OVER -ALL G WHERE SCAT IS THE N,2N SCATTERING MATRIX.-

CRC.CCcCLCCWc

FISSION POWKR CONVERSION FACTORS (TYPE 5)

ALWAYS PRESENT

(FPWS(I).I-l.NCMP)

MULT*NCMP

CDV*

c—

FPWS FISSIONS/WATT-SECOND FOR EACH COMPOSITION

CEOF

D.2 DIF3D

c***********************************************************************C REVISED 5/26/83CCF DIF3DCE ONE-, TWO-, AND THREE-DIMENSIONAL DIFFUSION THEORYCE MODULE DEPENDENT BINARY INPUTC(;**********«************•******************•****************************

C —CRCCLCCWCCDCDCDCDCI)cncc—

FILE IDENTIFICATION



HNAMF. HOLLERITH FILE NAME - DIF3D - (A6)

HUSE(I) HOLLERITH USER IDENTIFICATION (A6)IVERS FILE VERSION NUMBERMULT DOUBLE PRECISION PARAMETER


PROBLEM TITLE, STORAGE AND DUMP SPECIFICATIONS (ID RECORD)

(TITLF.(I),I-1,11),MAXSIZ,MAXBLK,IPRTNT

3+ll*MULT-NUMBER OF WORDS

C —CRCCLcCWcCDCDCDCDCDCDCDCDCDCD

TITLEMAXSIZ

MAXBLK

IPRINT

ANY ALPHANUMERIC CHARACTERSPOINTR CONTAINER ARRAY SIZE IN FAST COREMEMORY (FCM) IN REAL*8 WORDSPOINTR CONTAINER ARRAY SIZE IN EXTENDED COREMEMORY (ECM) IN REAL*8 WORDSPOINTER DEBUGGING EDIT0...NO DEBUGGING PRINTOUT1...DEBUGGING DUMP PRINTOUT2...DEBUGGING TRACE PRINTOUT3...BOTH DUMP AND TRACE PRINTOUT

CRCCLCLCLCLCCWCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDcrCDCD

cnCDCDCDC!)CDCDCDCDCDCDCDCD

r.nC!)CDCDCD

PROBLEM INTEGER CONTROL PARAMETERS (2D RECORD)

IPROBT,ISOLNT,IXTRAP.MINBSZ,NOUTMX,IRSTRT,LIMTIM,NUPMAX,IOSAVE, -IIOMEC,INRMAX,NUMORP,IRETRN,(IEDF(I),I-1,10).NOUTBQ,IOFLUX,2NOEDIT,NOD3ED,ISRHED,NrN,NSWMAX,IAPRX,IAPRXZ,NCMI,ISEXTR,NZSWP, -3NCMRZS,(IDUM(I).1-1,9)

45-NUMBER OF WORDS

IPROBT

ISOLNT

IXTRAP

MINBSZ

NOUTMX

IRSTRT

LIMTIM

NUPMAX

inSAVE

IOMKC

INRMAX

PROBLEM TYPEO...K-EFFECTIVE PROBLEM1...FIXED SOURCE PROBLEMSOLUTION TYPEO...REAL SOLUTION1...ADJOINT SOLUTION2...BOTH REAL AND ADJOINT SOLUTIONCHEBYSHEV ACCELERATION OF OUTER ITERATIONSO...YES, ACCELERATE THE OUTER ITERATIONS1...N0 ACCELERATION

MINIMUM PLANE-BLOCK (RECORD) SIZE IN REAL*8WORDS FOR I/O TRANSFERS IN THE CONCURRENT •ITERATION STRATEGYOUTER ITERATION CONTROL

-3...BYPASS DIF3D MODULE.-2...PERFORM NEUTRONICS EDITS ONLY-1...PERFORM NEUTRONICS EDITS AND CALCULATE

OPTIMUM OVERRELAXATION FACTORS ONLY•GE.O...MAXIMUM NUMBER OF OUTER ITERATIONS

RESTART FLAGO...THIS IS NOT A RESTART1...THIS IS A RESTARTJOB TIME LIMIT, MAXIMUM (CP AND PP (OR WAIT)) -PROCESSOR SECONDS ?-NUMBER OF UPSCATTER ITERATIONSPER OUTER ITERATIONCONCURRENT ITERATION EFFICIENCY OPTION0...PERFORM THE ESTIMATED NO. OF INNER

ITERATIONS FOR EACH GROUP1...AVOID THE LAST PASS OF INNER ITERATIONS

IN THOSE GROUPS FOR WHICH THE NUMBER OFINNER ITERATIONS IN THE LAST PASS ARE LESS -THAN A CODE DEPENDENT THRESHOLD

OPTIMUM OVERRELAXATION FACTOR ESTIMATIONACCK .ERATION OPTION.0...N0 ACCELERATION.1...ASYMPTOTIC EXTRAPOLATION OF ITERATIONS IN -

THE OPTIMUM OVERRELAXATION FACTORCALCULATION.

MAXIMUM NUMBER OF ITERATIONS PERMITTED DURING -

•

CDCDCDCDCD

cnCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCOCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

NUMORPIRFTRN

TEDF(l)

IEDF(2)

IEDF(3)

IEDF(4)

IEDF(5)

THE OPTIMUM OVERRF.LAXATION FACTOR ESTIMATIONPROCESS FOR EACH INKER (WITHIN CROUP)ITERATION MATRIX.NUMBER OF OPTIMUM OVERRELAXATION FACTORSFLAG INDICATING CAUSE OF OUTER ITERATIONTERMINATION0...INITIAL VALUE, PRIOR TO OUTER ITEr,,,rT0NS1...OUTER ITERATIONS CONVERGED2...MAXIMUM NUMBER OF OUTER ITERATIONS

PERFORMED1...TIME LIMITPROBLEM DESCRIPTION EDIT (IN ADDITION TO USER -INPUT SPECIFICATIONS WHICH ARE ALWAYS EDITED0...NO EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEGEOMETRY (REGION TO MESH INTERVAL) MAP EI1IT0...NO EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEGEOMETRY (ZONE TO MESH INTERVAL) MAP F.DIT0...N0 EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEMACROSCOPIC CROSS SECTION EDITENTER TWO DIGIT NUMBER SP WHERE

S CONTROLS THE . MATTERING CROSS SECTIONS EDIT -P CONTROLS TH7 PRINCIPAL CROSS SECTIONS EDIT

THE INTEGERS S AND P SHOULD BE ASSICNED ONE OF -THE FOLLOWING VALUES (LEADING ZEROES AREIRRELEVANT)0...NO EDITS1... PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FTLE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEBALANCE EDITSENTER 3 DIGIT NUMBER GBR WHERE

G CONTROLS GROUP BALANCE EDITS INTEGRATED OVER -THE REACTOR

B CONTROLS REGION BALANCE EDIT BY GROUPR CONTROLS REGION BALANCE EDIT TOTALS

(INCLUDING NF.T PRODUCTION AND ENERGY MEDIANS)-

THE INTEGERS G, B, AND R SHOULD BE ASSIGNED

CDCDCDCDCDCDCDCDCDCD

cnCDCD

cnCDCD

cnCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCI)CDCDCDCDCDCDCDCD

cnCD

cncnCDCI)

IEDF(6)

IF.nF(7)

IEDF(8)

IKDF(9)

IF.nF(lO)

ONE OF THE FOLLOWING VALUES (LEADING ZEROESARE IRRELEVANT)0...NO EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILESPOWER EDITSENTER 2 DIGIT NUMBER RM WHERE

R CONTROLS REGION POWER AND AVERAGE POWEREDITS

M CONTROLS POWER DENSITY BY MESH INTERVALEDIT (PWDINT)

THE INTEGERS R AND M SHOULD BE ASSIGNED ONE OF •THE FOLLOWING VALUES (LEADING ZEROES AREIRRELEVANT)0...N0 EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILETOTAL FLUX EDITSENTER 3 DIGIT INTEGER RMB WHERE

R CONTROLS TOTAL FLUX EDIT BY REGION AND GROUPINCLUDING GROUP AND REGION TOTALS

M CONTROLS TOTAL FLUX EDIT BY MESH INTERVALINTEGRATED OVER GROUP

B CONTROLS TOTAL FLUX EDIT BY MESH INTERVALAND GROUP (RTFLUX OR ATFLUX)

THE INTEGERS R, M, AND B SHOULD BE ASSIGNEDOFF. OF THE FOLLOWING VALUES (LEADING ZEROESARE IRRELEVANT)0...NO EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT TILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEZONE AVERAGED FLUX EDIT0...NO EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE EDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILEREGION AVERAGED FLUX EDIT0...N0 EDITS1...PRINT EDITS2...WRITE EDITS TO AUXILIARY OUTPUT FILE3...WRITE TDITS TO BOTH PRINT AND AUXILIARY

OUTPUT FILESTANDARD INTF.RFACE FILES TO BE WRITTEN IN

toIto

CDCDCDCDCDCDCDCDCDCDCDCDCD

enCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

enCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCD

NOUTBQ

IOFLUX

NOEDIT

NOD3ED

ISRHED

NSNNSWMAX

IAPRX

IAPRX7.

NCMI

ISEXTR

NZSWP

ADDITION TO RTFLUX AND/OR ATFLliXO...NONE'....WRITE PWDINT2...WRITE RZFLUX3...WRITE BOTH PWDINT AND RZFLUXNUMBER OF OUTER (POWER) ITERATIONS BEFOREASYMPTOTIC EXTRAPOLATION OF NEAR CRITICALSOURCE PROBLEM.FLAT FLUX GUESS SENTINEL.0...FLAT FLUX GUESS -1.01...FLAT FLUX GUESS - 0.0PRINT FILE MASTER CONTROL FLAG0...PRINT GENERAL RUN INFORMATION AND

REQUESTED EDITS1...SUPPRESS ALL OUTPUT EXCEPT DIAGNOSTIC

EDITS AND THE ITERATION HISTORY2...SUPPRESS ALL OUTPUT EXCEPT DIAGNOSTIC EDITSD3EDIT FILE MASTER CONTROL FLAC0...WRITE REQUESTED EDITS ON D3EDIT FILE1...DO NOT WRITE D3EDIT FILEMASTER NF.UTRONICS EDIT SENTINEL DURINGCRITICALITY SEARCHES ONLY.

-1...SUPPRESS ALL DIF3D EDITS EXCEPT ITERATION -

HISTORY AND ERROR DIAGNOSTICS.O...EDIT INPUT DATA ON 1ST SEARCH PASS, OUTPUT -

FLUX INTEGRALS UPON CONVERGENCE OR UPONACHIEVING THE MAXIMUM SEARCH PASS LIMIT.

N...ALSO EDIT SPECIFIED DIF3D EDITS EVERY N-TH -SEARCH PASS.

SN ORDER (TRANSPORT OPTION)MAXIMUM ALLOWED NUMBER OF LINE SWEEPS PER LINE •PER INNER ITERATION (TRANSPORT OPTION).ORDER OF NODAL APPROXIMATION IN HEX-PLANE(NODAL HEXAGONAL GEOMETRY OPTION)2...NH2 APPROXIMATION3...NH3 APPROXIMATION4...NH4 APPROXIMATIONORDER OF NODAL APPROXIMATION IN 7.-DIRECTI0N(NODAL HEXAGONAL GEOMETRY OPTION)2...QUADRATIC APPROXIMATION3...CUBIC APPROXIMATIONCOARSE-MESH REBALANCE ACCELERATION CONTROL(NODAL HEXAGONAL GEOMETRY OPTION)

-1...NO COARSE-MESH REBALANCE ACCELERATION.GF..0...NUMBER OF COARSE-MESH REBALANCE ITERATIONS •

PER OUTER ITERATIONASYMPTOTIC SOURCE EXTRAPOLATION OF OUTERITERATIONS (NODAL HEXAGONAL GEOMETRY OPTION)0...APPLY ASYMPTOTIC SOURCE EXTRAPOLATION TO

OUTER ITERATIONS1...N0 ASYMPTOTIC SOURCE EXTRAPOLATIONNUMBER OF AXIAL PARTIAL CURRENT SWEEPS PERGROUP PER OUTER ITERATION (NODAL HEXAGONALGEOMETRY OPTION)

CDCDCI)CC—

NCMRZS

IDUM(I)

NUMBER OF AXIAL C0ARfE-.'l5H REBALANCENUMBER PAIRS (NODAL dKVAGONAL GEOMETRY OPTION)RESERVED

C —CRCRCCLCLCCWCCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDcnCDCC-

C-CRCcccCLCcwcCDCDCD

CONVERGENCE CRITERIA AND )THER FLOATING POINT DATA(3D RECORD)

EPS1,EPS2,EPS3,EFKK,FISMIN,PSINRM,POWINISICBAR,EFFKQ,IEPSWP,(DUM(I),I»1,20)

30*MULT»N"MBER OF WORDS

EPS1

EPS2

EPS3

EFFKF1SMIN

PSINRM

POWINSTGBAREFFKO

EPSWP

1XJM( I)

EIGENVALUE CONVERGENCE CRITERION FOR STEADYSTATE CALCULATIONPOINTWISE FISSION SOURCE CONVERGENCE CRITERIONFOR STEADY STATE SHAPE CALCULATIONAVERAGE FISSION SOURCE CONVFRGENCE CRITERIONFOR STEADY STATE SHAPE CALCULATIONK-EFFECTIVE OF REACTORANY POINTWISE FISSION SOLRCE WILL BE NEGLECTEDIN THE POINTWISE FISSION SOURCE CONVERGENCETEST IF IT IS LESS THAN THIS FACTOR TIMESTHE R.M.S. FISSION SOURCEERROR REDUCTION FACTOR TO BE ACHIEVED BY EACHSERIES OF INNER ITERATIONS FOR EACH GROUPDURING A SHAPE CALCULATIONSTEADY STATE REACTOR POWER (WATTS)DOMINANCE RATIOEIGENVALUE OF THE HOMOGENEOUS PROBLEMCORRESPONDING TO THE NEAR CRITICALSOURCE PROBLEM. (PERTINENT WHEN NOUTBQ.GT.O)LINE SWEEP CONVERGENCE CRITERION (TRANSPORTOPTION)RESERVED

I

OPTIMUM OVF.RRELAXATION FACTORS (4D RECORD)

PRESENT IF NUMORP.GT.O

(OMEGA(I),1-1.NUMORP)

N1'MORP*MULT-NUMBER OF WORDS

OMKGA(I) OPTIMUM OVERRF.LAXATION FACTOR FOR GROUP ION THIS FILE, OPTIMUM OVERRF.LAXATION FACTORSARE — A L W A Y S — ORDERED BY THE — R E A L PROBLEM—

HNAME,(HirSE(I),I-l ,2),IVERS


HNAMF.HUSE(I)IVERSMULT

HOLLERITH FILE NAME - PWDINT - (A6)HOLLERITH USER IDENTIFICATION (Aft)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER


CIO PWDINT

C***********************************************************************

C REVISED 11/30/76

CCF PWDINT-IVCCF. POWER DENSITY BY INTERVALCC***********************************************************************

CR FILE IDENTIFICATIONCCLCCVcCDCDCDCDCDCDCC-C-CRCCLCCWCCDCDCDCDcnCDCDCDCDCDCc—c-CRCCLCCWCCScs


TIME, POWER, VOL, NINTI,NINTJ,NINTK,NCY,NBLOK

8-NUMBER OF WORDS

TIMEPOWER

VOLNINTININT.ININTKNCYNBLOK

REFERENCE REAL TIME, DAYSPOWER LEVEL FOR ACTUAL NEt/TRONTCS PROBLEM,

WATTS THERMALVOLUME OVER WHICH POWER WAS DETERMINED,CCNUMBER OF FIRST DIMENSION FINE INTERVALSNUMBER OF SECOND DIMENSION FINE INTERVALSNUMBER OF THIRD DIMENSION FINE INTERVALSREFERENCE COUNT (CYCLE NUMBER)DATA BLOCKING FACTOR. THE SECOND DIMENSION

VARIABLE IS BLOCKED INTO NBLOK BLOCKS.

POWER DENSITY VALUES (20 RECORD)

((PWR(I.J), 1-1,NINTI),J-JL.JU) SEE STRUCTURE BELOW-

NINTI*(JU - JL + 1) - NUMBER OF WORDS

DO 1 K-l,KMDO I M-l,NBLOK

CS 1 READ(N) *LIST AS ABOVE*

CCCCCcCDCCCF.OF

WIT« M AS THE BLOCK INDEX, JL-(M-I)*((NINTJ-I)/NBLOK +1)+lANb JU«MINO(NINTJ,JUP) WHERE JUP=M*((NINTJ-1)/NBLOK +1)

PWR(l.J) POWER DENSITY BY INTERVAL, WATTS/CC

IO

CDCC

C —CRCRCCCCaccwcCDCDCDCDCCNCNCNCNCNCC —

ORDERING

AXIAL COARSE-MESH REBALANCE BOUNDARIES FOR NODALHEXAGONAL GEOMETRY OPTION (5D RECORD)

PRESENT IF NCMRZS.GT.O

(ZCMRC(I),I-1,NCMRZS),(NZINTS(I),I-1.NCMRZS)

NCMRZS*(MIJLT+1)-NUMBER OF WORDS

ZCMRC(I)

NZINTS(I)

UPPER Z-COORDINATE OF AXIAL COARSE-MESHREBALANCE SPECIFICATION INTERVAL I.NUMBER OF AXIAL COARSE MESH REBALANCE INTERVALS-IN I-TH SPECIFICATION INTERVAL.

THERE ARE NZINTS(I) AXIAL COARSE-MESH REBALANCEINTERVALS BETWEEN ZCMRC(I-l) AND ZCMRC(I), WHEREWHERE ZCMRC(O) IS THE LOWER REACTOR BOUNDARYIN THE Z-DIRECTION. THE ZCMRC(I) ARE ORDERED SUCHTHAT ZCMRCU-)-l).GT.ZCMRC(I).

CEOF

D.3 LABELS

£*****•*********************/!************•******************************

C PREPARED 2/21/78 AT ANLC LAST REVISED 12/12/83CCF LABELSCCE REGION AND COMPOSITION LABELS, AREA DATA,CE HALF HEIGHTS, NUCLIDE SET LABELS, /.LIAS ZONE LABF.LS,CE CONROL-ROD MODEL DATACC * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * r * * * * * * * * * * * * * * * * * * * * *

c—CRCCLCCWC

FILE IDF.NTIFICATION

HNAMK,(HUSE(I),I-1,2),IVERS

1+3*MULT-NUMBF.R OF WORDS

CDenCDCDCDCDCC

c—CRcscscscscscscscscscscscscscscscscscscc—

HNAMEH1!SE( I )IVKRSMULT

HOLLERITH FILE NAME - LABELS - (A6)HOLLERITH CSER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER

1 - A6 WORD IS SINGLE WORD2 - A6 WORD IS DOUBLE PRECISION WORD

CRCCLCLCLCCWCCDCDCDCDCDCDCDCDCDCDCD

FILR STRUCTURE


FILE IDENTIFICATIONSPECIFICATIONSLABEL AND AREA DATAFINITE-GEOMETRY TRANSVERSE

DISTANCESNUCLIDE SET LABELSALIAS ZONE LABELSGENERAL CONTROL-ROD MODEL DATA

***********(REPEAT FOR ALL BANKS)* CONTROL-ROD BANK DATA*

* *******(REPEAT FOR ALL RODS IN BANK)* * CONTROL-ROD CHANNEL DATA**********

ALWAYSALWAYSALWAYSNHTS1.GT.0 ORNGTS2.GT.0

NSETS.CT.lNALIAS.GT.ONBANKS.GT.O

NBANKS.GT.O

(LLCHN+LLROD+MMESH).GT.0-

SPECIFICATIONS ( I D RECORD)

NTZSZ,NREG,NARF.A,LREGA,NHTS1,NHTS2,NSETS,NALIAS,NTRI,NRING,NCHAN,NBANKS,LINTAX,MAXTIM,MAXROD,MAXMSH,MAXLRD,MAXLCH,( I D U M ( I ) , 1 - 1 , 6 )

24-NI/MRER OF WORDS

NTZSZNRF.GNARKALREGANMTS1

NHST2

NUMBER OF ZONES AND SUBZONESNUMBER OF REGIONSNUMBER OF AREASLENGTH OF NRA ARRAYNUMBER OF HALF-HEIGHT AND EXTRAPOLATIONDISTANCE SPECIFICATIONS

0 - NONE1 - SINGLE VALUE USED EVERYWHERE.EQ.NREG - REGION DEPENDENT

NUMBER OF HALF-HEIGHT AND EXTRAPOLATIONDISTANCE SPECIFICATIONS FOR THE SECOND

enenCDenenCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCOCDCDCDCCNCNCNCNCc—

c-CRCCLCLCLCCWCCDCDCDCDCDCDCDCDCC ~

DIRECTION.0 - NONENHTS1 - SAME AS NHTS1

NSETS NUMBER OF NUCLIDE SETSNALIAS 0 IF RECORD 5D IS NOT PRESENT. IF GREATER

THAN 0, RECORD 5D IS PRESENT AND THE ALIASARRAY IS OF LENGTH NALIAS.

NTRI NO. OF TRIANGLES PER HEX FOR TRIANGULARGOEMETRIES

NRING MAX. NO. OF RINGS OF HEXAGONS FOR TRIANGULARGEOMETRIES

NCHAN NO. OF CONTROL-ROD CHANNELS IN THE MODELNBANKS NO. OF CONTROL-ROD BANKSLINTAX ORIGINAL NO. OF FINE MESH INTERVALS IN AXIAL

DIMENSIONMAXTIM MAXIMUM VALUE OF NTIMES(I) (1-1,NBANKS)MAXROD MAXIMUM VALUE OF NRODS(I) (1-1.NBANKS)MAXHSH MAXIMUM VALUE OF NMESH(K) (K-l,LRODS;

1-1,NBANKS) WHERE LRODS-NRODS(I)MAXLRD MAXIMUM VALUE OF LENROD(K) (K-l.LRODS;

1-1.HBANKS)MAXLCH MAXIMUM VALUE OF LENCHN(K) (K-l.LRODS;

1-1.NBANKS)IDUM RESERVED

THE AXIAL DIMENSION IS Z IN RZ, XYZ, HEX-Z ANDTRIANGULAR-Z GEOMETRIES. IT IS Y IN XY GEOMETRY.NCHAN IS THE SUM OF NROOS (RECORD 6D) OVER ALL CONTROLROD BANKS.

LABEL AND AREA DATA (2D RECORD)

(CMPNAM(I).I-l,NTZSZ),(REGNAM(I),I-1,NREG),1(ARANAM(I),I-1,NAREA),2(NRA(I),I-1,LREGA),

MULT*(NTZSZ+NREG+NAREA)+LREGA-NUMBKR OF WORDS

CMPNAM( I)REGNAM(I)ARANAMtI)NRA(I)

ZONE OR SUBZONE LABEL. SUBZONES FOLLOW ZONESREGION LABELAREA LABELREGION/AREA ASSIGNMENTS. NRA(N(J)) IS THENUMBER OF REGIONS IN AREA J. (NRA(I),I-N(J)+1,N(J+1)-1) IS A LIST OF THE REGION NUMBERS FORTHOSE REGIONS. N(l)-1. N(J+1)-N(J)+l+NRA(N(J)).LREGA-SUM (i+NRA(N(J))) FOR J-l.NAREA

C —CRCCCCCLCLCCWCCDCDCDCDCDCDCDCCNCNCN

C-CRCCCCCLCCWCCDCC —

CCRCCCCCLCCWCCDCCNCNCNCN

FINITE-GEOMETRY TRANSVERSE DISTANCES (3D RECORD)

PRESENT IF NHTS1.GT.0 OR NHTS2.GT.0

(HAFHT1(I),I-1,NHTS1),(XTRAP1(I),I-1.NHTS1),1(HAFHT2(I),I-1,NHTS2),(XTRAP2(I),I-1,NHTS2)

2*(NHTS1+NHTS2)=-NUMBER OF WORDS

HAFHTl(I)XTRAPl(I)

HAFHT2(I)

XTRAP2(I)

ACTUAL TRANSVERSE HALF HEIGHT FOR REGION ITRANSVERSE EXTRAPOLATION DISTANCE FORREGION IACTUAL TRANSVERSE HALF HEIGHT FOR REGION IIN THE SECOND DIRECTIONTRANSVERSE EXTRAPOLATION DISTANCE FORREGION I IN THE SECOND DIRECTION

IF HAFHTN(I)+XTRAPN(I)-0.0 (N - 1 OR 2)THE MODEL IS TREATED AS EXTENDING TOINFINITY IN THE NTH TRANSVERSE DIMENSION.

NUCLIDE SET LABELS (4D RECORD)

PRESENT IF NSETS.GT.1

(SETISO(I).I-l.NSETS)

MULT*NSETS-NUMBER OF WORDS

SETISO(I) LABEL OF THE I-TH NUCLIDE SET

to

ALIAS ZONE LABELS (5D RECORD)

PRESENT IF NALIAS .GT. 0

(ALIAS(I),I-1,NALIAS)

MULT*NAL1AS»NUMBER OF WORDS

ALIAS(T) ALIAS ZONE LABELS

WHEN RUNNING REBUS-3, THE ZONES AREPROLIFERATED TO THE REGIONS AND THE ZONELABELS BECOME IDENTICAL TO THE REGION LABELS.THE ARRAY ALIAS CONTAINS THE LIST OF ORIGINAL

CNCC~

ZONE LABELS "ASSIGNED TO THE VARIOUS REGIONS.

CCRCCCCCLCLCLCCWCCDCDCDCDCDCDCDCDCDCDCCNCNCNCNCNCNCC —

C—•CRCCCCCLCLCT.CCWcCDCDCD

c>CDCD

GENERAL CONTROL-ROD MODEL DATA (6D RECORD)

PRESENT IF NBANKS .GT. 0

(BNKLAB(I),1-1,NBANKS).(ZMESHO(I).I-l.LINTAX),(POSBNK(I),1-1,NBANKS),(NRODS(I),1-1,NBANKS),(NTIMES(I),.1 = 1,NBANKS),(KFINTO(I) ,1-1 .LINTX1 )

LINTAX*(MULT+1)+(2*MULT+2)*NBANKS-1-NUMBER OF WORDS

BNKLAB(I) CONTROL-ROD BANK LABELZHESHO(I) ORIGINAL LAST-DIMENSION MESH STRUCTURE

(CM.)POSBNK(l) CURRENT POSITION OF ROD BANK I (CM.)NRODS(I) NO. OF RODS IN BANK INTIMES(I) NO. OF TIME NODES IN POSITION VS. TIME

TABLE FOR BANK IKFINTO(I) ORIGINAL NUMBER OF FINE MESH BETWEEN ZMESHO(I)

AND ZMESHO(I+1)LINTXl LINTAX-1

ZMESHO(1)-0.0. THE ZMESHO ARRAY MUST ATLEAST CONTAIN ALL THE BOUNDARIES BETWEENDISSIMILAR MR ARRAYS (SEE GEODST FILEDESCRIPTION). THE ZMESHO ARRAY IN A LABELSFILE CREATED BY GNIP4C WILL NORMALLY CONTAINTHE ORIGINAL, COARSE-MESH BOUNDARIES.

CONTROL-ROD BANK DATA (7D RECORD)

PRESENT IF NBANKS .GT. 0

(RBTIME(J),J-1,LTIME),(RBPOS(J),J-1,LTIME),(NMESH(K).K-l,LRODS),(LENCHN(K),K-1.LRODS),(LENROD(K),K-1,LRODS)

2*MULT*LTIME+3*LRODS-NUMBER OF WORDS

RBTIME(J)

RBPOS(J)NMESH(K)

LF.NCHN(K)

TIME ENTRIES IN ROD POSITION VS. TIMETABLEROD-BANK POSITIONS IN TABLE (CM.)NO. OF PLANAR MESH CELLS IN ROD K OF CURRENTROD BANKNO. OF REGIONS DEFINED FOR THE IMMOVEABLE

CDCDCDCDCDC

LENROD(K)

LTIMF.LRODS

PORTION OF ROD CHANNEL KNO. OF REGIONS DEFINED FOR THE MOVEABLEPORTION OF ROD CHANNEL KNTIMES(I) FOR CURRENT ROD BANKNRODS(I) FOR CURRENT ROD BANK

CCRCCCCCLCLCLCCWCCDCDCDCDCDCβCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCDCCNCNCNCC

CONTROL-ROD CHANNEL DATA (8D RECORD)

PRESENT IF LLCHN + LLROD + MMESH .CT. 0

(POSCHN(L),L-1,LLCHN).(POSROD(L),L-1.LLROD),(MRCHN(L).L-l,LLCHN),(MRROD(L),L-1.LLROD),((MESH(L.M) ,L-l ,NO) ,M-1 .MHF.SH)

(MULT+1)*(LLROD+LLCHN)+ND*MMESH-NUMBER OF WORDS

POSCHN(L)

POSROD(L)

MRCHN(L)

MRROD(L)

LLCHNLLRODMESH(l.M)

MESH(2,M)

ND

MMESH

POSITION (RELATIVE TO THE BOTTOM OF THE MODEL) •OF THE LOWER BOUNDARY OF REGION L IN THEIMMOVEABLE PORTION OF THE CURRENT RODCHANNEL (POSCHN(l)-O.O)POSITION (RELATIVE TO ROD TIP) OF THELOWER BOUNDARY OF REGION L IN THE MOVEABLEPORTION OF THE CURENT ROD CHANNEL(POSROD(l)-O.O)REGION ASSIGNMENT FOR REGIONS IN THEIMMOVEABLE PORTION OF THE CURRENT RODCHANNEL, STARTING AT THE BOTTOM (Z-O.O)OF THE MODEL.REGION ASSIGNMENT FOR REGIONS IN THEMOVEABLE PORTION OF THE ROD, STARTINGWITH THE REGION ADJACENT TO THE ROD TIPLENCHN(K) FOR CURRENT ROD CHANNELLENROD(K) FOR CURRENT ROD CHANNEL1ST DIMENSION INDEX FOR PLANAR MESH CELL MIN THE CURRENT ROD CHANNEL2ND DIMENSION INDEX FOR PLANAR MESH CELL MIN THE CURRENT ROD CHANNEL1 IN XY AND RZ GEOMETRIES, 2 IN XYZ. R-THETA-Z,THETA-R-Z, HF.X-Z, AND TRIANGULAR-Z MODELSNMESH(K) FOR CURRENT ROD CHANNEL

NOTE THAT IF NBANKS .GT. 0 BUT LLCHN + LLROD +MMESH .EO. 0, AN ERROR CONDITION PROBABLYEXISTS.

u>

CEOF

D.4 NHFLUX

C***********************************************************************C PREPARED 3/01/82CCF NHFLUXCE REGULAR NODAL FLUX-MOMENTS AND INTERFACE PARTIAL CURRENTS -CC**************************************************.*********************CD ORDER OF GROUPS IS ACCORDING TO DECREASINGCD ENERGY. NOTE THAT DOUBLE PRECISION FLUXES ARECD GIVEN WHEN MULT-2

CSCSCSCSCSCSCSCSCSCSCSCSC

c-

FILE STRUCTURE

RECORD TYPE RECORD PRESENT IF

FILE IDENTIFICATION ALWAYSSPECIFICATIONS ID ALWAYS

**•********(REPEAT FOR ALL GROUPS)* FLUX MOMENTS 2D ALWAYS* XY-DIRECTED PARTIAL CURRENTS 3D ALWAYS* 2, -DIRECTED PARTIAL CURRENTS 4D NDIM.EQ.3***********

CRCCLCCWCCDCDCDCDCDCDCC —C —CRCCLCLCCWCCDCDCDCD

FILE IDENTIFICATION

HNAME,(HUSE(I),I-I,2),IVERS

1+3*MULT»NUMPER OF WORDS


HOLLERITH FILE NAME - NHFLUX - (A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER



NDIM,NGROUP.NINTI.NINTJ,NINTK,ITER.EFFK,POWER,NBLOK,NMOM.NINTXY.NPCXY

12 -NUMBER OF WORDS

NDIMNGROUPNINTININTJ

NUMBER OF DIMENSIONSNUMBER OF ENERGY GROUPSNUMBER OF FIRST DIMENSION FINE MESH INTERVALSNUMBER OF SECOND DIMENSION FINE MESH INTERVALS

CDCDCDCDCDCDCDCDCDCDCDC

CCRCCLCCWCCCCcnCDcC—- -c—CRCCLCCWCcccCDCDCCCCRCCLCCWCccccc0CD

NINTK

ITER

F.FFKPOWERNBLOKNMOMNINTXYNPCXY

NUMBER OF THIRD DIMENSION FINE MESH INTERVALS.WINTK.EQ.l IF NDIM.LE.2OUTER ITERATION NUMBER AT WHICH FLUX WASWRITTENEFFECTIVE MULTIPLICATION FACTORPOWER IN WATTS TO WHICH FLUX IS NORMALIZEDDATA BLOCKING FACTOR (ALWAYS EQUAL TO 1)NUMBER OF FLUX MOMENTS IN NODAL APPKOXIMATIONNUMBER OF MESH CULLS (NODES) ON XY-PLANENUMBER OF XY-DIKECTED PARTIAL CURRENTS ONXY-PLANE

REGULAR FLUX MOMENTS (2D RECORD)

((FLUX(I,J),I-1,NMOM),J-1,NINTXY) SEE STRUCTURE BELOW

NMOM*N1NTXY*MULT - NUMBER OF WORDS

DO 1 K-l.NINTK1 READ(N) *LIST AS ABOVE*

FLUX(I.J) REGULAR FLUX MOMENTS BY NODE FOR THE PRESENTGROUP

REGUIAR XY-DIRECTED PARTIAL CURRENTS (3D RECORD)

(PCURRH(I),I-1,NPCXY) SEE STRUCTURE BELOW

NPCXY*MULT - NUMBER OF WORDS


PCURRH(I) REGULAR XY-DIRECTED PARTIAL CURRENTS ACROSS ALL-XY-PLANE SURFACES FOR THE PRESENT GROUP

REGULAR Z-DIRECTED PARTIAL CURRENTS (4D RECORD)

((PCURRZ(I.J).I-l,NINTXY),J-l,2) SEE STRUCTURE BELOW

N1NTXY*2*MULT - NUMBER OF WORDS

DO 1 K-1.NINTK11 READ(N) *LIST \S ABOVE*

WITH N1NTK1 • NINTK + 1

PCURR7.(I,J) REGULAR /.-DIRECTED PARTIAL CURRENTS IN

CDCDCDCC —

MINUS- (J-l) AND PLUS- (J-2) Z DIRECTIONSACROSS ALL AXIAL BOUNDARIES FOR THE PRESENTCROUP

CEOF

D.', NAFLUX

c***********************************************************************C PREPARED 3/01/82CCF NAFLUXCE ADJOINT NODAL FLUX-MOMENTS AND INTERFACE PARTIAL CURRENTS -C£**************&*****•*******************•****************************•*

CD ORDER OF GROUPS IS ACCORDING TO INCREASINGCD ENERGY. NOTE THAT DOUBLE PRECISION FLUXES ARECD GIVEN WHEN MULT-2C

CSCSCSCSCSCSCSCSCSCSCSCS

cc—c—CRCCLCCWCCDCDCDCDCDCDCC —C-CRCCL

FILE STRUCTURE

RECORD TYPE RECORD PRESENT IF

FILE IDENTIFICATION ALWAYSSPECIFICATIONS ID ALWAYS

***********(REPEAT FOR ALL GROUPS)* FLUX MOMENTS 2D ALWAYS* XY-DIRECTED PARTIAL CURRENTS 3D ALWAYS* Z -DIRECTED PARTIAL CURRENTS AD NDIM.EO.***********

FILE IDENTIFICATION

HNAME,(HUSE(I),I-i,2),TVERS

l+3*MULT-NUMBER OF WORDS

HNAMEHUSE<I)IVERSMULT

HOLLERITH FILE NAME - NAFLUX - <A6)HOLLERITH USER IDENTIFICATION (A6)FILE VERSION NUMBERDOUBLE PRECISION PARAMETER



CLCCWCCDCDCDcncnCDCDCDCDCDCDCDCDCD

cncc—c-CRCCLCCWCcccCDCDCCC-CRCCLCCWCCCCCDCDCCQ

CRCCI.C

NMOM.NINTXY.NPCXY

12 -NUMBER OF WORDS

NDIMNGROUPN1NTININTJNINTK

ITER

EFFKADUMNBLOKNMOMNINTXYNPCXY

NUMBER OF DIMENSIONSNUMBER OF ENERGY GROUPSNUMBER OF FIRST DIMENSION FINE MESH INTERVALSNUMBER OF SECOND DIMENSION FINE MESH INTERVALSNUMBER OF THIRD DIMENSION FINE MESH INTERVALS.NINTK.F.Q.I IF NDIM.LE.2OUTER ITERATION NUMBER AT WHICH FLUX WASWRITTENEFFECTIVE MULTIPLICATION FACTORRESERVEDDATA BLOCKING FACTOR (ALWAYS EQUAL TO 1)NUMBER OF FLUX MOMENTS IN NODAL APPROXIMATIONNUMBER OF MESH CELLS (NODES) ON XY-PLANENUMBER OF XY-DIRECTED PARTIAL CURRENTS ONXY-PLANE

ADJOINT FLUX MOMENTS (2D RECORD)

((FLUX(I,J),1-1,NMOM),J-i,NINTXY) SEE STRUCTURE BELOW

NMOM*NINTXY*MULT - NUMBER OF WORDS

DO 1 K»l.NINTKI READ(N) *LIST AS ABOVE*

ain

FLUX(I.J) ADJOINT FLUX MOMENTS BY NODE FOR THE PRESENTGROUP

ADJOINT XY-DIRECTED PARTIAL CURRENTS (3D RFCORD)

(PCURRH(I).I-l,NPCXY) SEE STRUCTURE BELOW

NPCXY*MULT - NUMBER OF WORDS


PCIIRRH(I) ADJOINT XY-DIRF.CTED PARTIAL CURRENTS ACROSS ALL-XY-PLANE SURFACES FOR THE PRESENT GROUP

ADJOINT Z-DIRECTED PARTIAL CURRENTS (4D RECORD)

((PCURR7.(I,J),I-1 .NINTXY),J-l ,2) SKF. STRUCTURE BELOW

NDIM,NGROUP,NINTI,NINTJ,NINTK,ITER,EFFK,ADUM,NBLOK,

Appendix E

LINK EDIT INSTRUCTIONS FOR IBM 370 SYSTEMS

//LINKIBM JOB USER-B20245,/ / CLASS-W,TIME-5,REGION-1000K,MSGCLASS-W/ / */ / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ / *//* THIS JOB LINK EDITS THE LOAD MODULES STPO21 AND SIOSUB IN

THE LIBRARY &NESCLIB.THE JOB RUNS IN A REGION SIZE OF 1000K.

//*//*//*//*//*//*//STEP1//SYSLIB

***************************************************************

EXECUTE LINKAGE EDITOR.***************************************************************

EXEC PGM-IEWL.PARM-'DCBS.LIST.MAP.OVLY.SIZE-dOOOK.lOOK),

DD DISP-SHR.DSN-SYS1.AMDLIB// DD DISP-SHR.DSN-SYS1.FORTLIB//SYSLIN DD DSN-SOBJECT,DISP-(OLD,DELETE)// DD DDNAME-SYSIN//SYSLMOD DD DSN-&NESCLIB(STP021),// DISP-(NEW,CATLG),UNIT-PERM,// SPACE-(TRK,(100,20,1),RLSE).DCB-BLKSIZE-6144//SYSPRINT DD SYSOUT-A//SYSUT1 DD SPACE-(CYL,20),UNIT-(SASCR,SEP-(SYSLIN,SYSLMOD))//SYSIN DD *ENTRY MAININSERT LINKRO.LINKRl

REED,SEEKERROR,FFORM,FFORM1,FF0RM2.LINES,TIMER,SEKPHLINTSET,FLTSET,IEQUAT,FEQUATPOINTR,BULK,FREE,IPTERR,WIPOUT,IPT2,PUTM,ILAST,PURGEABEND.SQUEZE,INITIOSIO,RECFM,TRACER,ZEROIO,SIOERR,SI0WU6,SIOTRCJOBID,SECOND,LOCATE,TABLES,PTERR,LCMSIZ,BFLAGSPRTI1,PRTI2,PRTR1,PRTR2,PRTECM,STATUS,REDEFMREDEF,IGET,PUTPNT,GETPNTTIME,CLOCK*,DATEJGT.MYLCM,FRELCM,LOCF,LOCFWD,IGTLCM,IGTSCMIOPUT,PTITLE,ARRAY,STFARC

INSERTINSERTINSERTINSERTINSERTINSERTINSERTINSERTINSERTINSERTINSERTINSERTOVERLAY LEVELlINSERT SCANOVERLAY LEVELlINSERT STUFF,STUFF1OVERLAY LEVELlINSERT GNIP4C.ANIP01,ANIP02,ANIP14,ANIP23,GETZON,GETSZNINSERT BCDFLT.BCDINT.ISIZES

•WKRI AY l.F.VF.1,2INSKRT RANIP!OVKRI.AY '.EVKL3INSERT ANIPO3,ANIPO4,ANlPn'>,ANIPO6OVKRI.AY LEVEL3[NSKRT ANlPHX.ANIPn7,ANlPO9,CHEKn9,ANIP10OVKRI.AY I.EVKL3INSERT ANIP11,ANIP12,ANIP15,ANIP34OVKRI.AY LF.VEL2INSERT FCF.OnS.LOCHF.X.SF.THF.XOVKRLW LEVEL!INSKRT OF.THCT.GETREGOVERLAY LF.VEL3I NSF.RT fiETMSH, CMESH, FMF.SHOVERLAY LEVEL3INSERT GETBUC.GETBCOVERLAY LEVEL3INSKRT GETMR,RCMESH,TRIGOK,VOLREG,REDMSHOVERLAY LF.VEL2INSERT EGEODSOVERLAY LEVEI.3INSERT MAKMSHOVERLAY LEVEL3INSKRT PRGEOD.PRNTIXOVERLAY LEVF.L3INSERT ANIP43,MPGEOD,MSHMAPOVERLAY LF.VEL3INSERT TRIPLT.HEXPIC.HEXPCl ,HEXPC2,HEXPC3 >HEXPC6,HEXPC7 .HF.XPCOVERLAY LEVEL*INSERT HEXPC4OVERLAY IEVEL4INSERT HF.XPC5OVERLAY LEVEL3INSERT ORTMAP,ORTPC1,ORTPC2,ORTPC3,ORTPC4,ORTPC5,ORTPC6,ORTPCOVERLAY LF.VEL2INSERT RANIP2,ANIP13,GETMAT,RETISO,ANIP39,GETSETOVERLAY LKVEL2INSERT FADENS,SORT13,VALU2D,SET2D,INDEX,EDTMAT,SORT14,HNDXSROVERLAY LEVF.L2INSERT BCnXST.RWIEOT,RUDELY,RWDY1.RUDY2OVERLAY LEVEL2> NSKRT WRSRCHIIVK«LAY LKVEI.3INRKUT ANIP2I ,ANIP22,SRCH4D,ANIP24,SRCH3o,ANIP25,SRCH6l),ANIP26ilVKHLAY I.EVEL3IMRKRT KDSRCMOVKKI \Y 1.KVEI.2IUSEKT WKSORCIIVKHLAY I.KVKL3INSERT ANIPI9.ANIP4O.ANIP41.ANIP42flVKKLAY LKVKI.3INSKRT SORDAT,SORLAB,SORMSH,SORNZN,SORDIF

OVERLAY LEVEL3INSERT ADS,ADS1,ADS2,ADS3OVERLAY LEVEL3INSERT WRS,WRSO,URS1,W?S2OVERLAY LEVEL3INSERT EDSORCOVERLAY LEVEL2INSERT URRODS,AN1P44,SORROD,HAKROD,WRTROD,EDTRODOVERLAY LEVEL1INSERT HMG4CINSERT REF.HMGPTROVERLAY LEVEL2INSERT OVL1,RDNDX,EDTISO,IDLR13,ISOR14,RDATDN,ATDN3OVERLAY LF.VEL2INSERT OVL2,SCAT,ISOR58,EDTR5,EDTR6,EDTR8,FISPEC,MAXBND,SVSCATINSERT UPDATE,FARSET.ZROSETOVERLAY LEVEL2INSERT OVL3,WREC1.UREC2,WREC3.WREC4OVERLAY LEVEL2INSERT OVL4,SVXS,EI)FPWS,£DTXS1 .F.DTXS2OVERLAY LEVEL1INSERT HODCXS,ANIP35,ANIP37,DOMODS,COPIEROVERLAY LEVEL1INSERT RCDINP.RADF3D.PDIF3DOVERLAY LEVEL1INSERT SRCH4C,GETBS0,GErALP,GETDIH,GETCON,SRCHX,PARABINSERT DMDBSO.DMDALP,DMDDIM,DHDCON,HODBSQ,MODDIM,MODCONOVERLAY LF.VEL1INSERT CONTRL,IOCOM,NHIOCM,VERNUM,NHCNTL.SPECS,IOCOMC,IOCOMDINSERT NHIOPC.NHIOPD,DEBUG,CFTABLINSERT DIF3D,VOLUME,START,WDIF3D.GETBND,AREAS,REVRSEINSERT DEFICF,OPENCF,CLOSCF,PURGCF,BLKGET,PNTGET,DEFIDF,OP£NDFINSERT CLOSDF.STATCF.PCREDINSERT LINKR2OVERLAY LEVEL2INSERT BININP,RATFLX,RCMPXS,RDIF3D,RFIXSR,RCEODS,RLABEL,RRTFLXINSERT RSEARC,ADSCTM,FORMSH,RNHFLX,RCMPXS,FORHCMOVERLAY LEVEI.2INSERT SSINIT.EDITCROVERLAY LEVEL3INSERT FDINIT.SSCORE.SSDISKOVERLAY LEVEL3INSERT ZMINIT,INEDIT,FORMMZ,REGMAPOVERLAY LF.VEL3INSERT NHINIT.NHnEOM.KEXMAP.GETIJ.NHZHAP.NHPNT.NHCCPT.NHINED.NHCORF.INSERT NHDISKOVERLAY LF.VEL3INSF.RT XS INIT.XSGET1 ,XSCET2 .XSEDITOVERLAY LEVF.L2INSERT SSTATE,SCTSRC,TRISRC,TSWF.EP,PSWEEP,TOTSRC,SORINV,ROWSRCINSERT FISSRC .OSWEEP .OUTEDO, CHEBE, DACOSH, FILCPY, ZF.ROBAOVERLAY LEVEL3INSERT nXSREV.XSCREV.NHSICAOVERLAY LKVEL3INSERT DFDCAL.FDCAL.ORTFDC.TRIFnCOVERLAY LEVEL3

INSERT FSRCIN,DORPES,ORPES1,ORPES2,RFLXIN,ORPIN1,MLTPLY,ORPI:J2OVERLAY LEVEL3INSERT DOIJTR1.0UTER1 .CHEBY1, INNER1OVERLAY LEVEL3INSERT DOUTR2,OUTER2,CHEBY2,FISSD2,IFISD2,INNER2,SCTSD2,TOTSD2OVERLAY LEVEL2INSERT NHSST.NHOEDO,INVERT,NHXSECOVERLAY LEVEL3INSERT DNHCCC,NHCC2D,NHCC3D,NHTVLC,NHINNROVERLAY LEVEL3INSERT DNHSTT.FXREAD.FXINIT.FSINITOVERLAY LEVEL3INSERT DNHOUT.OUTR1,OUTR2,OUTR3,OUTR4.OUTR5,ACCEL,ACCL3DINSERT LEAK3D,SRCFIS,SRCSCT,SRCHEX,PCHEX,PCHEXB,SRCZ1.SRCZ2.PCZINSERT PCZB,FLXHEX,FLXZ.FSUPDT,CMMTRX,BKRING,AXLEAK,CMSOLV,FSERRNINSERT CONVCK.NHSFCHOVERLAY LEVEL3INSERT DNHFIN,NHEDDM,CPYFIL,NHVOL,FXSHAPOVERLAY LEVEL2INSERT DSSTOU,TWODTB,TWODPR,EDITDM,BRED,DSEQUAINSERT SCALPK,WPKEDT,NHSHAP,NHPEAK,NHPKEDOVERLAY LEVEL3INSERT DSSTO1,BKLWGT,FORMMR,POWINT,SSTOU1,WPOWER,APWADD,RPWADDINSERT ORTSRF.TRISRFOVERLAY LEVEL3INSERT DSSTO2,SSTOU2,EDCORE,WFLUX,ORTBAL,PPSADD,TRIBALINSERT WNHFLX.HEXBALOVERLAY LEVEL3INSERT FLXINT,BALINT,DSSTO3,FLXRZ,ADDVEC,DIVVEC,APSADD,BALBUFINSERT ABLADD,RBLADD,RBLFIS,RBLMED,WRZFLX/*//* ***************************************************************//* EXECUTE LINKAGE EDITOR.//* ***************************************************************//STEP7 EXEC PGM=IEWL,PARM-'DCBS,LIST,MAP,RENT,SIZE-(230K,100K) '//SYSLIB DD DISP-SHR.DSN-SYS1.AMDLIB// DD DISP-SHR.DSN-SYS1.FORTLIB//SYSLIN DD DSN-iOBJECT,DISP-(OLD,DELETE)// DD DDNAME-SYSIN//SYSLMOD DD DSN-SNESCLIB(SIOSUB).DISP-OLD//SYSPRINT DD SYSOUT-A//SYSUT1 DD SPACE-(CYL,20),UNIT-(SASCR,SEP-(SYSLIN,SYSLMOD))

m

Appendix F.I

SEGMENTED LOADER INSTRUCTIONS FOR SEGLINK ON THE CDC 7600

SF.GLD3D,7,400,20000.XXXXXX

:<compUe source and pass LGO file lo SEGLINK>

SFL,170000,100000.SECLINK(F-LGO,P-FTN4LIB,B-DIF3D,LO-BEX)

EXIT.

•*

** TREE STRUCTURE DEFINITION WITH IMPLICIT INCLUDES**ROOT TREE D3DRIV-(SCAN,STUFF,CNIP4,HMG4 ,M0DCXS,BCDINP,SRCH4C,BININP,,SSINI,SSTAT,NHSS,DSSTO,UDOITl,UDOIT2,UDOm,UDOIT4)*

GNIP4 TREE GNIP4C-(RNIP1,FGEOD,EGEOD,RANIP2,FADENS,BCDXST,WSRCH.WSORC,1/UROnS)RNIP! TREE RANIPI-(ANIPO3,ANIPHX,ANIP11)FGEOD TREE FGEODS-(GETHGT,GE1MSH,GETBUC,GETMR)EGEOD TREE EGEODS-(MAKMSH,PRGEOD,ANIP43 ,HEXMP,ORTMAP)HEXMP TREE HEXMAP-(HEXPC4.HEXPC5)WSRCH TREE WRSRCH-(ANIP21.EDSRCH)WSORC TREE WRSORC-(ANIP19,SORDAT,ADS,WRS,EDSORC)*HMG4 TREE HMC4C-(OVL1.OVL2.OVL3.0VL4)*

SSINI TREE SSINIT-(FDINIT,ZMINIT,NHINIT,XSINIT)SSTAT TREE SSTATF.-(DXSREV,DFDCAL,DORPES,DOUTRt .DOUTR2)*NHSS TREE NHSST-(DNHCCC,DNHSTT,DNHOUT,DNHFIN)*DSSTO TREE DSST0U-(DSST01.DSST02.DSST03)**

** EXPLICIT SEGMENT DEFINITIONS**

D3DRIV INCLUDE D3DRIV,CRED,DOPC,DRED,DRED1,DRED2.ERROR,FEQUAT,FFORM,EC,MV,ECZF.RO, FFORM1 , FFORM2, FLTSET, IEQl!AT, IGTLCM, JGTSCM, FRELCM,l.OCFWD, 1 NTSE.T.IN2LIT,LINES,POINTR.PUTPNT,BULK,FREE,WIPOUT.GETPNT,IGET,IPT2,PUTM,IPT,ERR.ILAST.REDEF.REDEFM,PURGE,STATUS,PRTI1.PRTI2.PRTR1.PRTR2.PRTECM.RKED..ZEROIO,SEEK,SEKPHL,SPACE,SQUEZE.SRLAB,TIMER,DIF3D,START, VOLUME,Wr,iF3D,.GF.TBND,AREAS,REVRSE,DEFICF,OPENCF,CLOSCF,PURGCF,BLKGET.PNTGET.DEFIDF,OP,ENDF,CLOSDF,STATCF,CODECD,READEC,WRITEC,PCRED

STUFF

GNIP4CANIP03ANIPHXANIPtl

INCLUDE STUFF,STUFF1

INCLUDE GNIP4C.ANIP01 .ANIP02 .ANIP14 .ANIP23 .CETZON.GETSZNINCLUDE ANIP03,ANIP04,ANIP05,ANIP06INCLUDE ANIPHX,ANIP07.ANIP09.CHEK09.ANIP10INCLUDE ANIPI1.ANIPI2.ANIP15.ANIP34

FGEODS, LOCHF.X , SETHEXGETHGT.GETRF.GGETHSH, CMF.SH, FMESHGSTBUC.GETBC

GETMR,RCMESH,TRIGOM,VOLRF.G,R£DMSHPRGEOD.PRNTIXAN1P43,MPGEOD,MSHMAPTRIPLT.HEXPIC.HEXPC1,HEXPC2.HEXPC3.HEXPC6.HEXPC7ORTHAP.ORTPCI.ORTPC2.ORTPC3.ORTPC4.ORTPC5.ORTPC6RANIP2,ANIP13,GETMAT,CETISO,ANIP39,CETSETFADENS,SORT13,VAI.U2D,SET2D,INDEX,EDTMAT,SORT14,WNDXSRBCDXST, RWI SOT, RWDF.LY, RWDY1, RWDY2

ANIP21,ANIP22,SRCH4D,ANIP24.SRCH3D,ANIP25,SRCH6D,ANIP26ANIPI9.ANIP40.ANIP41.ANIP42SORDAT,SORLAB,SORMSH,SORNZN,SORDIFADS,ADS1,ADS2,ADS3WRS.WRSO.WRS1,WRS2WRRODS,ANIP44,SORROD,SORMSH,SORNZN,SORDIF

*

HMG4C INCLUDE HMG4COVL1 INCLUDE OVL1,RDNDX,RDATDN,ATDN3,ISOR14.EDTISO,IDLR13OVL2 INCLUDE OVL2,ISOR58.SVSCAT,FARSET,ZROSET,UPDATE, MAXBND.FISPEC.E,DTR5,EDTR6,EDTR8OVL3 INCLUDE OVL3.WREC1.WREC2,WREC3.WRECiOVL4 INCLUDE OVL4,SVXS.EDTXS1,EDTXS2.EDFPWS*

MODCXS INCLUDE MODCXS.ANIP35.ANIP37.DOMODS,COPIER

BCDINP INCLUDE BCDINP,RADF3D,PDIF3D*SRCH4 C INCLUDE SRCH4C.GETBSQ,GETALP,GETDIM,GETCON,SRCHX,PARAB,DMDBSO,D,MDALP,DMDDIM,DMDCON,MODBSO,MODDIM,MODCON*

BININP INCLUDE BININP,RDIF3D,RLABEL,RSEARC,RCMPXS,ADSCTM,RGEODS.FORMSH,.RRTFLX.RATFLX,RFIXSR,RtfflFLX.RCMPXS.FORMCM

FGF.onSGF.THGTCF.TMSHGETBUCGETMRPRCF.ODANIP43TRIPLORTMAPRANIP2FADENSBCDXSTANIP21ANIP19SORDATADSWRSWRRODS

INCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDEINCLUDE

SSINIT.EDITCRFDINIT.SSCORE.SSDISKZMINIT,INEDIT,FORMMZ,REGMAPNHINIT.NHGEOM.HEXMAP.GETIJ.NHZMAP.NHPNT.NHCCPT.NHINED.N

XSINIT,XSGF.TI,XSGET2,XSEDrr

SSINIT INCLUDEFDINIT INCLUDEZMINIT INCLUDENHINIT INCLUDE,HCORE,NHDISKXSINIT INCLUDE*

SSTATF. INCLUDE SSTATE,CHF.BE,DACOSH,OUTED0,FILCPY.OSWEEP,PSWEEP,TSWEEP

,SORINV,FISSRC.TOTSRC,SCTSRC,ROWSRC,TRISRC,ZEROBADXSREV INCLUDE DXSREV.XSCRF.VDFDCAL INCLUDE DFDCAL,FDCAL,ORTFDC,TRIFDCDORPES INCLUDE DORPES.ORPESI .ORPINI ,RFLXIN,FSRCIN,ORPF.S2 .ORPIN2.MLTPLYDOUTR1 INCLUDE DOUTR1.OUTER1,INNER1.CHEBY1DOUTR2 INCLUDE DOUTR2 .OUTER2 , INNF.R2 .CHEBYI, IFISD2,SCTSD2 ,TOTSD2 ,FISSD2

NHSST INCLUDE NHSST.NHOEDO,INVERT,NHXSECDNHCCC INCLUDE DNHCCC,NHCC2D,NHCC2D,NHCC3D,NHTVLC,NHINNRDNHSST INCLUDE DNHSST,FXREAD.FXINIT.FSINITDNHOUT INCLUDE DNHOUT,OUTR1,OUTR2,OUTR3,OUTR4,OUTR5,ACCEL,ACCL3D.LEAK3,D,SRCFIS,SRCSCT,SRCHEX,PCHEX,PCHEXB,SRCZ1,SRCX2,PCZ,PCZB,FLXHF.X,FLXZ,FS,UPDT,CMMTRX,BKRINC,AXLEAK,CMSOLV,FSERRN,CONVCK,NHSFCMDNHFIN INCLUDE DNHFIN.NHEDDM.CFmL.NHVOL.FXSHAP*DSSTOU INCLUDE DSSTOU.TWODPR.TWODTB,BRED,DSEOUA,EDITDM,SCALPK,WPKEDT.NHSHAP.NHPEAK,DSSTOI INCLUDE DSSTO1.FORHMR.BKLWGT.SSTOUl,POWINT,RPWADD,APWADD,WPOWER,ORTSRF,TRISRFDSSTO2 INCLUDE DSSTO2,EDCORE,SSTOU2,RPSADD,WFLUX,ORTBAL,TRIBAL,HNHFLX,DSSTO3 INCLUDE DSSTO3,ADDVEC,DIVVEC,BALINT,RBLADD,RBLMF.D,RBLFIS,ABLADn,,APSADD,FLXINT,FLXRZ,WRZFLX**** GLOBAL COMMON BLOCK DECLARATIONS**

GLOBAL STFARC,PTITLE,IOPUT.ARRAY,VERNUM,IOCOM,SPECS,CONTRL,IOCO,MD,DEBUG,IOCOMC,SINGLE,POINTS,PNAMES,LOCATE,TNAMES, IDENT,LABSPC .FILEID,.NHCNTL.MHIOCM.NHIOPC.NHIOPDGNIP4C GLOBAL BCDFLT.BCDINT.ISIZESHEXMAP GLOBAL HEXPCORTHAP GLOBAL ORTPCHMC4C GLOBAL REF.HMGPTRDSSTOU GLOBAL EDITDMDSSTO3 GLOBAL BALBUF**** END OF SEGLINK INPUT**

END D3DRIV

G.l-1

G.I

Appendix G

SAMPLE PROBLEM OUTPUT

Sample Problem 1 (entire output)

1/01/84 Jill.700 PACE

BCD INPUT FILE - 1PRtKT HIE - 6AUXILIARY PRINT PILF '

jfcooi 30

04 i n o i i i n in IDD i o nOb l .n 0.001 0 .04 0.5UHFOHM-A.NIPl01 *••• SAMPLE PROIILFK I ••••n i n i 10000 o IOOO n n

1 4 0 4Xll .WOO I 4VU .MOO 1 4TCORE 1C OCTHOD CR CFPVYM. 1C OC KB CR C?

3D RNfl (LENCHKMK - RO!»S IK - TOW.

1 0 CF * 1

SCAN

ID 4 620 *NA COOI.F.D m

« * ii i20.768 0.212l.72336fi-*O9 ft.O2410000. 1000.

1/05/84 2221.700 PACE 2

BENCHMARK FOUR CROUP CROSS SECTIONS •1 1 14 II 160.0 0.0

i3P+O8 7.97003E+O7 3.|5946E*O7 1.01 E+07 8.00 E+05

1i

0.0 O.O 0.0 0.0

1"iD . 1 1 5 8 ? . 2 1 7 2 0 Ah

.2/220 -4ftl17 ,34571.173OS E~OI .39123 E-02 .18286 E-02 ,36134 E-02 .9341) F-Oi J.Olfc2.912171 2.flfl|R74 3.879S1 I70 0.0 0.0 .O21W7 0.0 .lbl^> E-0?.40791 E-OS 0.0 .46838 p-02 .42309 E-0," .44493 E-0741) 12 C.VK 1100. 0.0 0.0 O.lJ 0.0

I 3 Ii 0 200

5D .JliSfl '1213 .46770 .31349 .11188.21113 .46770 .35149 .66221 E-O1I.H395& E-0] 1.O0354E-O2,10k76 F.-Ol .4BM1 E-02 .1MJ? E-02 .11332 C-02 .1)238 E-OI 1.0790632.914926 2.61494J 2.8821117D 0.0 0.0 .021262 0.0 .15718 E-02.4641) E-01 0.0 .41414 E-02 .40'?* E-07 .49966 £-07w i) zn100.

zn0.0

i0.0 0.0 0.0 0.0

•I2999SE-OI .27688 F-02 .4<1.440977 2.42)l'l 2,<7D 0,0 0.0.)HBeo E-05 0.0 ,51*n 14 r,n i

I

I 1.1I127E-O33.06J463C-01| .OU2Il f tE-02

47 E-04 .11274 1-01 .3*152 K-03 J.796*JO

I J1 0 200

.231)3 .46274 .33149 a.ZZtS e-Otl.WQim-43 ?.triOftH-03,9116$ E-OI .1941) E-02 .JlOiS E-0* ,8756b E-01> .2)769 E-01 1.790264Z.44IR80 2.411086 J.*?298e70 0.0 0.0 .016)22 0.0 .!28fl9 E-01

in is era i*100. 0.0 0.0 0,0 0.0 0.0

0 0 0 0 0 0 0 0 I 1 0 1001 1 1 1 * 1 1 1 1

in .13317 ,1*3)1 ,580*4 .5*169 .13117.»]» .SIOU .54I6B .I86696Z-O2 .li*inE-OI .6U40SE-O1.IM6BTD O.n 0,0 .02394b 0.1 .37*17 C-02.10310 E-05 0.0 .96811 E-02 .70)61 β-ll .1041* 1-07ID 16 era i100. 0.0 0.0 0.0 D.O 0.0

G.l-2

1/Q5/H4 2221.7U0 PACE 1

1 I

.I14fl7 .12647 .19272

.7B660 F.-037D fl.ij 0.0

.6A7RO fc-0fi 0 . 0BLOCK-STP021,3REH0VF-CE0DSTREMOVE-COHPXSRF.MOVE-NDXSRFREMOVE-ZNATDNREMOVE"LABELSREMOVE-RTFLUXRFHOVF.-DIP3DHOniFY-A.DIF3D

01 * * • * SAMPLE PROBLEM 2 ***'02 4000 570004 1 0 0 00 111 10 100 1 0 0II I 40.0 1 87.5 1 135.0II I 175.0M0DIPY-A.NIP301 ***• SAMPLE PROBLEM 2 ***'02 0 1 lOfMO 0 1000 0 003 IU43-DELf.TEB1.OCK-STP021.3REHOVE-fiEODSTREHDVE-COMPXSREHOVE-NDXSRPREMOVE-ZNATDNREHOVE-LABELSR1.N0VE-RTFUJXRF.MOVE-NHFl.UXHF.M0VE-DIF3DUNF0RM-A.D1F3D

01 **** SAHPLE PROBLEM 3 **•«02 2finno 27000 o01 0 0 0 4500 5004 I 0 0 00 110 10 100 1 0 005 J .OF-7 I ,OE-b 1.OE-506 1.0 0.001 0.04 (1.5II I 40.0 1 87 .5 I 135.011 I 17'

0 | • • • * SAMPLE PROBLEM 3 * • * *02 0 I 8000 0 1000 0 0

.2I6305K-O3 .16880 E-03 -11468 E-OZ

.012942 O.O , 12H7 | E-02. 3 4 5 3 ) E-02 .43633 E-M . 6 9 9 0 1 E-Ofl

2D SNR BEKCHHARK - RODS IN - NODAL

2D SHR BENCHMARK - RODS IN - NODAL

0304

3D SNR HENCHHARK - RODS [N - NODAL

BENCHMARK - 8 PLANES - NODAL

7 4 0 4 4 4XII .5000 1 4tit ."bflflO 1 4Zl. .5000 I 4ZU .5000 1 '.Z 2 40 .0 2 87 .5 2 135.0Z 2 175.0HI II 1.0

1.0H3 n 1.0

1/05/S4 2221.700 PACE 4

30303f)3030

30303030303030303030303D30

11.2003 II I

1C h 0 0AB h 0 01C 6 0 0

AB a o oOC 8 0 0

RR 10 0 0

9 45 4i9 45 41

7 37 35 3!4 1

0.0 175.040.0 135.00.0 175.0

40.0 135.00.0 175.0

40.0 135.00.0 175.0

40.0 135.00.0 175.C

40.0 135.00.0 175.0

40.0 135.00.0 175.0

40.0 135.00.0 175.0

40.0 135.00.0 175.00.0 175.00.0 175.0

40.0 135.00.0 175.00.0 175.0

40.0 135.00.0 175.0

40.0 135.00.0 175.00.0 175.00.0 135.00.0 87.50.0 87.5

135.0 175.067.5 175.087,5 175.0

7 37 35 35

BLOCK-STPO21.3REHOVE-GEODSTREMnVE-COHPKSREMOVE-NDXSRfREM0VE-2NATDNREMOVE-LABELSREHOVE-RTFLUXREHOVE-NHFLIIXREH0VE-D1F3DMODIFY-A.0IF3D

01 • • • * SAMPLE PROBLEM 4 • • • *02 12000 164000MODIFY-A.N1P301 " * • SAMPLE PROBLEM 4 * * * •03 90

SNR BENCHMARK - III-OS IN - FDO636

$D SNK BENCHMARK - RoDS IN - FD0636

G.l-3

SCAN

0909

1/05/84 2221.700 PAGE 5

Z 8 40.0 10 87.5 10 135.0Z 8 175.0

STUFF BCD FILES FORMED FROM BLOCK STPO21

A.DIF3D VERSION - 1, MAXIMUM CARD TYPE - 6, NOSORT CARDS - 0CARDS-PER-CARD-TYPE 1 1 1 1 0 1THIS FILE CONTAINS UNFORMATTED CARDS.

01 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD0602 3600 600003 0 0 0 0 3004 1 0 0 11 111 10 100 1 0 006 1.0 0.001 0.04 0.5

1/05/84 2221.700 PAGE 6

A.NIP3 VERSION - 1, MAXIMUM CARD TYPE - «',, NOSORT CARDS - 0CARDS-PER-CARD-TYPE 1 1 1 1 2 0 3 0 0

0 0 0 0 0 0 0 0 10 0 1

THIS FILE CONTAINS UNFORMATTED CARDS.**** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD060 1 10000 0 1000 0 0 0 0 1707 4 0 4XU .5000 1 4YU .5000 1 4TCORE 1C OCTROD CR CFTOTAL 1C OC RB CR CFMl II 1.0

1.01.01.01.01.0

0102030405050707071414141414141515151515293030303030303030303030303030303030

019

M2M3M4M5M6MlM2M3M51-16

12131415161COCRBCRCF

11.2003 11 11C1C1C1C1C1COCOCOC 8RB 9RB 10RB 8 1OC 9 4 5OC 9 45 46RB 11 5 6RB 11 56 57CR 7 3

1

G.l-4

STUFF BCD FILES FORMED FROM BLOCK STPO2) 1/05/84 2221.700 PAGE

303043

CRCF1

740

3510 .6

A.ISO VERSION - 1 , MAXIMUM CARD TYPE -CARDS-PER-CARD-TYPE - 0

OV ISOTXS HH2 *GFK 3D BNCH * 1ID 4 6 0 3 0 1 1 12D *NA COOLED FBR BENCHMARK FOUR GROUP CROSS SECTIONS

* II 12 13 14 15 160 . 7 6 8 0 . 2 3 2 0 .0 0.01.72336E+O9 4.O2463E+O8 7.97OO3E+O7 3.15946E+O7 1.0510000. 1000. 0 .0

0 3 6 9 1210.0

0 03 4

0, NOSORT CARDS - 66

<vfO7 8.00 E+05

154D II100.

01

GFK0.0 0.0

12

.21220

0.01 0 200

0.00 01 1 1 1

5D .11587 .21220 .46137 .34571 .11587.21220 .46137 .34571 .69059 E-031.830758E-03 .92948 E-02.17305 E-01 .39121 E-02 .18286 E-02 .36334 E-02 .92415 E-02 3.0360662.912173 2.881874 2.879511

.023597 0.0 .16153 E-02.46838 E-02 .42309 E-07 .44493 E-07

10.0 0.0 0.0 0.0

1 0 0 0 0 0 1 1 0 2002 3 4 1 1 1 1.21213 .46770 .35349 .11588

.21213 .46770 .35349 .66221 E-031.83956 E-03 1.O0354E-O2

.20476 E-01 .48531 E-02 .26377 E-02 .51332 E-02 .13238 E-01 3.0790632.91492b 2.884945 2.882535

.023262 0.0 .15718 E-02.43414 E-02 .40724 E-07 .49968 E-07

7D 0.0 0.0.40791 E-05 0.04D 12 GFK100. 0.0

0 0 11 1

5D .11588

7D 0.0 0.0.46451 E-05 0.04D 13 GFK100. 0.0

0 0 11 1 2

0.0 0.0 0.0 0.00 0 0 0 0 1 1 0 2003 4 1 1 1 1

5D .14584 .28443 .52703 .40732 .14584.28443 .52703 .40732 I.11527E-033.063463E-031.O02116E-O2.129995E-O1 .27688 E-02 .44347 E-04 .12274 E-03 .34952 E-03 2.7964102.440977 2.42317! 2.422951

.032071 0.0 .27776 E-02.58971 E-02 .90018 E-07 .45039 E-07

10.0 0.0 0.0 0.0

0 0 0 0 0 1 1 0 2003 4 1 1 1 1

.46274 .33749 .12270

7D 0.0 0.0.38880 E-05 0.04D 14 UFK100. 0.0

0 0 11 1 2

5D .12270 .23133.23133 .46274 .33749 8.2278 E-042.170873E-03 7.64O83E-O3.97185 E-02 .19453 E-02 .31065 E-04 .87566 E-04 .23769 E-03 2.7902642.441880 2.423086 2.4229887D 0.0 0.0 .026322 0.0 .22889 E-02.28907 E-05 0.0 .53536 E-02 .62133 E-07 .33248 E-07

4D 15 GFK 1

IRMED FROM BLOCK STP021 1/05/84 2221.700 PAGE

0.0 0.0 0.0 0.00 0 0 0 0 1 1 0 2003 4 1 1 1 1

.58044 .54168 .13317.54168 .186696E-02 .126433E-01 .634405E-01

.022946 0.0 .37687 E-02.86815 E-02 .70361 E-ll .10489 E-07

10.0 0.0 0.0 0.0

0 0 0 0 0 1 1 0 2001 1 2 3 4 1 1 1 1

50 .072206 .11487 .32642 .19272 .072206.11487 .32642 .19272 .216305E-03 .16880 E-03 .11468 E-02.78660 E-037D 0.0 0.0 .012942 0.0 .12871 E-02.68780 E-06 0.0 .34533 E-02 .43633 E-ll .69903 E-08

SUBROUTINE STUFF USED 2048 WORDS OF CORECP TIME- 0.38 SECONDS, PP TIME- 0.0 SECONDS

STUFF

100.0

BCD FILES

0.00 0

5D .13317 .25.25355.168687D 0.0

.58044

0.0.10320 E-05 0.04D 16100.

0

GFK0.00 0

G.l-5

GNIP4C 11/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/81 2221.700 PACE 9

*** GNIP4C - GENERAL NEUTRONICS BCD INPUT PROCESSOR TO CREATE CCCC BINARY INTERFACE FILES ***

lonoo0ni0i

IMAINGIBUI.KGIPRNTGIGMEDTIMAPRIMAPZ

*** CNIP4C CONTROL PARAMETERS ***

NO. OF WORDS OF MAIN MEMORY REQUESTEDNO. OF WORDS OF BULK MEMORY REQUESTEDBPOINTER TRACE AND DUMP CONTROL (0/1/2/3, NEITHER/DUMP/lRACE/BOTH)OEOMETRY PROCESSING EDIT CONTROL (0/1/2/3, NO EDITS/PRxNT EDITS/EDITS TO AUXILIARY FILE/BOTH)REGION MAP OPTION (0/1/2/3, NO MAP/PRINT MAP/MAP TO AUXILIARY FILE/BOTH)ZONE (COMPOSITION) MAP OPTION (0/1/2/3, SEE IMAPR)

*** MODEL DESCRIPTION ***

9r>si3116311642

21

24100I1

1.1200D+016.4665D+00

IGOMNZONENREGNZCLNCINTINC1NTJNINTININTJIMBIIMB2JMB1JMB2NBSNBCSNIBCSNZWBBNRASSNTRIAGNTHPTFLATSIDE

GEOMETRY TYPE, TRIANGULARN, . OF ZONES (COMPOSITIONS)NO. OF REGIONSNO. OF ZONE CLASSIFICATIONSNO. OF 1ST DIMENSION COARSE MESH INTERVALSNO. OF 2ND DIMENSION COARSE MESH INTERVALSNO. OF 1ST DIMENSTON FINE MESH INTERVALSNO. OF 2ND DIMENSION FINE MESH INTERVALSFIRST BOUNDARY CONDITION, FIRST DIMENSION, PERIODIC, NEXT FACE CLOCKWISELAST BOUNDARY CONDITION, FIRST DIMENSION, EXTRAPOLATEDFIRST BOUNDARY CONDITION, SECOND DIMENSION, PERIODIC, SEE IMBILAST BOUNDARY CONDITION, SECONP DIMENSION, EXTRAPOLATEDNO. OF BUCKLING SPECIFICATIONSNO. OF CONSTANTS FOR EXTERNAL BOUNDARIESMO. OF CONSTANTS FOR INTERNAL BOUNDARIESNO. OF BLACKNESS THEORY ZONES0/1, REGION ASSIGNMENTS TO COARSE/FINE MESHOUTER BOUNDARY SHAPE, 60 DEGREE RHOMBUSORIENTATION OF (1,1) MESH TRIANGLE - POINTS AWAY FROM 1ST DIMENSION AXISHEXAGON FLAT-TO-FLAT DISTANCELENGTH OF MESH-TRIANGLE SIDE

EXTERNAL BOUNDARY CONDITION CONSTANTS C (D * DEL PHI - - C * PHI), BY GROUPLAST VALUE SHOWN IS USED FOR REMAINING GROUPS

LAST TRIAG BOUNDARY

1 5.00000D-01 2 5.00000D-01 3 5.00000D-01 4 5.00000D-01

LAST BOUNDARY

1 5.00000D-01 2 S.00000D-01 3 5.00000D-01 4 5.00000D-O1

GNIP4C 11/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FDO6 1/05/84 2221.700 PAGE 10

REGION/ZONE SPECIFICATIONS

REGION REGION RFGIONNO. NAME VOLUME

1COCRBCRCF

1.430E+031.521E+O31.955E+032.173E+O21.O86E+02

ZONENO.

ZONENAME

1 Ml2 M23 M35 M56 M6

ZONECLASS.

00000

BUCKLING BY GROUP (REPEAT LAST VALUE FOR RE.IAINING GROUPS)

0.00.00.00.00.0

0.0

INTERNAL BOUNDARY CONDITION CONSTANTS C (D * DEL PHI - - C * PHI), BY GROUPLAST VALUE SHOWN IS USED FOR REMAINING GROUPS

REGIONS COMPRISING AREAS

AREANO. NAME

1 TCORE2 TROD3 TOTAL

REGIONNO. NAME

1 1C4 CR1 1C

REGIONNO. NAME

2 OC5 CF2 OC

RFGIONNO. NAME

3 RB

RF.UIONNO. NAME

4 CR

REGIONNO. NAME

5 CF

REGIONNO. NAME

REGIONNO. NAME

G.l-6

16

IS

M

13

12

11

10

S

8

7

6

5

*

3

2

1

-17 -15 -13 -11 - 9 - 7 - 5 - 3 - 1 1 3 5 7 9 11 13 IS

RB

0C

9 11 13 15 17 19 21 23 25 27 29 31 33

GN1P4C Generated Calcomp 780 Plot of 2D SNR Benchmark Model

G.l-7

GNIP4C 11/83 •••* SAMPLE PROBLEM 1 *•"" 2D SNR BENCHMARK - RODS IN - FDO6 1/05/84 2221.700 PACE II

-17 -15 -|3 -|| - 9 . 7 - 5 - 3 - 1 | 3 5 7 9 H 13 15 |7

II, t • * * •H3 • •

15 * RB • 15

• • • • 11, 5 •

• • H3 •

14 • RB * • 14

• 10, 5 • • • •

* M3 « *

13 OC * • RB « 13

9 , 5 • * • • 10, 4 » • • •

H2 * * H3 * *

12 • OC * • BB • 12

• • • * 9, 4 • • • • 10, 3 • • • •

* * H2 * * H3 * *

II • OC * • RB * * RB * 11

• 8, 4 • • • • 9, 3 . » • • 10, 2 • • • •

• M2 • • M3 » * H3 • *

10 OC • • OC * * RB * * RB • 10

7 , 4 • • • • 8 , 3 • • • • 9 , 2 * * • • 1 0 , I *M 2 • • M 2 • * M 3 • ' ( 1 3 •

9 * C R • « O C « • R B • « 9* * * * 7 , 3 * * * * 8, 2 « * * * 9, 1 * « « «

• * M5 • * M2 • • H3 • •

8 • 1C • * O C • • RB • * RB * 8

* 6 , 3 * * • * 7 , 2 * * * * 8 , 1 * * * * 10, 54 *

• Ml * * H2 • » H3 * * M3 •

7 1C • • 1C • • O C • * RB * • 7

5 , 3 • • • • 6 , 2 • • • • 7 , 1 « • • • 9 , 4 8 • • • •M l • • M l • • M 2 • * H 3 • •

6 * 1 C * • O C » • O C * * R B * 6* * * * S, 2 • * » * 6 , 1 # • * * 8, 42 * * • * 10, 53 *

* * Ml * * M2 * * M2 * * M3 *

5 • 1C • • 1C • • OC • « RB • « 5

* 4 , 2 * * * * 5 , 1 * * * * 7, 36 * * • * 9, 47 • # * *

* Ml • "Ml * • M2 • • Hi • *

4 1 C * » CF • • 1C • • OC * • RB • 4

3, 2 • • • • 4 , 1 • • • • 6, 30 • • • « 8, 41 • • • • 10, 52 • « * *

Ml • • M6 * * HI « • M2 * * M3 « *

3 • 1C * • 1C * * CR • * OC • * RB • 3

• . • • 3 >

1 • « • • 5 >

24 • « • • 7, 35 • • • « 9, 46 • • * • 11, 57

* • HI • * Ml « * H5 * • H2 • * M3 •

2 • 1C * * 1C • • 1C • * OC • * RB • • 2

* 2, 1 * * * * 4, 18 * • * * 6, 29 * * * * 8, 40 • * * * 10, il * * * *

• Ml * • Ml • • Ml • * M2 * * M3 • *

1 1C • • 1C • • 1C • • OC • * OC * •Rβ * 1

I . I • • * « 3, 12 • » • • 5, 23 • • • • 7, 34 • « • * 9, 45 • « * * 11, 56

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

CNIP4C 11/83 •••• SAMPLE PROBLEM I •••• 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2221.700 PACE 12

•** GRAPHICS OUTPUT SPECIFICATIONS •••

1 IPLOT 0/1, NO GRAPHICS OUTPUT/GRAPHICS OUTPUT

7.8488D+00 XPAGE WIDTH OF GRAPHICS PACE (INCHES)

6.2OOOD+OO YPACE HEIGHT OF GRAPHICS PAGE (INCHES)

6.0000D-OI FTOF FLAT-TO-FLAT DISTANCE (INCHES)

GRAPHICS COMPLETE

••* ISOTXS FILE CONTROL INFORMATION ••*

NA COOLED FBR BENCHMARK FOUR GROUP CROSS SECTIONS

NUMEE. OF ENERGY GROUPS IN SET

NUMBER OF ISOTOPES IN SET

MAXIMUM NUMBER OF UPSCATTER GROUPS

MAXIMUM NUMBER OF DOWN SCATTER CROUPS

MAXIMUM SCATTERING ORDER

FISSION SPECTRUM FLAG

MAXIMUM NO. OF BLOCKS OF SCATTERING DATA

BLOCKING CONTROL FOR SCATTER MATRICES

*** ISOTXS ISOTOPE LABELS ***

ISOTOPE ISOTOPE ISOTOPE ISOTOPE ISOTOPE ISOTOPE ISrTOPE ISOTOPE

NO. LABEL NO. LABEL NO. LABEL N1. LABEL NO. LABEL NO. LABEL NO. LABEL NO. LABEL

•»• NDXSRF CONTROL PARAMETERS •••

NUMBER OF NUCLIDES

NUMBER OF NUCLIDE SETS

MAXIMUH NUMBER OF NUCLIDES IN A SET

NUMBER OF UNIQUE ISOTOPES

KUHBER OF MATERIALS SPECIFIED

NUMBER OF SIIBZONES SPECIFIED

NUHBER OF ZONES SPECIFIED

*•* DESCRIPTION OF NUCLIDE SET I * «

ISOTOPES INCLUDED II 12 I] 14 15 16

ZONES A5SIGUED HI M2 M] H4 M5 H6

46

0

30

11

1

NGROUP

NISO

HAXUP

MAXON

MAXORD

ICH1ST

NSCMAXNSBLOK

6

16

6

0

0

6

NONNSNNNSNANNUMMAT

NSZNZONE

G.l-8

GNIPAC 11/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FDO6 1/05/84 2221.700 PAGE 13

CONTENTS OF ZNATDN SPECIFICATIONS RECORD

0.00661

TIMENCYJJTZSZNNSNBLKAD

REFERENCE REAL TIME, DAYSREFERENCE CYCLE NUMBERNUMBER OF ZONES PLUS NUMBER OF SUBZONESMAXIMUM NUMBER OF NUCLIDES IN ANY SETNUMBER OF BLOCKS OF ATOM DENSITY DATA

GNIP4C 11/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2221.700 PAGE 14

*** ATOM DENSITIES OF ZONES (INCLUDING CONTRIBUTIONS FROM SUBZONES) ***THE ISOTOPE NUMBERS SHOWN ARE THE ISOTXS NUCLIDE NUMBERS

ZONE NUCLIDE ISOTOPE ATOM DENSITY ISOTOPE ATOM DENSITY ISOTOPE ATOM DENSITY ISOTOPE ATOM DENSITYNO. NAME SET NO. NAME (ATOMS/B-CM) NO. NAME (ATOMS/B-CM) NO. NAME (ATOMS/B-CM) NO. NAME (ATOMS/B-CM)

1 Ml

2 M2

3 M3

4 M4

5 M5

6 M6

1

2

3

4

5

6

11

12

13

14

15

16

1.0000D+00

1.0000D>00

1.0000D+00

1.0000D+00

1.0000D+00

1.0000D+00

*** THE FOLLOWING BINARY FILES HAVE BEEN WRITTEN ***

FILE NAME VERSION NO. LOGICAL UNIT

ELAPSED CP TIME -ELAPSED PP TIME -MAIN CORE REQUIRED -MAIN CORE REQUESTED -BULK CORE REQUIRED -BULK CORE REQUESTED -

0.860.0542

1000000

ISOTXSGEODSTLABELSZNATDNNDXSRF

SECONDSSECONDSWORDSWORDSWORDSWORDS

2726202928

HMG4C 6/83

G.l-9

**** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - ROUS IN - FD06 1/05/84 2221.900 PAGE 15

* * * HMG4C - CCCC TO ARC SYSTEM CROSS SECTION HOMOGENIZATION * * *

TIME,

DATE,

2221.900

1/05/8*

FILE A.HMG4C DOES NOT EXIST . . . DEFAULT VALUES WILL BE USED

FILE NDXSRF IS LUN 28 AND CONTAINS THE USER ID - 1/05/2221.9-

FILE ZNATDN IS LUN 29 AND CONTAINS THE USER ID - 1/05/2221.7-

FILE ISOTXS IS LUN 27 AND CONTAINS THE USER ID -GFK 3D BNCH -

FILE COMPXS WILL NOW BE WRITTEN ON LUN 19

SIZE OF CONTAINER ALLOCATED FOR HMG4C - 1000

SIZE OF CONTAINER ACTUALLY USED BY HMG4C - 415

ELAPSED CPU TIME -

ELAPSED PP TIME -

2.14 SEC.

0.0 SEC.

* * * END OF HMG4C * * *

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06

INPUT FILE DIF3D , VERSION 1, USER IDENTIFICATION -

INPUT FILE COMPXS, VERSION 1, USER IDENTIFICATION -

INPUT FILE GEODST, VERSION 1, USER IDENTIFICATION - 1/05/

INPUT FILE LABELS, VERSION 1, USER IDENTIFICATION - 1/05/

1/05/84 2222.000 PAGE 16

HAS BEEN PROCESSED.

HAS BEEN PROCESSED.

HAS BEEN PROCESSED.

HAS BEEN PROCESSED.

PROCEDURE DEFAULT RECOMMENDED DISKPARAMETERS CYLINDERS CYLINDERS TYPE

ZONCYL

FLXCYL

PSICYL

FDCCYL

PSUCYL

SRFCYL

DMY1CYL

DMY2CYL

DMY5CYL

RTCYL

ATCYL

1

1 .

5

20

3

12

21

7

4

5

5

1

1

1

1

0

1

2

3

1

1

1

3330

3330

3330

3330

3330

3330

3330

3330

3330

3350

3350

G.l-10

DIF3D 4 . 0 7 / 8 3 • " • SAMPLE PROBLEM 1 *•*• 2D SNR BENCHMARK - RODS IN - FD06 1 /05 /84 2 2 2 2 . 0 0 0 PACE 17

• * • DIP3D STORAGE ALLOCATION * * *


MINIMUM NUMBER OF WORDS REQUIRED TO RUN THIS PRnKLEM

WITH ALL DATA FOR t GROUP IN CORE



FCM

3600

417

417

417

ECM

6000

42S9

5777

10953

LOCATION OF SCRATCH FILES DURINC STEADY STATE CALCULATION

FILE CONTENTS

NEW FISSION SOURCE

OLD FISSION SRC. 1

OLD FISSION SRC. 2

TOTAL SOURCE

COMPOSITION MAP

FLUX ITERATE

CROSS SECTIONS

FINITEDIFF. COEFS.

NO. OFRECORDS

1

1

1

1

1

4

4

4

RECORDLENGTH

496

496

496

496

US

496

72

1488

FILELENGTH

496

496

496

496

248

1984

288

5952

LOCATION

CORE

CORE

DISK

CORE

CORE

CORE

CORE

DISK

RECORDSIN CORE

1

0

1

'

4

4

1

TOTAL NUMBER OF WORDS USED FOR T H I S PROBLEM 417 5993

OIF3D 4 . 0 7 / 8 3 **** SAMPLE PROBLEM 1 * • * * 2D SNR BENCHMARK - RODS IN - FD06 1 /05 /84 2 2 2 2 . 1 0 0 PAGE 18

* • • USER INPUT SPECIFICATIONS FOR THIS PROBLEM * • *

000000

IPROBTISOLNTIXTRAPIRSTRTIOSAVEIOMEG

0/10/10 /10 / 10/10 /1

EIGENVALUE/FIXED SOURCE PROBLEMREAL/ADJOINT SOLUTIONYES/NO CHEBYSHEV OUTER ACCELERATIONNO/YES THIS IS A RESTARTNO/YES BYPASS LAST CONCURRENT INNER ITERATION PASS IN GROUPS 1EL0W THE LAST PASS THRESHOLD

0 / 1 NO/YES ASYMPTOTIC EXTRAPOLATION DURING THE OPTIMUM OVERRELAXATION FACTOR ESTIMATION ITERATIONS

3600 MAXSIZ6000 MAXBLK4500 MINBSZ

30 NOUTMX1000000000 LIMTIM

50 INRMAX

STORAGE, ITERATION, TIME LIMITS

NO. OF WORDS REQUESTED FOR FCM DATA STORAGE CONTAINERNO. OF WORDS REQUESTED FOR ECH DATA STORAGE CONTAINERMINIMUM DESIRED (PLANE-BLOCK) RECORD LENGTH (IN WORDS) FOR CONCURRENT INNER ITERATIONMAXIMUM NUMBER OF OUTER ITERATIONS ALLOVED(-1/-2 BYPASS OUTERS/AND SLOR FACTOR CALCULATION)MAXIMUM PROCESSOR TIME (SECONDS) ALLOWEDMAXIMUM NUMBER OF ITERATIONS PERMITTED DURING THE OPTIMUM OVERRELAXATION FACTOR ESTIMATION PROCEDURE.

EDIT OPTIONS (REGION INTEGRAL EDITS INCLUDE AREA EDITS)

100

!111110

1001000

IEDF(1)IEDF(2)IEDF(3)IEDF(«)IEDF(5)IEDF(6)IEDF(7)TEDF(B)IEDF(9)lEDF(lO)ISRHSD

0/1/2/30/1/2/30/1/2/30/1/2/30/1/2/30/1/2/30/1/2/30/1/2/30/1/2/30/1/2/3-1/0/N

•IONE/PRINT/ AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/BOTHNONE/PRINT/AUXILIARY/IOTHNONE/PRINT/AUXILIARY/BOTHNONE/PWDINT/RZFLUX/BOTH

PROBLEM DESCRIPTIONGEOMETRY REGION MAPGEOMETRY ZONE MAP

MACROSCOPIC CROSS SECTIONS (SCATTERING+PRINCIPAL, PRINCIPAL ONLY)BALANCE INTEGRALS BY (GROUP, REGION AND GROUP, REGION)POWER (REGION INTEGRALS, DENSITY BY MESH CELL)FLUX (Rr.^ION INTEGRALS, BY MESH CELL, BY MESH CELL AND GROUP)ZONE AVERAGED FLUXREGION AVERAGED FLUXFILES TO BE WRITTEN

N0NE/INPUT-1ST PASS, OUTPUT-LAST SEARCH PASS/REQUESTED EDITS (ABOVE) EVERY N-TH SEARCH PASS

1.OOOO00D-O71.OOOOOOD-05l.OOCOOOD-05

EPS2EPS3

CONVERGENCE CRITERIA

DESIRED EIGENVALUE CONVERGENCEDESIRED POINTWISE FISSION SOURCE CONVERGENCEDESIRED AVERAGE FISSION SOURCE CONVERGENCE

OTHER FLOATING POINT DATA

l.OOOOOOD+00 EF«C K-EFFECTIVE OF REACTORI.OOOOOOD-03 rtSMIN CUT-OFF POINT FOR CONSIDERATION OF A FISSION SOURCE IN CALCULATING FLAMUP AND FLAMLO4.OOOOO0D-O2 PSINRM INNER ITERATION ERROR REDUCTION FACTOR PER OUTER ITERATION5.000000D-01 POWIM STEADY STATE REACTOR POWER (WATTS)

I

G.l-11

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.100 PAGE 19

*** PROBLEM DESCRIPTION ***

NO. OF FIRST DIMENSION MESH INTERVALS - 31NO. OF SECOND DIMENSION MESH INTERVALS - 16NO. OF THIRD DIMENSION MESH INTERVALS - 1NO. OF ZONES - 6NO. OF REGIONS - 5NO. OF ENERGY GROUPS - 4MAXIMUM NO. OF DOWNSCATTER GROUPS - 3MAXIMUM NO. OF UPSCATTER GROUPS - 0

PROBLEM GEOMETRY - 2-DIMENSIONAL TRIANGULAR

RHOMBIC BOUNDARY WITH 60 DECREE (SIXTH CORE) SYMMETRY

TRIANGLE SIDE LENGTH - 6.466496D+00

BOUNDARY CONDITIONS (ORIGIN AT LOWER LEFT)

0 - ZERO FLUX 1 - ZERO CURRENT 2 - EXTRAPOLATED 3 - PERIODIC OPPOSITE FACE4 - PERIODIC NEXT ADJACENT FACE 5 - INVERTED PERIODIC A LONG FACE

X - LEFT4

X - RIGHT2

Y - FRONT4

Y - BACK2

BOUNDARY CONDITION 2 IS APPLIED TO MESH CELL SURFACES ADJACENT TO EXCLUDED BACKGROUND CELLS.

GROUP1234

TRIAG - 0.04.69200OD-O14.692000D-014.692000D-014.692000D-01

TRIAG - 0.04.999999D-014.999999D-014.999999D-014.999999D-01

EXTRAPOLATED BOUNDARY CONDITION CONSTANTS C(DEL PHI/PHI - C/D , LAST VALUE USED FOR REMAINING GROUPS

- 0.04.692000D-014.692000D-014.692000D-014.692000D-01

- 0.04.999999D-O14.999999D-014.999999D-014.999999D-01

INTERNAL BLACK BOUNDARY CONDITION CONSTANT C FOR ALL GROUPS(DEL PHI/PHI - C/D

0.0


BUCKLING SPECIFICATION FOR ALL ZONE

BUCKLING > 0.0

REGION ZONE ZONENO. NAME NO. NAME

1 1C5 CF

1 Ml6 M6

REGION NUMBI2R AND ASSIGNMENT TO ZONE



2 OC 2 M2 RB 3 M3


4 CR 5 M5

G.l-lZ

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 20 SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.100 PACE 21

*** EDIT OF MACROSCOPIC CROSS SECTION DATASET COMPXS ***

NO. OF COMPOSITIONS

NO. OF PRECURSOR FAMILIES

NO. OF ENERGY GROUPS

MAXIMUM NO. OF DOWNSCATTER GROUPS

MAXIMUM NO. OF UPSCATTER GROUPS

MAXIMUM ENERGY BOUND (EV)

MINIMUM ENERGY BOUND (EV)

6

0

4

3

0

1.O5O0OD+O7

0.0

GROUP NEUTRON VELOCITYNO. (CM/SEC)

1 1.72336OOD+O9

2 4.0246298D+08

3 7.97003040+07

4 3.15946O8D+O7

MAXIMUM ENERGY

(EV)

1.O50O0OOD+O7

8. OOOOOOOD+05

1.0000000D+04

J.OOOOOOOD+03

MAX DOWNSCATTER MAX UPSCATTER

DIF3D 4.0 7/83 *•** SAMPLE PROBLEM 1 ••*• 2D SNR BENCHMARK - RODS IN - FD06

*£•*••• E1JIT op FISSIONABLE COMPOSITION 1 (Ml ) IN COMPXS

1/05/84 2322.100 PAGE 22

GROUPABSORPTION

CROSS SECTIONDIRECTIONAL DIFFUSION COEFFICIENTS

Dl D2 D3REMOVAL FISSION FISSION NEUTRONS POWER CONVER.

CROSS SECTION CROSS SECTION SPECTRUM(CHI) PER FISSION FACTOR

1 4.602890D-03 2.876787D+00 2.876787D+OO 2.876787D+OO 2.820400D-O2 3.912300D-03 7.68OO0OD-O1 3.036066D+00 1.262032D-132 3.659358D-03 1.57O845D+OO 1.570845D+00 1.5708450+00 5.274700D-O3 1.828600D-03 2.32OOOOD-O1 2.912173D+OO 5.89871ID-143 I.292820D-02 7.224859D-O1 7.224859D-O1 7.224859D-O! I.7612000-02 3.6134OCD-O3 0.0 2.881874D+00 J.J72065D-134 2.654650D-02 S.641993D-01 9.641993D-01 9.641993D-01 2.654650D-O2 9.241499D-03 0.0 2.879511D+OO 2.981I29D-13

INTO GROUP234

FROM GROUP1 2.359700D-021 4.079100D-061 4.449300D-08

SCATTERING CROSS SECTION (TOTAL)

2 1.6153OOD-O32 4.230900D-08 3 4.683800D-03

G.l-13

n m n 4.0 7/83 ••** SAMPLE PROBLEM 1 *•** 21) SNR BENCHMARK - RODS IN - FD06

•**•*•• EDI T OF FISSIONABLE COMPOSITION 2 (M2 ) IN COMPXS

1/05/84 2222.100 PAKE 23

ABSORPTION DIRECTIONAL DIFFUSION COEFFICIENTS REMOVAL FISSION FISSION NEUTRONS POWER CONVER.CROUP CROSS SECTION nl D2 D3 CROSS SECTION CROSS SECTION SPECTRUM'ruj) PER FISSION FACTOR

3.O79O63D+OO 1.565516D-132.9I4926D+OO 8.5O8711D-142.8B4945D+00 1.65587ID-132.8821150+00 4.27O324D-13

1234

5.5153100-034.47726OD-O31.5168600-023.17I4OOD-O2

2179

.8765390+00

.5713630+00

.1270760-01

.4297810-01

2.1.7.9.

8765390+005713630+001270760-0142978ID-OI

2.1.7.9.

876539D+OO57I363D+OO1270760-01429781D-H1

2613

.B782OOO-02

.O491O1D-O3•951OOOD-O2. 371400U-O2

4251

.8531OOD-O3

.637700D-O3

.1132000-03

.32J8OOD-O2

7.680000 D-012.32OO00D-010.00.0

INTO CROUP234

FROM CROUP1 2.3762O0D-021 4.6451000-061 4.9968000-08


2 1.5718OOO-O3

2 4.O724OOD-O8 3 4.1414010-03

0IF30 4.0 7/83 SAMPLE PROBLEM 1 **** 20 SNR BENCHMARK - RODS IN - FII06

•* EDIT OF FISSIONABLE COMPOSITION 3 (Hi ) IN COMPXS

1/05/84 2222.ICO PAGE 24

ABSORPTIONCROUP CROSS SECTION

DIRECTIONAL DIFFUSION COEFFICIENTSDl D2 D3

1234

3.3.1.1.

8840700-031O781OD-O30143900-02334902D-O2

2.1.6.8.

2R5610D+O01719340+00324751D-O11835730-01

2.1.6.8.

2856100+00171934D+OO3247510-011835730-01

2.1.6.

a.

2856103+00171934D+OO32475ID-O1183573D-O1

3.5959OOD-O25.8855OOD-O31.6O41OOO-O21.3349O2D-O2

2413

.768ROOD-O3

.4347010-05

.2274000-04

.4952OOD-O4

7.680000 D-012.32O0O0D-O10.00.0

REMOVAL FISSION FISSION NKUTRONS POWER CONVER.CROSS SECTION CROSS SECTION SPECTRIIMtCHI) PER FISSION FACTOR

2.796410D+00 8.93I614D-142.44O977D+OO 1.430549D-152.423I71D+OO 3.959356D-152.422951O+O0 1.127484O-14


INTO GROUP234

FROM111

GROUP3.707100D-023.8880000-064.5039000-08

22

29.7776OOD-O3.001798D-08 3 5.8971O1D-O3

G.l-14

DIF3D 4.0 7/83 •*** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06

• •***»* EDIT OF FISSIONABLE COMPOSITION 4 (M4 ) IN COMPXS

1/05/84 2222.100 PACE 25

ABSORPTIONCROSS SECTION

2.768O8OD-O32.2O1938D-O37.728397D-O39.956190D-03


REMOVAL FISSION FISSION NEUTRONS POWER CONVER.CROSS SECTION CROSS SECTION SPECTRUM(CHI) PER FISSION FACTOR

2.716654D+OO 2.716654D+OO 2.716654D+OO 2.9O93OOD-O2 1.9453O0D-03 7.68OOOOD-O] 2.790264D+O0 6.275163D-14I.44O943D+OO 1.440943D+00 1.44O943D+OO 4.490900D-O3 3.106501D-05 2.32OOOOD-O1 7.441880D1-00 1.OO2O97D-157.2O3469D-O1 7.2O3469D-O1 7.2O3469D-O1 L.3O82OOD-O2 8.7566OOD-O5 0.0 2.423086D+00 2.824710D-159.876835D-01 9.876835D-0I 9.876835D-0] 9.956190D-03 2.3769OOD-O4 0.0 2.422988D+00 7.667421D-15

INTO GRr IP234

FROMIIi

(IROUP2.6322OOD-O22.89O7OOD-Oh3.3248OOD-OB


2 2.28B900D-03

2 6.2H29SD-Oa 1 5.3536OOD-03


********* E D I T O F NON-FISSIONABLE COMPOSITION 5 (M5 ) IN COMPXS ******************************

ABSORPTION DIRECTIONAL DIFFUSION COEFFICIENTS REMOVAL POWER CONVERSIONGROUP CROSS SECTION Dl D2 D3 CROSS SECTION FACTOR

1234

1161

.866960D-03

.264330D-02

.344O5OD-O2

.686800D-01

2.].5.6.

503066D+00314665D+0074277OD-O1153695D-01

2156

.503066D+00

.314665D+00

.74277OD-01

.153695D-01

2156

.503066D+00

.314665D+00

.74277OD-O1

.153695D-O1

2171

.481400D-02

.6412OOD-02

.212200D-02

.686800D-01

0000

.0

.0

.0

.0


INTO GROUP234

FROM GROUP1 2.294600D-021 1.032000D-061 1.048900D-08

3.7687OOD-O37.O361OOD-12 3 8.681498D-03

G.l-15

DIF3D 4.0 7/83 *••• SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.100 PAGE 27

********* EDIT OF NON-FISSIONABLE COMPOSITION 6 (M6 ) IN COMPXS ******************************

ABSORPTIONGROUP CROSS SECTION


REMOVAL POWER CONVERSIONCROSS SECTION FACTOR

1 2.163O5OD-O4 4.616420D+00 4.616420D+O0 4.61642OD+O0 1.3I59OOD-O2 0.02 1.688000D-04 2.901831D+00 2.901831D+0O 2.90183ID+O0 1.4559O0D-O3 0.03 1.146800D-03 1.O21179D+OO 1.O21179D+OO 1.O21179D+OO 4.600I00D-O3 0.04 7.865999D-O4 1.729625D+OO 1.729625D+OO t.729625D+OO 7.865999D-O4 0.0

INTO GROUP FROM GROUP2 1 1.294200D-023 1 6.87800OD-074 1 6.990302D-09


2 1.2871OOD-O32 4.3633OOD-I2 3 3.4533OOD-O3

0IF3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.100 PAGE 28

GROUPNO.

1 i

OUTERIT. NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

OUTER ITERATION

OPTIMIZED INNEROPTIMUM NO. OFOMEfiA INNERS

1.42O92D+OO 7

REL. POiNTERROR

6.055469D-01

4.704232D-01

1.767146D-01

8.69O13OD-O2

3.722962D-O2

1.O64O5OD-O2

3.829818D-03

1.806451D-03

4.606560D-04

1.203257D-04

2.823481D-05

1.556538D-05

4.066891D-06

9.684399D-07

2.0495220-07

1.

1.

7.

4.

2.

6.

2.

1.

2.

7.

1.

1.

1.

7.

1.

SUMMARY

ITERATIONGROUPNO.

2 1.

REL. SUMERROR

686693D-01

306399D-01

337978D-02

552O07D-O2

073863D-02

314254D-03

197660D-03

012883D-03

32O342D-O4

173725D-O5

472779D-05

O3179OD-O5

710762D-06

739674D-O7

272518D-O7

REAL SOLUTION

STRATEGYOPTIMUM NO. OFOMEGA INNERS

57656D+00 11

EIGENVALUECHANGE

5.676263D-O2

3.3913IOD-O2

1.908419D-02

8.680460D-03

5.1O7754D-O3

2.468417D-03

8.781398D-04

2.399321D-04

9.278793D-05

3.893697D-05

1.O5O2O5D-O5

2.4279O2D-O6

7.286502D-07

3.O97159D-07

8.601389D-08

POLY.ORDER

0

0

0

1

2

3

1

2

3

4

1

2

3

4

1

K-EFF. PROBLEM

GROUP OPTIMUM

NO. OMEGA1 NO. OF

INNERS

3 1.27169D+O0 5

DOM. RATIO[ USED

0.0

0.0

0.0

5.957153D-01

5.957153D-O1

5.957153D-01

6.280142D-O1

6.280142D-01

6.280142D-01

6.280142D-01

6.331385D-O1

6.331385D-01

6.331385D-01

6.331385D-O1

6.577679D-O1

DOM. RATIOESTIMATED

0.0

8.269922D-01

5.957153D-O1

5.957153D-01

6.254OO9D-O1

6.280142D-01

6.280142D-01

6.305913D-01

6.203958D-01

6.331385D-01

6.331385D-O1

7.953652D-01

6.304855D-01

6.577679D-01

6.577679D-O1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

GROUP OPTIMUM NO. OF

NO. OMEGA INNERS

4 1.26615D+00 5

K-EFFECTIVE

.O5676263D+OO

.O9O67574D+OO

.10975993D+O0

.11844039D+O0

.12354814D+OO

.12601656D+00

.126B9470D+00

.12713463D+00

. 12722742D+OO

.12726635D+00

. 12727686D+OO

.12727928D+00

. 12728001D+0O

. 12728032D+00

. 12728041D+00


K-EFFECTIVE - 1.12728040833


DOMINANCE RATIO (SIGBAR) - 6.577679231397D-O!


GROUP OPTIMUM GROUP OPTIMUM GROUP OPTIMUMNO. OMEGA NO. OMEGA NO. OMEGA

1 1.42092D+00 2 1.57656D+OO 3 1.27169D+00

MAXIMUM POWER DENSITY 2.68379D-04 OCCURS AT MESH CELL (I,J,K) - ( 1, 1, 1)


GROUPNO.4

OPTIMUMOMEGA

1.26615D+OO

GROUPNO.

OPTIMUMOMEGA

G.l-16

DIF3D ' . . 0 7 / R 1 • • • • SAMPLE PROBLEM I * • • * 20 SWR BENCHMARK - RODS IN - FD06 1 / 0 5 / 8 4 2 2 2 2 . 2 0 0 PAGE 29

REGION AND AREA POWER INTEGRALS FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) - ( 0 . 0 , I . O 5 O D + O 7 )

REGIONNO. NAME

ZONENO.

1COCRRCRCFTOTALS

ZONENAHE

2 M2

VOLUME(CC)

I . 4 3 O 4 3D+03I.52O96D+031.95552D+O32.I72BOD+021.O864OD+O25.23283D+O3

INTEGRATION!)WEIGHT FACTOR

1.00000D+001.0000OD+001.00000D+001.00000D+00I.OOOOOD+000.0

POWER(WATTS)

2.864390-012.O4546D-O19.OI489D-O30.00.05.00000D-0]

POWER DENSITY(WATTS/CC)

2.00247D-O41.34485D-044.6O997D-O60.00.09.55506D-O5

PEAK DENSITY PEAK TU AVG.CWATTS/CC)(2) POWER DENSITY

2.68379D-O42.26994D-O41.81598D-G50.00.02.68379D-04

I.34024D+O01.68788D+003.93925D+000.00.02.8O876D+O0

POWERFRACTION

5.72878D-O14.09092D-O11.3O298D-O20.00.0l.OOOOOD+00

AREANO.

AREANAMF


VOLUME(CC)

INTEGRATION 1 )WEIGHT FACTOR

2.95139D+03 0 . 03.2592OD+O2 0 . 05.23283D+03 0 . 0

POWER(WATTS)

4.90985D-010.05.00000D-OI


1.66357D-O40.09.555O6D-O5

PEAK DENSITY PEAK TO AVG.( W A T T S / C C X 2 ) POWER DENSITY

2.60379D-O40.02.68379D-O4

1.61327D+OO0.02.80876D+00

POWERFRACTION

9.81970D-OI0.0I.OOOOOD+00

(1) INTEGRATION WEIGHT FACTOR - (2/B)«SIN(B»H) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT(2) THE PEAK POWER DENSITY IS CALCULATED BY SAMPLING THE AVERAGE FLUX ON THE CELL SURFACES AND WITHIN THE CELL.

REGIONNO. >IAME

1COCRBCRCFTOTALS

ZONENO.

1

2

3

ZONENAME

MlM2M3M5M6

PEAK INDEX'X,

I.OOOOOD+00I.OOOOOD+01I.40000D+01

0.00.0I.OOOOOD+00

I.OOOOOD+005.00000D+00

7.00000D+000.00.0l.OOOOOD+00

PEAK INDEX'Z,

I.OOOOOD+00I.OOOOOD+00

I.OOOOOD+000.00.0I.OOOOOD+00

AREA AREANO. NAME

3 TOTAL

PEAK INDEX' X ,

l.OOOOOD+000.0l.OOOOOD+00

PEAK INDEXlyl

1.OOOOOD+000.0

1.OOOOOD+00

PEAK INDEX'Z,

l.OOOOOD+000.0

l.OOOOOD+00

DIF3D 4 . 0 7 / 8 3 * • * • SAM1 PROBLEM 1 * * • * 2D SNR BENCHMARK - RODS IN - FD06 1 / 0 5 / 8 4 2 2 2 2 . 2 0 0 PAGE 30

REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) - (8 .00OD+O5,I .O5OD+O7) For. ( tOUP 1

REGIONNO. NAME

1COCRBCRCFTOTALS

ZONENO.

1235

ZONENAME

MlM2M3M5

NET +LEAKAGE

1.57665D+O93.27O7OD+O9

-2.51636D+O9-1.28618D+09-5.62O52D+08

4.82764D+08

ARoO,.PTION +KATE(l)

2.64407D+091.81707D+093.28O94D+O89.67696D+O79.23891B+064.89524D+O9

SCATTER -0UT(2)

1.355730+107.66543D+O92.7O94 3D+O9

18941D+0952814D+O8

SCATTER -IN

2.56744D+10

0.00.00.00.00.00.0

FISSION -PRODUCTION 3)

1.7778ID+1O1.27532D+1O5.21158D+080.00.03.1O524D+1O

EXTK ,ALSOWCE

0.00.00.00.00.00.0

BALANCE

-9.77753D+O2I.63776O+O31.02278D+O2

-6.99544D-01-3.63760D+00

7.57947O+O2

AREA AREANO. NAME


NETLEAKAGE

ABSORPTION •RATE(l)

4.84735D+O9 4 .46U4D+09-1.84823D+09 1.06009D+08

4.82764D+O8 4.89524D+09

( 1 ) ABSORPTION - CAPTURE + FISSION( 2 ) SCATTER OUT - TOTAL OUTSCATTER - (N,2N) SOURCE( 3 ) FISSION PRODUCTION - FISSION SOURCE / K-EFF

SCATTER -OUT(2>

SCATTER - FISSION - EXTERNAL - BALANCEIN PRODUCTION 3) SOURCE

2.12228D+1O 0 . 01.74222D+O9 0 . 02.56744D+10 0 . 0

3.O5313D+10 0 . 00.0 0.03.I0524D+10 0.0

6.60O06D+O2-4.33714D+OO

7.57947D+O2

REGIONNO. NAI!a

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

LEAKAGEPLANAR

1.57665D+O93.27O7OD+O9

-2.51636D+09-1.28618D+09-5.62052D+084.827640+08

LEAKAGEY

4.06954D+088.03841l>+08

-4.82004D+08

-4.48257D+O8-1.774140+081.O3121D+O8

LEAKAGE BUCKLING(4) BUCKLING*4) BUCKLING(4) BUCKLiNG(4)D*(B**2) TOTAL PLANAR Y Z

0.00.00.00.00.00.0

9.54O84D-O4

3.45119D-O3-1.3O334D-O2-9.91344D-O3-2.85048D-O31.5472ID-O4

9.54084D-O4

3.45119D-O3-1.303340-02-9.91344D-03-2.85048D-O31.54721D-O4

2.4626ID-048.482O0D-O4

-2.49653D-O3-3.455O2D-O3-8.99762D-O43.30493D-O5

0.00.00.00.00.00.0

AREA AREANO. NAME

1 TCORE

2 TROD

3 TOTAL

LEAKAGEPLANAR

4.84735D+O9-1.84823D+O94.82764D+08

LEAKAGEY

LEAKAGED*(B»*2)

1.2I080D+09 0 . 0-6.25670D+08 0.0

1.O3I21D+O8 0 . 0

( 4 ) BUCKLINC - B « 2 - LEAKAGE / (D«F1UX*VOLUME) 1/CM*«2

BUCKLTNG(4)TOTAL

BUCKLINGC4)PLANAR

BUCKLING(4)Y

BUCKLtNG(4)Z

I.8642OD-O3 1.86420D-O3 4 .656490-04 0 . 0-5.65348D-03 -5.6534BD-O3 -1.91384D-O3 0.01.54721D-O4 1.54721D-04 3.30493D-05 0.0

G.l-17


REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) -(8.O0OD+05,1.050D+O7) FOR GROUP 1


12345

1CocRBCRCFTOTALS

12356

MlM2MlM5M&

CAPTURERATE

3.9670OD+082.18171D+089.42088D+079.67696D+O79.23891D+068.15089D+08

FISSIONRATE

2.24737D+091.59890D+092.3"<885D+O80.00.04.08015D+O9

AREA AREANO. NAME


CAPTURERATE

FISSIONRATE

6 . 1 4 8 7 1 D + 0 8 3 . 8 4 6 2 7 D + 0 91.06009D+08 0 . 08 . 1 5 0 8 9 D + 0 8 4 . 0 8 0 1 5 D + 0 9

DIF3D 4 . 0 7 /83 **** SAMPLE PROBLEM 1 **** 2D SNK BENCHMARK - RODS IN - FD06 1 /05 /84 2222 .300 PAGE 32

REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) - ( ! . 0 0 0 D + 0 4 . 8 . 0 0 0 D + 0 5 ) FOR GROUP 2

REGIONMO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

M2M3

5 M56 M6

NET +LEAKAGE

.74742D+09

.62129D+0960597D+08.71777D+O912795D+O8

ABSORPTIONRATE(1)

SCATTER -0UT(2)

1.05293D+10 4.64816D+O96.58375D-I09 2.31137D+O91.91529D+09 1.71184D+O93.OO993D+O9 8.97197D+083.94190D+O7 3.OO57OD+O8

SCATTER - FISSION - EXTERNALIN PRODUCTIONO) SOURCE

1.35550D+107.66388D+092.7O9C9D+O91.18935D+O95.52784D+08

5.37046D+O9 0.03.85253D+09 0.01.57433D+08 0.00.0 0.00.0 0.0

3.1O313D+O9 2.20782D+10 9.86914D+09 2.56701D+10 9.38042D+09 0.0

BALANCE

-4.3437OD+O24.53192D+022.75525D+O1

-3.16520D+00-1.69340D+012.62747D+O1

AREA AREANO. NAME


NETLEAKAGE

ABSORPTIONRATE(l)

6.36871D+09 1.71136D+10-2.5O498D+O9 3.O4935D+O9

3.1031311+09 2.20782D+10

(1) ABSORPTION - CAPTURE + FISSION(2) SCATTER OUT - TOTAL OUTSCATTER - (N,2N) SOURCE(3) FISSION PRODUCTION - FISSION SOURCE / K-EFF

SCATTER -OUT(2)

SCATTER - FISSION - EXTERNAL - BALANCEIN PRODUCTIONO) SOURCE

6.95954D+O9 2.121B9D+101.15777D+O9 1.74214D+099.86914D+O9 2.567O1D+1O

9.22298D+09 0.00.0 0.09.38042D+09 0.0

1.88213D+01-2.00992D+012.62747D+01

REGIONNO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

MlM2M3M5M6

LEAKAGEPLANAR

3.74742D+092.62129D+09

-7.60597D+08-2.71777D+O92.12795D+O83.1O313D+O9

LEAKAGEY

8.49477D+085.90552D+082.79571D+07

-8.74492D+088.81135D+076.8160eD+08

LEAKAGE BUCKLING(4) Bl'CKLING(4) BUCKLING(4) BUCKLING(4)D*(B**2) TOTAL PLANAR Y Z

0.00.00.00.00.00.0

8.29053D-041.13443D-03

-1.O5311D-O3-8.68365D-033.14O2OD-O43.63209D-04

8.29O53D-O41.13443D-03

-1.05311D-03-8.68365D-033.14020D-043.63209D-04

1.87932D-042.55576D-O43.87088D-05

-2.79412D-031.3O028D-O47.97793D-O5

0.00.00.00.00.00.0

AREA AREANO. NAME


LEAKAGEPLANAR

LEAKAGEY

LEAKAGED*(B**2)

6.36871D+09 1.44003D+09 0.0-2.50498D+O9 -7.86378D+O8 0.03.10313D+09 6.816O8D+O8 0.0

BUCKLING(4)TOTAL

BUCKLING(4)PLANAR

BUCKLING(4)Y

9.32353D-04 9.32353D-O4 2.108I4D-04-2.52868D-03 -2.52868D-O? -7.93820D-043.63209D-04 3.63209D-04 7.97793D-O5

BUCKLING(4)Z

0.00.00.0

(4) BUCKLING - B**2 - LEAKAGE / (D*FLUX*VOLUME) 1/CM**2

G.l-18

DIF3D 4.0 7/83 **** SAMPLE PROBLEM I **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.300 PAGE 33

REGION AND AREA BALANCE INTEGRALS FOR REAL K-F.FF PROBLEM WITH ENERGY RANGE (EV) - O .000D+04 .8.000D+O5) FOR GROUP 2

REGIONNO. NAME

1 1C2 OC345

ZONE ZONENO. NAME

12

RB 3CR 5CF 6TOTALS

MlM2M3M3M6

CAPTURERATE

5.268O3D+O92.70505D+091.88795D+093.00993D+0S3.94190D+071.291O4D+1O

USSIONRATE

5.26182D+093.87870D+092.73302D+L7U.O0.09.16785D+09

AREA AREANO. NAME


CAPTURERATE

FISSIONRATE

7.973O8D+O9 9 .14052D+093.O4935D+O9 0 . 01.291O4D+1O 9 . 1 6 7 8 5 0 + 0 9

DIF3D 4 . 0 7 /83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222 .300 PAGE 34

REGION AND AREA BALANCE INTEGRALS FOIt REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) - (1 .000D+03,1 .000D+O4) FOR GROUP 3

REGIONNO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

MlM2M3M5M6

ilET +LEAKAGE

6.45877D+07-6.58282D+07

3.63142D+08-2.41728D+08

1.84679D+08

ABSORPTION +RATEO)

3.36623D+091.84936D+O98.53O52D+O81.00188D+092.88988D+07

SCATTER -OUT(2)

1.21956D+O95.29306D+084.95917D+081.371O2D+O88.7O215D+O7

SCATTER -IN

4.65O39D+O92.31284D+O91.71211D+O98.9725OD+O83.OO599D+O8

FISSION -PRODUCTIONO)

0.00.00.00.00.0

EXTERNALSOURCE

3.O4852D+O8 7.09943D+09 2.46891D+09 9.173190+09 0.0

0.00.00.00.00.00.0

BALANCE

-7.18331D+O19.56224D+001.71880D+006.93582D-01-6.75876D+00-6.66173D+OI

AREA AREANO. NAME


NETLEAKAGE

ABSORPTIONRATE(l)

-1.24O53D+O6 5.2156OD+O9-5.7O492D+07 1.03078D+093.04852D+08 7.09943D+09

(1) ABSORPTION - CAPTURE + FISSION(2) SCATTER OUT » TOTAL OUTSCATTER - (N.2N) SOURCEO ) FISSION PRODUCTION - FISSION SOURCE / K-EFF

SCATTER - SCATTER - FISSION - EXTERNAL - BALANCE0UT(2) IN PRODUCTIONO) SOURCE

1.74887D+O9 6.96323D+09 0.02.24123D+08 1.19785D+O9 0.02.46891D+09 9.87319D+O9 0.0

0.00.00.0

-6.227O9D+O1-6.O6518D+OO-6.66173D+O1

REGIONNO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

MlM2M3M5M6

LEAKAGEPLANAR

6.45877D+O7-6.58282D+073.63142D+0B

-2.41728D+081.84679D+083.04852D+08

LEAKAGEY

-1.34218D+O6-7.24701D+069.O8582D+O7

-7.65302D+O76.19366D+O76.76754D+07

LEAKAGED*(B**2)

0.00.00.00.00.00.0

BUCKLING(4)TOTAL

3.43332D-O4-7.57571D-O4

6.82751D-03-2.66537D-02

7.17668D-038.39803D-04

BUCKLING(4) BUCKLING(4) BUCKLING(4)PLANAR Y Z

3.43332D-O4-7.57571D-O4

6.82751D-03-2 .66537D-02

7.17668D-038.39803D-04

-7 .13467D-06-?.34OO9D-<15

1.7C24D-03-8.43847D-03

2.40687D-O31.86431I>-04

0.00.00.00.00.00.0

AREA AREANO. NAME

TCORETRODTOTAL

LEAKAGEPLANAR

LEAKAGEY

LEAKAGED*(B**2)

-1.24053D+06 -8.58919D+06 0 .0-5.7O492D+O7 -1.45936D+07 0 .03.04852D+08 6.76754D+07 0.0

BUCKLING - B**2 - LEAKAGE / (D*FLUX*VOLUME) 1/CM**2

BUCKLING(4)TOTAL

BUCKLINGC4)PLANAR

BUCKLINJ(4)1

BUCKLING(4)Z

-4.51O77D-O6 -4.51077D-06 -2.12318D-O5 0.0-1.63923D-O3 -1.639?3u-O3 -4.19328D-O4 0.08.39803D-04 8.3r003D-04 1.86431D-O4 0.0

G.l-19

D1F3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.300 PAGE 35

REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) -(I.0000+03,1.000D+04) FOR GROUP 3

REGIONNO.

12345

NAME

1COCRBCRCFTOTALS

ZONENO.

12356

ZONENAME

MlM2M3M5M6

218125

CAPTURERATE

.42O17D+O9

.22352D+O9

.42730D+08

.r->188D+09

.t' *988D+07

.51720D+09

961001

FISSIONRATE

•46062D+08.258430+08.03218D+07.0.0.58223D+09

AREA AREANO. NAME


CAPTURERATE

3.64369D+091.03078D+095.5172OD+O9

FISSIONRATE

1.57190D+090.01.58223D+09


REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WtTH ENERGY RANGE (EV) =(0.0

1/05/84 2222.300 PAGE 36

.1.C00D+03) FOR GROUP 4

REGIONNO. NAME

12345

AREANO.

123

1COCRBCRCFTOTALS

AREANAME

TCORETRODTOTAL

ZONENO.

12356

ZONENAME

MlM2M3M5M6

7-71

-t81

-7-3

NET +LEAKAGE

.11501D+O5

.542O5D+O7••3332D+08J602D+07

.29646D+07

.14628D+08

NET +LEAKAGE

.47O90D+O7

.99564D+O6

.14628D+O8

ABSORPTION +RATE(l)

1.21900D+096.O48O3D+O83.02644D+082.24062D+O84.05718D+062.35457D+O9

ABSORPTION +RATE(l)

1.82380D+092.28120D+082.35457D+09

000000

000

SCATTEROUT(2)

o o

o o

o o

SCATTER0UT(2)

.0

.0

.0

SCATTER -IN

1.2197ID+095.29383D+O84.95977D+081.37I02D+088.7O218D+O72.46919D+09

SCATTER -IN

1.74909D+092.24124D+082.46919D+09


000000

.0

.0

.0

.0

.0

.0


000

.0

.0

.0

EXTERNALSOURCE

0.00.00.00.00.00.0

EXTERNALSOURCE

0.00.00.0

BALANCE

-1.95O35D+O13.47536D+OO2.38I6OD+OO1.01616D-01

-2.94183D+00-1.64868D+01

BALANCE

-1.60282D+01-2.84021D+00-1.64868D+O1

(1) ABSORPTION - CAPTURE + FISSION(2) SCATTER OUT - TOTAL OUTSCATTER - (K,2N) SOURCE(3) FISSION PRODUCTION - FISSION SOURCE / K-EFF

REGIONNO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

1 MlM2M3M5M6

LEAKAGEPLANAR

7.115O1D+O5-7.54205D+071.93332D+08

-8.69602D+078.29646D+071.14628D+08

LEAKAGEY

-6.°4211D+06-1.26134D+074.50569D+07-2.7217OD+O72.76208D+072.59O53D+O7

LEAKAGED*(B**2)

0.00.00.00.00.00.0

BUCKLING(4) BUCKLING(4) BUCKLINGC4) BUCKLINGC4)TOTAL PLANAR Y Z

1.60699P-O5-4.45845D-O31." 2O3D-O2

-l.Uo385D-019.29974D-031.28099D-03

1.60699D-O5-4.45845D-031.O4203D-O2

-1.06385D-O19.29974D-031.28O99D-O3

-1.56794D-04-7.45634D-042.42849D-O3

-3.32965D-O23.09609D-032.89496D-04

0.00.00.00.00.00.0

AREA AREANO. NAME


LEAKAGEPLANAR

LEAKAGEY

LEAKAGED*(B**2)

-7.47090D+O7 -1.95555D+O7 0.0-3.99564D+06 4.038O4D+O5 0.01.14628D+08 2.59053D+07 0.0

BUCKLING(4)TOTAL

BUCKLING(4)PLANAR

BUCKLING(4)Y

BUCKLING(4)Z

-1.22O9OD-O3 -1.22090D-03 -3.19577D-O4 0.0-4.10290D-04 -4.1O290D-O4 4.14643D-O5 0.01.28099D-03 1.28099D-03 2.89496D-04 0.0

(4) BUCKLING - B**2 » LEAKAGE / (D*FLUX*VOLUME) 1/CM**2

G.l-20

DIF3D 4.0 7/83 **** SAMPLE PROBLEM ] **** 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 2222.300 PAGE 37

REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0,1.OOOD+03) FOR GROUP 4

REGtONNO. NAME

ZONE ZONENO. NAME

CAPTURERATE

FISSIONRATE

1C

ocRBCRCFTOTALS

MlM2M3M5M6

7.94636D+083.67324D+082.94720'"+082.24O62D+O84.05718D+061.68480D+09

4.24364D+082.37479D+O87.92419D+O60.00.06.69768D+08

AREA AREANO. NAME


CAPTURERATE

FISSIONRATE

1.16196D+09 6.61844D+082.28120D+08 0.01.68480D+09 6.69768D+08


REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) =(0.0

1/05/84 2222.300 PAGE 38

.1.050D+O7)

REGIONNO. NAME

1COCRBCRCF

ZONENO.

ZONENAME

MlM2M3M5M6

NETLEAKAGE

ABSORPTION +RATE(1)

SCATTER -0UT(2)

SCATTER -IN


EXTERNALSOURCE

5.38937D+09 1.77591D+10 1.94251D+10 1.94251D+10 2.31485D+10 0.05.75074D+09

-2.72048D+09-4.33264D+09-8.16137D+074.00538D+09

1.08550D+103.39908D+O94.33264D+098.16139D+O73.64275D+1O

1.05061D+104.91718D-l092.22371D+099.40405D+083.80125D+10

1.O5O61D+1O4.91718D+092.22371D+099.40405D+083.8O125D+1O

1.66057D+106.78592D+080.00.04.04328D+10

0.00.00.00.00.0

BALANCE

-1.50346D+O32.1O399D+O31.33931D+O2

- 3 . 0 6 9 5 5 D + 0 0-3 .02721D+01

7.O1U8D+O2

AREA AREANO. NAME


NET + ABSORPTION +LEAKAGE RATE(l)

1 .11401D+10 2.86141D+10-4.4H25D+09 4.41425D+09

4.00538D+09 3.64275D+10

SCATTER -OUT(2)

2.99312D+103.16411D+09J.80125D+10

SCATTER - FISSION - EXTERNALIN PRODUCTIONO) SOURCE

2.99312D+103.1641ID+093.8O125D+1O

3.97542D+10 0.00.0 0.04.04328D+10 0.0

BALANCE

6.00528D+02-3.33417D+017.O1118D+O2

(1) ABSORPTION - CAPTURE + FISSION(2) SCATTER OUT - TOTAL OUTSCATTER - (N,2N) SOURCE(3) FISSION PRODUCTION = FISSION SOURCE / K-EFF

(N,2N) SOURCE - SCATTER IN - SCATTER OUT

REGIONNO. NAME

1COCRB

4 CR5 CF

2.82831D-07TOTALS

ZONE ZONENO. NAME

1 Ml2 M23 M35 M56 M6

0.0

LEAKAGEPLANAR

5.38937D+095.75074D+09

-2.72O48D+O9-4.33264D+09-8.16137D+07

LEAKAGEY

1.24815D+091.37453D+09

-3.18132D+O8

2.5773OD+O5

LEAKAGED*(B**2)

0.00.00.00.00.0

BUCKLING(4) BUCKLING(4) BUCKLING(4)TOTAL PLANAR Y

8.41426D-041.71042D-03

-2.75617D-03-9.5727OD-O3-8.97364D-05

8.41426D-O41.71042D-03

-2.75617D-O3-9.5727OD-O3-8.97364D-05

1.94869D-044.08821D-O4-3.223O5D-O4-3.15176D-03

BUCKLING(4)Z

0.00.00.00.0

4.00538D+09 8.783O9D+O8 0.0 3.30576D-04 3.30576D-04 7.24895D-05 0.0

AREA AREANO. NAME


LEAKAGEPLANAR

LEAKAGEY

LEAKAGED*(B**2)

1.11401D+10 2.62268u+09 0.0-4.41425D+O9 -1.42624D+09 0.04.00538D+09 8.78309D+O8 0.0

BUCKLING(4)TOTAL

BUCKLING(4)PLANAR

BUCKLING(4)Y

BUCKLING(4)Z

1.14056D-03 1.I4056D-03 2.68518D-O4 0.0-3.24080D-03 -3.24080D-03 -1.04710D-O3 0.03.30576D-04 3.30576D-04 7.24895D-O5 0.0


G.l-21

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 **** 2D SNF BENCHMARK - KODS IN - FDQ6 1/05/84 2222.300 PAGE 39

REGION AND AREA BALANCE INTEGRALS FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0 .1.050D+O7)

REGIONNO. NAME

1 1C2 OC345

ZONE ZONENO. NAME

I Ml2

RB 3CR 5CF 6TOTALS

M2M3M5M6

CAPTURERATE

8.879530+094.5I4O7D+O93.U961D+O94.33264D+098.16139D+072.09275D+10

FISSIONRATE

8.87961D+096.34093D+092.79462D+080.00.01.55OOOD+1O

(N2.N)SOURCE

4.58523D+031.93424D+033.30957D+O21.64067D+022.407O5D+O27.2552OD+O3

NET MEDIAN ENERGY MEDIAN ENERGY MEDIAN ENERGYPRODUCTION^) FISSION SRC. ABSORPTN RATE FLUX

2.31485D+1O1.66057D+106.78592D+081.64067D+022.4O7O5D+O24.04328D+10

1.96454D+061.96454D+061.96454D+060.00.01.96454D+O6

5.97212D+O47.23545D+O43.47O39D+O43.93165D+042.39350D+O45.68942D+04

1.O97O2D+O51.18641D+058.26269D+041.231O9D+0')1.00436D+O51.08645D+05

AREA AREANO. NAME

ABSORPTN RATE


FLUX

CAPTURERATE

1.33936D+104.41425D+092.09275D+10

FISSIONRATE

1.522O5D+1O0.01.55OO0D+1O

(N2.N)SOURCE

6.51947D+O34.04772D+027.2552OD+O3

(5) NET PRODUCTION = FISSION PRODUCTION + (N,2N) SOURCE

NET MEDIAN ENERGY MEDIAN ENERGY MEDIAN ENERGYPRODUCTIONS) FISSION SRC".

3.97542D+104.O4772D+O24.04328D+10

1.96454D+060.01.96454D+06

6.42968D+043.90651D+O45.68942D+04

1.12647D+O51.I1305D+051.08645D+05

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 1 •**** 2D SNR BENCHMARK - RODS IN - FD06

BALANCE INTEGRAL TOTALS BY GROUP FOR REAL K-EFF PROBLEM WITH ENERGY RANGE (EV) =(0.0

1/05/84 2222.300 PAGE 40

.1.050D+07)

GROUPNO.

EMIN(EV)

1 8.00D+052 l.OOD+04

EMAX(EV)

1.O5D+078.00D+05

NET + ABSORPTIONLEAKAGE RATE(l)

4.82764D+083.10313D+09

4.89524D+092.2O782D+1O

SCATTER -OUT(2)

2.56744D+109.86914D+09

SCATTER - FISSION - EXTERNAL » BALANCEIN PRODUCTIONS) SOURCE

0.02.567O1D+1O

3.10524D+109.38O42D+O9

0.0

0.0 2.62747D+013 l.OOD+03 l.OOD+04 3.04852D+08 7.09943D+09 2.46891D+09 9.87319D+09 0.0 0.04 0.0 l.OOD+03 1.14628D+08 2.35457D+09 0.0 2.46919D+09 0.0 0.0

TOTALS 4.00538D+09 3.64275D+10 3.80125D+10 3.80125D+10 4.04328D+10 0.0

7.57947D+02

-6.66173D+O1-1.64868D+01

7.0H18D+02

(1) ABSORPTION - CAPTURE + FISSION(2) SCATTER OUT - TOTAL OUTSCATTER - (N,2N) SOURCF(3) FISSION PRODUCTION =• FISSION SOURCE / K-EFF

GROUPNO.

EMIN(EV)

1 8.O0D+052 l.OOD+043 l.OOD+034 0.0

TOTALS

EMAX(EV)

1.O5D+O78.00D+05l.OOD+04l.OOD+03

LEAKAGEPLANAR

4.82764D+O83.10313D+O93.04852D+081.14628D+084.00538D+09

LEAKAGE LEAKAGE BUCKLING(4) BUCKLING(4) BUCKLING(4) BUCKLING(4)Y D*(B**2) TOTAL PLANAR Y Z

1.O3121D+O86.81608D+086.76754D+072.59053D+O78.78309D+08

0.00.00.00.00.0

1.54721D-043.63209D-048.39803D-041.28099D-033.30576D-04

1.54721D-O43.63209D-048.39803D-041.28099D-033.30576D-04

3.3O493D-O57.97793D-O51.86431D-042.89496D-047.24895D-05

0.0.0.0.0.

00000


GROUPNO.

EMIN(EV)

1 8.00D+052 l.OOD+043 l.OOD+034 0.0

TOTALS

EMAX(EV)

1.O5D+O78.OOD+O5l.OOD+04l.OOD+03

CAPTURERATE

8.15089D+081.29104D+105.5172OD+O91.68480D+092.09275D+10

FISSIONRATE

4.08015D+099.16785D+091.58223D+096.69768D+081.55000D+10

G.l-22


REGION AND AREA REAL FLUX INTEGRALS FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0

1/05/34 2222.300 PAGE 41

,1.O5OD+O7)

REGIONNO. NAME

12345

AREANO.

23

1COLRBCRCFTOTALS

AREANAME

TCORETRODTOTAL

ZONENO.

12356

ZONENAME

MlM2M3M5M6

VOLUME(CC)

1.43043D+031.52096D+031.95552D+O32.17280D+021.08640D+025.23283D+03

VOLUME(CC)

2.95139D+033.2592OD+O25.23283D+03

TOTAL FLUX PEAK FLUX (1) TOTAL FAST FLUX PEAK FAST FLUX(l)(NEUTRON-CM/SEC) (NEUTRON/CM2-SECXNEUTRON-CM/SEC) (NEUTRON/CM2-SEC)

3.75825D+121.93981D+128.07520D+113.07019D+113.06595D+117.11919D+12

3.52624D+092.14926D+091.20060D+091.7213OD+O92.96550D+093.52624D+O9

1.93993D+121.02726D+123.76921D+1I1.64804D+111.53529D+113.66244D+12

1.82299D+091.12598D+O96.14409D+089.09090D+081.49456D+O91.82299D+O9

TOTAL FLUX PEAK FLUX (1) TOTAL FAST FLUX PEAK FAST FLUX(1)

(NEU1 KON-CM/SEC) (NEUTRON/CM2-SECXNEUTRON-CM/SEC) (NEUTRON/CM2-SEC)

5.69805D+126.13613D+1L7.11919D+12

3.52624D+092.96550D+093.52624D+09

2.96719D+123.18333D+113.66244D+12

1.82299D+091.49456D+O91.82299D+09

(1) PEAK FLUX CALCULATIONS ARE COMPUTED BY SAMPLING AVERAGE FLUXES ON THE SURFACE AND WITHIN EACH MESH CELL.

REGION

NO.

12345

NAME

1COCRBCRCF

ZONENO.

12356

ZONENAME

MlM2M3M5M6

TOTALS

GROUP

5.74436D+113.29459D+118.44717D+105.18327D+104.27124D+101.08291D+12

GRO'lP2

2.87751D+121.47049D+126.16281D+112 . 3 8 0 6 5D+112.33525D+115 .43587D+12

GROUP3

2.60379D+111.21921D+1;8.40951D+101.57924D+102.51995D+105.07387D+11

GROUP4

4.59194D+101.79392D+102.26716D+101.32833D+O95.15786D+099.30165D+10

AREA AREANO. NAME

1 TCORE

2 TROD3 TOTAL

GROUP1

9.03896D+119.45451D+101.08291D+12

GROUP2

4.34800D+124.7159OD+115.43587D+12

GROUP3

3.823OOD+114.09919D+105.07387D+11

GROUP4

6.38586D+106.48619D+099.30165D+10


REAL ZONE FLUX AVERAGES FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0

1/05/84 2222.300 PAGE 42

.1.O5OD+O7)

ZONENO.

123456

ZONENAME

MlM2M3M4M5M6TOTALS

VOLUME(CC)

1.43O43D+031.52O96D+031.95552D+030.02.17280D+021.08640D+025.23283D+03

AVG. TOTAL FLUX(NEUTRON/CM2-SEC)

2.62736D+O91.27538D+094.12944D+080.01.41301D+092.82211D+O91.36049D+09

GROUPI

4.0J584D+082.16613D+084.31965D+070.02.38553D+O83.93155D+082.06946D+08

2930121

GROUP2

.01164D+09

.66815D+08

.I5149D+O8

.0

.09566D+O9

.14953D+O9

.038B0D+O9

GROUP3

1.82029D+088.01603D+074.30039D+O70.07.26822D+O72.31954D+O89.696220+07

3110641

CROUP4

.21011D+O7

.179*7D+O7

.15937D+O7

.0

. 11344D+06•74766D+O7.77756D+07

Appendix F.2

TYPE 01 OVERLAY DIRECTIVES FOR THE LDR LOADER ON THE CRAY-1

FILE,$BLD.OVLDN.DIF3D.SBCA,????. (ADDRESS OF LONGEST OVERLAY MUST BE OBTAINED FROM LOADER OUTPUT)ROOT, D3DRIV, CRED, DOPC, DRED, ERROR, FEQUAT, FFORM, FFORM1, FFORM2, FLTSET,IEQUAT,IGTLCM,JGT,FRELCM,LOCF,LOCFWD,INTSET,IN2LIT,LINES ,POINTR,PUTPNT .BULK.FREE .WIPOUT .GETPNT ,IGET, IPT2 ,PUTM, IPTERR,ILAST , REDEF, REDEFM, PURGE, STATUS, PRTI1, PRTI2, PRTR1, PRTR2, PRTECM, REED,ZEROIO, SEEK, SEKPHL, SPACE , SQUEZE, SRLAB, TIMER, DIF3D, START, VOLUME, WDIF3D,GETBND.AREAS,REVRSE .DEFICF,OPENCF,CLOSCF,PURGCF,BLKGET,PNTGET,DEFIDF,OPENDF .CLOSDF, STATCF .CODECD , PCRED.POVL, 1, SCAN.POVL, 2, STUFF, STUFF1.POVL,3,GNIP4C,ANIP01,ANIP02,ANIP14,ANIP23,GETZON,GETSZN,CPYLBG.SOVL, 1 .RANIP1, ANIP03, ANIP04, ANIP05, ANIP06,ANIPHX, ANIP07, ANIP09, CHEK09, ANIP10,ANIP11,ANIP12,ANIP15,ANIP34.SOVL,2,FGEODS,LOCHEX,SETHEX,GETHGT, GETREG ,GETMSH, CMESH, FMESH, SRFLT,GETBUC.GETBC,GETHR,RCKESH,TRIGOM,VOLREG,REDMSH.SOVL, 4, EGEODS, MAKMSH, PRGEOD, PRNTIX,ANIP43 .MPGEOD.MSHMAP,TRIPLT, IEXPIC,HEXPC1,HEXPC2,HEXPC3,HEXPC6,HEXPC7,HEXPC4,HEXPC5,ORTMAP.ORTPC1 .ORTPC2 .ORTPC3 .ORTPC4,0RTPC5,0RTPC6.SOVL,4,RANIP2,ANIP13,GETMAT,GETISO,ANIP39,GETSET.SOVL,5 .FADENS, SORT13 ,VALD2D,SET2D, INDEX,EDTMAT ,SORT14 ,WNDXSR.SOVL, 6, BCDXST, RWISOT, RWDELY, RWDY1, RWDY2 .SOVL,8,WRSRCH,ANIP21,ANIP22,SRCli4D,ANIP24,SRCH3D,ANIP25,SRCH6D,ANIP26,EDSRCH.SOVL,7,WRSORC,ANIP19,ANIP40,ANIP41,ANIP42,SORDAT,SORLAB,SORMSH,SORNZN,SORDIF,ADS,ADS1,ADS2,ADS3,WRS,WRSO,WRS1,WRS2,EDSORC.POVL,4,HMG4C.SOVL.l ,OVL1 ,RDNDX,RDATDN,ATDN3,ISOR14,EDTISO,iDLRl3.SOVL,2,OVL2,ISOR58,SVSCAT,FARSET,ZROSET,UPDATE,MA XBND,FISPEC,EDTR5,EDTR6,EDTR8.

_ SOVL,3,OVL3,WREC1,WREC2,WREC3,WREC4.SOVL, 4, 0VL4, SVXS, EDTXS1 .EDTXS2, EDFPWS.Pf'L, 5 .MODCXS, AHIP35 ,ANIP37 .DOMODS .COPIER.POVL,21,BCDINP,RADF3D,PDIF3D.POVL, 6, SRCH4C, GETBSQ, GETALP, GETDIM, GETCON , SRCHX, PARAB ,DMDBSQ ,DMDALP ,DMDDIM,DMDCON,MODBSQ,MODDIM,MODCON.POVL,22,BININP,RDIF3D,RLABEL,RSEARC,RCMPXS,ADSCTM,RGEODS,FORMSH,FORMCM.RRTFLX.RATFLX.RFIXSR.RNHFLX.POVL,23,SSINIT,EDITCR.SOVL,1,FDINIT,SSCORE,SSDISK.SOVL, 2, ZMINIT, INEDIT, FORHMZ, REGMAP .SOVL, 3, NHINIT, NHGEOM, HEXMAP, GETIJ, NHZMAP, NHPNT, NHCCPT, NUINED, NHCORE,NHDISK.SOVL,4,XSINIT,XSGET1,XSGET2,XSEDIT.POVL,24,SSTATE,CHEBE,DACOSH,OUTED0,FILCPY,OSWEEP,PSWEEP,TSWEEP,SORINV,FISSRC,TOTSRC,SCTSRC,ROWSRC,TRISRC,ZEROBA,RBOSOR,RBOSRC.SOVL,1,DXSREV,XSCREV,NHSIGA.SOVL,2,DFDCAL,FDCAL,ORTFDC,TRIFDC.SOVL,3,DORPES,ORPES1,ORPIN1,RFLXIN,FSRCIN,ORPES2,ORPIN2,MLTPLY.SOVL,4.DOUTR1.OUTER1.INNER1,CHEBY1.SOVL, 5, DOUTRT , 3UTER2, INNER2, CHEBY2, IFISD2, SCTSD2, TOTSD2, FISSD2 .PO VL, 2 5, NHS ST, NHOEDO, INVERT, NHXSEC .SOVL,1,DNHCCC,NHCC2D,NHCC3D,NHTVLC,NHINNR.SOVL, 2, DNHSTT, FXREAD, FXINIT, I-SINIT.SOVL,3,DNHOUT,OUTR1,OUTR2,OUTR3,OUTR4,OUTR5,ACCEL,ACCL3D,LEAK3D,SRCFIS.SRCSCT,SRCHEX,PCHEX,PCHEXB,SRCZ1,SRCZ2,PCZ,PCZB,FLXHEX, FLXZ, FSUPTD, CMMTRX, BKRIMG, AXLEAK,CMSOLV,FSERRN,CONVCK.SOVL,4,DNHFIN,NHEDDM,CPYFIL,NHVOL,FXSHAP.PO VL, 2 9, DSSTOU , THODPR, TWODTB, BRED, DSEOUA, SCALPK, WPKEDT, NHSHAP, NHPEAK ,NF"KED.SOVL.l ,DSSTO1 ,FORMMR,BKLWGT,SSTOU1 ,POWINT,RPWADD,APWADl ,WPOWER,ORTSRF,TRISRF.SOVL,2,DSSTO2,EDCORE,SSTOU2,RPSADD,WFLUX,ORTBAL,TRIBAL,WNHFLX,HEXBAL.SOVL, 3, DSSTO3, ADDVEC, DIWEC, BALINT, RBLADD, RBLMED, RBLFIS, ABLADD,P SADD.FLXINT.FLXRZ.WRZFLX.

G.l-23

D1F3D 4.0 7/83 **** SAMPLE PROBLEM 1 **•* 2D SNR BENCHMARK - RODS IN - FD06 1/05/84 222.I.3OO PAGE 43

*** THE FOLLOWING BINARY FILES HAVK BEEN WRITTEN •**

FILE NAME VERSION NO. LOGICAL UNIT

RTFLUXDIF3D

3018

BPOINTER SPACE USED, FCM 409 ECM - 5992 WORDS

COMPUTING TIME SUMMARY

BINARY FILE 'NPUT PROCESSINGINITIALIZATION AND INPUT EDITTINGSTEADY STATE REAL FLUX CALCULATIONEDTT REAL CALCULATION OUTPUTSTcADY STATE ADJOINT FLUX CALCULATIONEDIT ADJOINT CALCULATION OUTPUTNODAL MATHEMATICAI-ADJOINT CALCULATIONTOTAL FOR THIS STEP

CENTRAL PROCESSOR (SEC)

0.100.201.550.770.00.00.02.65

PERIPHERAL PROCESSOR (SEC)

0.00.00.00.00.30.00.00.0

TOTAL ELAPSED COMPUTING TIME (SEC) 4.89 0.0 4.89

G.2-1

G.2 Sample Problem 2 (selected pages)

GNIP4C 11/85 ••** SAMPLE PROBLEM 2 • « • 21) SNR BENCHMARK - RODS [N - NODAL 1/05/84 2222.300 PAGE 44

••« GN1P4C - GENERAL NKIITRON1CS BCI1 INPUT PROCESSOR TO CREATE CCCC BINARY INTERFACE FILES *•*

**• GNIP4C CONTROL PARAMETERS •••

1000000100

IMAINGIBULKG1PRNTG1GMEDTIMAPRIMAPZ

NO. OF WORDS OF MAIN MEMORY REQUESTEDNO. OF WORDS OF BULK MEMORY REQUESTEDBPOINTER TRACE AND DUMP CONTROL (0/1/2/3, NEITHER/DUMP/TRACE/BOTH)GEOMETRY PROCESSING EDIT CONTROL (0/1/2/3, NO EDITS/PRINT EDITS/EDITS TO AUXILIARY FILE/BOTH)REGION MAP OPTION (0/1/2/3, NO MAP/PRINT MAP/MAP TO AUXILIARY FILE/BOTH)ZONE (COMPOSITION) MAP OPTION (0/1/2/1, SEE IHAPR)

WHEN HEXAGONAL GEOMETRY (A.NIP3 TYPE 03 CARD GEOMETRY TYPE SENTINEL VALUESBETWEEN 110 AND 128) AND PERIODIC BOUNDARY CONDITIONS ARE SPECIFIED, GNIP4C MAYUSE THE PERIODICITY TO ASSIGN HEXES NOT REFERENCED ON TYPE 30 CARDS TOAPPROPRIATE REGIONS. THIS IS DONE SO THAT TYPE 30 CARDS COMPOSED FOR TRIANGULARMESH MODELS CAN ALSO BE USED FOR HEXAGONAL MESH MODELS. DIFFERENT SETS OF HEXESCOMPRISE THE REGIONS OF SOLUTION IN TRIANGULAR AND HEXAGONAL GEOMETRIES.

CELL ( 6 , 6 ) HAS BEEN ASSIGNED TO REGION OCCELL ( 8, 8) HAS BEEN ASSIGNED TO REGION RBCELL ( 9 , 6 ) HAS BEEN ASSIGNED TO REGION OCCELL (II, 7) HAS BEEN ASSIGNED TO REGION RBCELL ( 7, 5) HAS BEEN ASSIGNED TO REGION CRCELL ( 4 , 4 ) HAS BEEN ASSIGNED TO REGION CF

*** MODEL DESCRIPTION

li-ft511010101042

21

241001

I.1200D+01

IGOMNZONENREGNZCLNCINTINCINT.ININTIKINTJ1MB IIMB2JMB1JMB2NBSNBCSNIBCSNZWBBNRASSNTRIAGFLAT

GEOMETRY TYPE, HEXAGONALNO. OF ZONES (COMPOSITIONS)NO. OF REGIONSNO. OF ZONE CLASSIFICATIONSNO. OF 1ST DIMENSION COARSE MESH INTERVALSNO. OF 2ND DIMENSION COARSE MESH INTERVALSNO. OF 1ST DIMENSION FINE MESH INTERVALSNO. OF 2ND DIMENSION FINE MESH INTERVALSFIRST BOUNDARY CONDITION, FIRST DIMENSION, PERIODIC. NEXT FACE CLOCKWISELAST BOUNDARY CONDITION, FIRST DIMENSION, EXTRAPOLATEDFIRST BOUNDARY CONDITION, SECOND DIMENSION, PERIODIC, SEE IMBILAST BOUNDARY CONDITION, SECOND DIMENSION, EXTRAPOLATEDNO. OF BUCKLING SPECIFICATIONSNO. OF CONSTANTS FOR EXTERNAL BOUNDARIESNO. OF CONSTANTS FOR INTERNAL BOUNDAPIESNO. OF BLACKNESS THEORY ZONES0/1, Ri ;ION ASSIGNMENTS TO COARSE/FINE MESHOUTER BOUNDARY SHAPE, 60 DEGREE RHOMBUSHEXAGON FLAT-TO-FLAT DISTANCE

GNIP4C 11/83 •*•• SAMPLF. PROBLEM 2 *••• 2D SNR BENCHMARK - RODS IN - NODAL 1/05/84 2222.300 PAGE 45

EXTERNAL BOUNDARY CONDITION CONSTANTS C (D * DEL PHI » - C • PHI), BY GROUPLAST VALUE SHOWN IS USED FOR REMAINING GROUPS

LAST HEX BOUNDARY

1 5.00000D-0I 2 5.00000D-01 3 5.00000D-01 4 5.00000D-01

LAST BOUNDARY

1 5.00000D-01 2 5.00000D-0I 3 5.00000D-01 4 5.00000D-C1

REGION/ZONE SPECIFICATIONS

REGION REGION REGIONNO. NAME VOLUME

1C 1.43OE+O3OC 1.521E+O3RB l."56E+O3CR 2.173E+O2CF 1.O86E+O2

ZONENO.

ZONE ZONENAME CLASS.

1 Ml2 M23 M35 M56 M6

BUCKLING BY GROUP (REPEAT LAST VALUE. FOR REMAINING GROUPS)

0.00.00.00.00.0

INTERNAL BOUNDARY CONDITION CONSTANTS C (D * DEI. PHI - - C « PHI), BY GROUPLAST VALUE SHOWN IS USED FOR REMAINING GROUPS

REGIONS COMPRISING AREAS

AREANO. NAME


REGIONNO. NAME

I 1C4 CR1 1C

REGIONNO. NAME

2 OC5 CF2 OC

REGIONNO. NAME

REGIONNO. NAME

REGIONNO. NAME

REGIONNO. NAME

REGIONNO. NAME

G.2-2

DIF10 4.0 7/81 **** SAMPLE PROBLEM 2 **** 21) SNR BENCHMARK - RODS IN - NODAL 1/05/84 2222.500 PACE 52

*** PROBLEM DESCRIPTION **•

NO. OP FIRST DIMENSION MESH INTERVALSNO. OF SECOND DIMENSION MESH INTERVALSNO. OF THIRD DIMENSION MESH INTERVALSNO. OF ZONES

NO. OF REGIONSNO. OF ENERGY GROUPSMAXIMUM NO. OF DOWNSCATTER GROUPSMAXIMUM NO. OF UPSCATTER GROUPS

1010165I,30

PROBLEM GEOMETRY - 2-DIMENSIONAL HEXAGONAL

BOUNDARY CONDITIONS (ORIGIN AT LOWER LEFT)

0 - ZERO FLUX 1 - ZKRO CURRENT 2 - EXTRAPOLATED 3 - PERIODIC OPPOSITE FACE

'. - PERIODIC NKXT ADJACENT FACE 5 - INVERTED PERIODIC A LONG FACE

HEX - 0.0 HEX - 0.0 0.0 - 0.0

X - LEFT4

X - RIGHT

2

Y - FRONT4

Y - BACK

2

BOUNDARY CONDITION 2 IS APPLIED TO MESH CELL SURFACES ADJACENT TO EXCLUDED BACKGROUND CELLS.

GROUP1234

HEX - 0.04.692000D-01

4.6920O0D-O14.692000D-014.692O0OD-OI

HEX - 0.04.999999D-O14.999999D-014.999999D-01

4.999999D-O1

EXTRAPOLATED BOUNDARY CONDITION CONSTANTS C(DEL PHI/PHI - C/D , LAST VALUE USED FOR REMAINING GROUPS

- 0.04.692OOOD-O14.692000D-014.692000D-014.692000D-01

- 0.04.999999D-014.999999D-014.999999D-014.999999D-01

INTERNAL BLACK BOUNDARY CONDITION CONSTANT C FOR ALL GROUPS

(DEL PHI/PHI - C/D

0.0

DIF3D 4.0 7/B3 **** SAMPLE PROBLEM 2 **** 2D SNR BENCHMARK - RODS IN - NODAL

BUCKLING SPECIFICATION FOR ALL ZONE

BUCKLING - 0.0

1/05/84 2222.500 PAGE 53

REGION ZONE ZONE

NO. NAME NO. NAME

1 1C

5 CF

I Ml6 M6

REGION NUMBER AND ASSIGNMENT TO ZONE



2 OC 2 M2 3 RB 3 M3


4 CR 5 M5

G.2-3

n m n 4.0 7/83 *•** SAMPLE PR0M.RM 2 *•*• 21) SNR BENCHMARK - RODS IN - NODAL I/O5/B4 2222.600 PAGE 54

*** UIF3D (NODAL HEXAGONAL GEOMETRY OPTION) ***

402l>0

IAPRXIAPRXZNCMIISRXTRNZSWP

*** NODAL PARAMETERS •**

ORDER OF NODAL APPROXIMATION IN HEX-PLANEORDER OF NODAL APPROXIMATION IN Z-DIRECTIONNUMBER OF COARSE-MKSII REBALANCE ITERATIONS PER OUTER ITERATION (-1 - NO COARSE-MESH REBALANCE)0/1 YES/NO ASYMPTOTIC SOURCE EXTRAPOLATION APPLIED TO OUTER ITERATIONSNUMBER OF AXIAL PARTIAL CURRENT SWEEPS PER GROUP PER OUTER ITERATION

*** PROBLEM DESCRIPTION ***

NO. OF RINGS OF HEXAGONSNO. OF 60 DEGREE SECTORSNO. OF HEXAGONS IN PLANENO. OF ACTIVE HEXAGONS IN PLANENO. OF AXIAL PLANESNO. OF HEXAGONAL-Z NODESNO. OF UNIQUE NODE TYPES

111

5649I

565

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 2 **** 2D SNR BENCHMARK - RODS IN - NODAL 1/05/84 2222.600 PAGE 55

*** DIF3D (NODAL OPTION) CYLINDER ALLOCATION ***

PROCEDURE DEFAULT RECOMMENDED DISKPARAMETERS CYLINDERS CYLINDERS TYPE

ZONCYL

FLXCYL

PSICYL

FDCCYL

PSUCYL

SRFCYL

DMY1CYL

DMY2CYL

DMY5CYL

RTCYL

ATCYL

NHCYL

NACYL

1

1

5

20

3

12

21

7

4

5

5

5

5

0

1

1

1

1

1

1

3

2

1

0

1

0

3330

3330

3330

3330

3330

3330

3330

3330

3330

3350

3350

3350

3350

G.2-4

•*** SAMPLE PROBLEM ? •*•' 21) SHK HKNCHHARK - RODS I N - NODAL I / D V H 4 2 2 2 2 . 6 0 0 K Qγ,

••»• D1F10 (NODAL OPTION) STORAGE ALLOCATION ***

NUMBER OP WORDS IN DATA STORAGE CONTAINER

H1NIHUM NUHRFK OP WORD!! RKQMIHKn TO RUN THIS I'RORI.RH

WITH AM. DATA FOR I GROUP IN CORK -

WITH SCATTERING BAND OF FLUXES IN CORK

WITH AM. FI1.KS IN CORK (DURING OLJTKR ITERATIONS)

WITH AM. FILES IN CORK (DURING KDIT OVKRLAY)

FCM

0000

531

5)1

531

531

ECH

5700

2393

2551

5014

5660

LOCATION OF SCRATCH FILES MIRIVC OUTER ITF.RATIONS

FILE CONTENTS

N.UX HOMKNTS

NEW HFX-PLANK PARTIAL CURRENTS

(1M) HEX-PLANE PARTIAL CURRENTS

CROSS SECTIONS

NODAL COUPLING COEFFICIENTS

NO. OFRECORDS

4

',

/,

4

4

RECORDLENGTH

224

35?

357

72

35

FILELENGTH

H96

1128

1428

28B

140

LOCATION

CORE

CORF.

CORE

CORE

CORF.

RECORDSI N CORE

4

4

4

4

4

LOCATION OF SCRATCH FILES DURING EDIT OVERLAY

FILE CONTENTS

NODE-AVERAGE FLUXES

FLUX SHAPE COEFFICIENTS

FLUX MOHENTS

NEW HEX-PLANE PARTIAL CURRENTS

NO. OF

RECORDS

4

4

4

4

RECORD

LENGTH

100

336

224

357

FILE

LENGTH

400

1344

896

1428

LOCATION

CORE

CORE

CORE

CORE

RECORDS

IN CORE

4

A

4

4

TOTAL NUH8ER OF WORDS USED FOR THIS PROBLEM

0IF3D 4 . 0 7/83

OUTER ITERATION SUMMARY


SOLUTION K-EFF. PROBLEM

1/05/84 2 2 2 2 . 6 0 0 PAGE 57

GROUP

NO.

OPTIMIZED INNER ITERATION STRATEGYKAPPA* NO. OF GROUP KAPPA*PITCH INNERS NO. PITCH

NO. OFINNERS

GROUPNO.

KAPPA*PITCH

NO. OFINNERS

GROUPNO.

KAPPA*PITCH

NO. OFINNERS

OUTERI T . NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

RF.L. POINTERROR

5.3O1156D*O1

4.5H973D+00

3.532498D-O1

1.I170O4D-OI

5.7B2O4BD-O2

3.326939D-O2

1.825124D-02

9.89O957D-O3

5. 3881630-03

1.538594D-03

3.B85185D-O4

1.471937D-O4

5.365769D-O5

3.0218900-05

1.6P')2BBD-O5

9.609080D-06

2.O2O246D-O6

4.497O27D-O7

1

1

1

b

3

1

1

5

3

1

1

6,

J,

1.

B

A,

1.

2.

REL. SUMERROR

.225204 D»00

.1470410-01

.286835D-O2

.3331540-03

.3I1B17D-O3

.92OB69H-O3

.062688D-O3

.7941810-04

. 1607890-04

.092786D-O4

.8729110-05

,8867!18D-O6

.O99757D-O6

.6226230-06

,7f)«6SD-O7

.792744D-O?

223496D-O7

8745I5D-O8

1

3

-1

-1

-7

-4

-2

-1

-7

-9

1

1.

5,

2,

1,

9,

1.

- 1 .

EIGENVALUECHANCE

.643987D-O1

.873i>«D-O3

.5158310-02

. IO4(>45D-O2

.160BI7D-O3

.26O461D-O3

.4O1477D-O3

.32114OD-03

.243I47D-O4

.5O2524P-O4

.4B749BD-O5

.0883690-05

. 18891 3D-O6

,9I447ID-O6

,fi51*9BD-06

,29933OD-O7

,2360970-06

727949D-O8

FSRC.EXTRAP.

NO

NO

NO

NO

NO

NO

NO

NO

VES

NO

NO

NO

NO

NO

HO

YES

NO

NO

2

1

6

7

6

5

5

5

5

3

1

4,

5.

5.

5.

5.

2.

2.

DOM. RATIOESTIMATED

.O37725D-O1

.865114D-01

.625057D-0I

.8998I4D-O1

.375314D-O1

.7449670-01

.5O6B5ID-O1

.45O372D-OI

.4792990-01

.39184 3D-O1

.3386I3D-OI

.5I6936D-OI

,1O5981H-O1

,J98057D-O1

.47492611-01

.478645D-OI

563080D-OI

OO576OD-O1

5

5

1

2

1

8

4

2

1

1

2.

1.

8.

5.

1.

1.

2.

REBALANCEERROR

.819746D-0I

.533OO2D-O2

.325572D-O2

.O53395D-O2

.482393D-O2

.79O292D-O3

.82O466D-O3

.57700ID-O3

.38I935D-O3

.0I3904D-O4

.404337D-O5

.28O539D-O5

.3O3633D-O6

356616D-06

2B1977D-Of>

9256510-O6

373004D-O7

879097D-O8

1

1

1

1

1

I

1

1

1

1,

1.

1.

1.

1.

1.

1.

1.

1.

K-EFFECTIVE

.16439865D+OO

.16R27231D+OO

.I5311399D»OO

. 142O6754DM1O

. 1349O673D*OO

. 13Q64f>26D+OO

.128244 791X00

.I2692345IHOO

.12619913D+00

. I25248BBD*OO

, I2526376DWO

. I2527464IHOO

I2527983D«O

I2528274D*OO

12528439D»00

12528532D«OO

I2528656D<OO

12528654DWO

OUTER ITERATIONS COHPLETED AT ITERATION 1 8 , ITERATIONS HAVE CONVERGED

K-EFFECTIVE - 1 . 1 2 5 2 8 6 5 4 2 7 9

MAXIMUM POWER DENSITY ? ' n - " ; e D - 0 4 OCCURS AT: RING NO. 1

POSITION NO. 1SURFACP NO. 0

Z-COORDINATE • 0 . 0

G.3-1


Dion ».o 7/as •"*• SAHi'i.e PROBLEM 3 •••• n> SNR BENCHMARK - Rons IN - NODAL 1/05/84 2223,000 FACE 86

••• DIP3D (NODAI. OPTION) STORAGE ALLOCATION •**


NINIHUH NIINBER OF WORM RFUIIIRED TO RUN THIS PROBLEM

UITII Al.l. OATA FOR I CROUP IN CORF

W1TII SCATTERING HAND OF FLUXES IN CORE

B1TH AM. FILES IN CORE (DURINC OUTER ITERATIONS)

UITII ALL FILES IN CORE (DURING EDIT OVERLAY)

FCM

20000

594

594

594

594

P.CM

27000

26314

26314

47013

5933B

LOCATION OF SCRATCH FILES DURING OUTER ITERATIONS

PILE CONTENTS

FLUX MOMENTS

NKU KEX-PLANf PARTIAL CURRENTS

NEW AXIAL PARTIAL CURRENTS

OLD HEX-PLANE PARTIAL CURRENTS

OLD AXIAL PARTIAL CURRENTS

CROSS SECTIONS

NODAL COUPLING COEFFICIENTS

NO. OF

RECORDS

4

4

4

4

4

4

4

RECORD

LENGTH

2210

2856

1008

2B56

1008

72

117

FILE

LENCTH

8960

1 1 4 2 .

4032

11424

4032

268

468

LOCATION

CORE

DISK

CORE

DISK

DISK

CORE

CORE

RECORDS

IN CORE

4

1

4

1

1

4

4

LOCATION OF SCRATCH FILES CURING EDIT OVERLAY

FILE CONTENTS

NODE-AVERAGE FLUXES

FLUX SHAPE COEFFICIENTS

FLUX MOMENTS

NEW HEX-PLANE PARTIAL CURRENTS

NEW AXIAL PARTIAL CURRENTS

NO. OF

RECORDS

4

4

4

4

4

RECORD

LENGTH

800

4032

2240

2856

1008

PILE

LLNGTH

3200

16128

8960

11^24

4032

LOCATION

DISK

DISK

DISK

DISK

DISK

RECORDS

IN CORE

1

1

1

]

1

TOTAL NUMBER OF WORDS USED FOR THIS PROBLEM

4 . 0 7/E

GROUP

NO.

1

OUTER

I T . NO.

1

2

3

4

5

6

7

8

9

10

n

12

13

14

1*

16

17

I β

19


OPTIMIZED INNER ITERATION

KAPPA* NO. OF GROUP

PITCH INNERS NO.

1.216 2

REL. POINTEHROR

4.1156000*02

2.672773D+O1

1.I608J5D+O0

2.29893OD-OI

5.5183I6O-O2

2.789854D-O2

1.523165D-O2

1.O517I5D-O2

4.990391O-03

2.365442D-O3

1.1963050-03

O.64I5S5D-04

3.865679D-04

1.992933D-O4

9.6071I5D-O5

5.797460O-O5

2.7I9733D-O5

1.O7351OD-O5

5.221B94D-O6

2

REL. SUMFRROH

I.882773D*OO

8.4O9265D-O2

8.729627D-O3

2.O7O839U-O3

7.276B64D-O4

4.976351D-O4

3.751465D-O4

I.452125D-O4

6.762I3ID-O5

3.5J9278D-O5

J.I403IID-05

1.325022D-O5

7.85O677D-O6

4.539753D-06

2.643262D-O6

9.IO7678D-O7

4.7123840-07

2.236516D-O7

1.O9I903D-O7

REAL SOLUTION

STRATEGY

KAPPA* NO. OF I

PITCH INNERS

0.703 4

F.IGENVALUECHANGE

-5.468500D-O5

3.835296D-O2

-I.142393D-O2

-7.7508400-03

-4.OI928ID-O3

-1.92868OD-O3

-B.745156D-04

-9.8656I6D-O4

1.259094D-04

4.2325I2D-O5

I.OMt53D-05

2.28O02OD-O6

1.726237D-O6

2.226419D-O6

2.193967D-O6

3.92O51BD-O6

3.679485D-O7

5.633647D-O8

- 5 . 1 5 4 9 8 6 0 - 0 8

FSRC.

EXTRAP

NO

NO

NO

NO

NO

NO

YES

NO

NO

NO

140

NO

NO

NO

YES

NO

NO

NO

NO

K-EFF. PROBLEM

3R0UP KAPPA'NO. PITCH

3 1.729

DOM. RATIOESTIMATED

3.O24159D-O1

2.7O2862D-OI

5.893127D-O1

5.8112620-01

5.429634D-O1

5.502596D-OI

5.6OOI24D-OI

2.874426D-OI

4.852630D-O1

6.223060D-O1

6.289434D-O1

5.86724ID-O1

5.493155D-O1

5.317598O-OI

5.357585O-OI

4.I96934D-OI

4.702059D-O1

5.O43417D-O1

5.125455D-OI

' NO. OFINNERS

2

REBALANCEERROR

5.313486O-O1

7.O47214D-O2

1.559124D-O2

1.17O?29D-O2

6.06366SD-03

3.922947D-O3

2.I25458D-O3

5.627SI6O-O4

2.319I52D-O4

I.47O948D-O4

9.649634D-O5

5.B95393D-O5

3.282776D-O5

I.9I762O0-05

1.087603D-O5

2.329277O-O6

1.3O1975D-O6

8.163573D-O7

4.6509O0D-O7

1/05/84 2223.000 PAGE

GROUP KAPPA* NO. OFNO. PITCH INNERS

4 1.573 2

K-EFFECTIVE

9.999453150-01

1.038298280*00

I.O26B7435D+OO

1.O1912351IXOO

1.01510423DtO0

I.O1317555D*OO

1.012301040*00

1.01I3I447I«00

1.011440380*00

I.OU4e27ID*W<t

1.011493140*00

1.011495420*00

1.0ll497!4O*00

I.OIU9937D*OO

1.011501560*00

1.011505480*00

1.011505850*00

1.O1I50591D+O0

l.OU5O5B5D*O0


K-EFFECTIVE - 1.01150585498

MAXIMUM POUER DENSITY 3.O3072D-O6 OCCURS AT: RING NO. I

POSITION NO. ISURFACE NO. 0

G.3-2

DIF3D 4,0 7/83 **** SAMPLE PROBLEM 3 **** 3D SNR BENCHMARK - RODS IN - NODAL

REGION AND AREA POWER INTEGRALS FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0

l/OS/84 2223.600 PAGE 88

.1.O5OD+O7)


4 M41 Ml

123456

AB1COCRBCFCR

2365

M2M3M6M5

VOLUME(CO

INTEGRATIONC1) POWERWEIGHT FACTOR (WATTS)


PEAK DENSITY PEAK TO AVG. POWER(WATTS/CC)(2) POWER DENSITY FRACTION

2.361UD+O5 1.00000D+00 6.84613D-03 2.89954D-08 1.75349D-O7 6.O4747D+OO 1.36923D-O21.35891D+051.44411D+O53.42216D+053.36784U+042.33576D+O4

1.00000D+00l.OOOOOD+001.00000D+00l.OOOOOD+00l.OOOOOD+00

2.63252D-012.18689D-011.12126D-O20.00.0

1.93723D-061.51351D-063.27647D-080.00.0

3.O3O72D-O62.89S93D-062.68292D-O70.00.0

1.56446D+OO1.91338D+008.18846D+000.00.0

5.26504D-014.37379D-012.24252D-O20.00.0

TOTALS 9.15745D+O5 0 . 0 5 . 0 0 0 0 0 D - 0 1 5 . 4 6 0 0 3 D - 0 7 3.O3O72D-06 5.55O74D+OO l.OOOOOD+00

( 1 ) INTEGRATION WEIGHT FACTOR - ( 2 / B ) * S I N ( B * H ) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT

REGION ZONE ZONE

NO. NAME NO. NAME

123456

AB1COCRBCFCRTOTALS

4I2365

M4MlM2M3M6M5

PEAK INDEX

' X '

l.OOOOOD+00l .OOOOOD+006.00000D+008.00000D+000.00.0l.OOOOOD+00

PEAK INDEX

•Y,

l.OOOOOD+00l.OOOOOD+00l.OOOOOD+00l.ooooon+oo0.00.0i.nooooD+oo

PEAK INDEX

•z,

2.00000D+004.00000D+004.00000D+004.00000D+000.00.04.00000D+00

DIF3D 4.0 7/83 SAMPLE PROBLEM 3 **** 3D SNR BENCHMARK - RODS IN - NODAL 1/05/84 2223.600 PAGE 89

MAXIMUM TOTAL FLUX 3.9525OD+O7 OCCURS AT: RING NO. 1POSITION NO. 1SURFACE NO. 0

Z-COORDINATE - 8.5125OD+O1

G.4-1


niFID 4.0 1/84 *»** SAMPLE PROBLEM 4 •*»• 3D SNK BENCHMARK - RODS IN - FDO636 1/23/84 1608.700 PACE 104

**• n » ID STORAGE ALLOCATION ••*

NUMBER OF WORDS IN DATA :.lORAGE CONTAINER



WITH ALL DATA FOR 1 CROUP IN COM



FCM

12000

508

508

508

508

ECM

164000

12225

152345

205913

438257

LOCATION OF SCRATCH FILI'S DURING STEADY. STATE CALCULATION

FILE CONTENTS

NEW F I S S I O N SOURCE

OLD F I S S I O N SRC. 1

OLD F I S S I O N SRC. 2

TOTAL SOURCE

COMPOSITION MAP

FLUX ITERATE

CROSS SECTIONS

F I N I T E D I » F . COEFS.

NO. OF

RECORDS

1

1

1

1

1

4

4

4

RECORD

LENGTH

17856

17856

17B56

17856

8928

17856

72

71424

FILE

LENGTH

17856

[7856

17856

17856

8928

71424

288

285696

LOCATION

CORE

CORE

DISK

CORE

CORE

DISK

CORE

DISK

RECORDS

IN CORE

1

1

0

1

1

L

4

1

TOTAL NUMBER OF WORDS USED FOR THIS PROBLEM 508 152561

DIF3D 4 . 0 1/84 *••• SAMPLE PROBLEH 4 •••• JD SNR BENCHMARK - RODS IN - FDO636

OUTER ITERATION SUMMARY REAL SOLUTION K-EFF. PROBLEM


1/23/84 1 6 0 8 . 9 0 0 PAGE 108

GROUPNO.

1 1

OUTERI T . NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Iβ •


.52724IHOO 10

5

6

4

REL. POINTERROR

.9080240-01

.733313D-OI

.764514D-01

I.B88638D-0I

5

2

1

7.

2

2

5,

1.

2,

3,

1.

1.

3.

1.

.631559D-O2

.92I216D-O2

.735I53D-02

.88161OD-O3

•2O9185D-O3

.O72177D-O3

.335848D-04

.5137010-04

.O44381D-O4

.648853D-O5

,588739D-O5

.772728D-O5

3I297ID-O6

530I63D-CO

I

2

7

4

2

9.

4

2,

7.

2.

1,

5.

2.

1.

4 .

I .

8 .

2 .

GROUPNO.

2 1 .

REL. SUMERROR

. 179524D-O1

.024667D-0I

.901021D-O2

.2278I3D-O2

.03907ID-O2

.729249D-03

.993231D-03

.3860630-03

,190380D-04

.7/«078r-O4

518552D-04

494587D-O5

275OO5D-O5

2B2983D-O5

165C14D-06

480040D-06

225556D-O7

4930040-07


66503D-tfl0 14

- 3

2

1

7

3

1

7

3

1

3

4,

2,

- 2 ,

- 1 ,

- 3 .

- 5 .

- 1 .

- 4 .

EIGENVALUECHANGE

.8756OOD-O2

.1O6814D-02

.674584D-O2

.0570550-03

.679833D-O3

.783O28D-O3

.18311OD-O4

.O47675D-O4

.613694D-O4

.9O49O3D-O5

.664759D-O6

.434434D-O6

,5038170-06

•270115D-O6

,76 76910-07

193528D-O7

774384D-O7

6144MD-O8

CROUP OPTIMUH NO. OFNO. OMECA INNERS

POLY.ORDER

0

0

0

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

0

0

0

4

4

4

6

6,

6,

6.

6.

6.

6.

6.

6 .

6 .

6 .

6 .

3 1.39934D-HI0 7

DOM. RATIOUSED

. 0

.0

. 0

. 3 7 7 5 8 7 D - O I

-377587D-O1

.377587D-O1

. 2 2 7 8 6 9 D - 0 1

.22 7869D-O1

.227869D-O1

.43O465D-O1

.43O46SD-OI

430465D-OI

855575D-O1

855575D-OI

B55575D-OI

992496D-OI

9 9 2 4 9 6 D - 0 1

992496D-O1

DOM. RATIO

ESTIMATED

0 . 0

9.913276D-O1

4 . 3 7 7 5 8 7 D - O I

4 . 3 7 7 5 8 7 D - O 1

6.O3743OD-O1

6 . 2 2 7 8 6 9 D - O '

6.227869D-01

6.4I1442D-OI

6.430465D-0I

6.430465D-O1

6.924204D-01

6.B55575D-O1

6.855575D-OI

7.I34I72D-O1

6.992496D-01

6.992496D-OI

7.H0B09D-O1

b.99O13SD-01

9

9

9

1

1

1

1

1

1

1

1.

1.

1,

1.

1 .

1 .

1 .

1 .


4 l.47889D*O0 8

K-EFFECT1VE

•61244003D-O1

.82312139D-O1

.99O57983D-O1

.006115040*00

.O0979487IXO0

.O1I57790D+OO

.O1229621D+OO

.01260098D+O0

.01276235D+OO

.OI280140D«00

.OI280606DHOO

.01280850D4O0

,O1280599IW)0

0I280472D+O0

012804 34frtOO

O128O3S3DKIO

OI2B0365IHOO

01280360D^H)

OUTER ITER»T10NS COMPLETED AT ITERATION I β , ITERATIONS HAVE CONVERGED

K-EFFECTIVE - 1 . O I 2 8 O 3 6 O 1 7 2

G.4-2



DOMINANCE RATIO (SIGBAR) - 6.990136..98443D-01

1/23/84 1610.200 PAGF. 109

OPTIMIZED OVER-RELAXATION FACTORSGROUPNO.

1

OPTIMUMOMEGA

1.52724D-I00

GROUPNO.

2

OPTIMUMOMEGA

1.665O3D+0O

GROUPNO.

3

OPTIMUMOMEGA

1.39934D+O0

GROUPNO.

4

* SUBROUTINE* 0RPES1

ERROR

ERRORNO.100

COUNT

TYPENONFATAL

NO. OF *ERRORS *

2 *

OPTIMUMOMEGA

1.47889D+OO

GROUPNO.

OPTIMUMOMEGA

MAXIMUM POWER DENSITY 3.C/935D-06 OCCURS AT MESH CELL (l.J.K) - ( 1, 1, 18)



REGION AND AREA POWER INTEGRALS FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) -(0.0 , 1.05OD+17)

REGIONNO.

123456

NAME

AB1COCRBCFCR

ZONENO.

412365

ZONENAME

M4MlM2M3M6M5

TOTALS

2113329

VOLUME(CO

.36111D+O5

.35891D+05•44491D+O5.42216D+05.36784D+04.33576D+04.15745D+05

INTEGRATION 1)WEIGHT FACTOR

1111110

.00000D+00

.000000+00

.OOOOOD+00

.00O0OD+O0

.OOOOOD+00

.OOOOOD+00

.0

POWER(WATTS)

6.79240D-032.62993D-O12.19122D-011.1O924D-O20.00.05.00CGOD-01

POWER DENSITY

2113005

(WATTS/CO

.87678D-08

.93533D-06

.51651D-O6

.24135D-O8

.0

.0

.46OO4D-07

PEAK DENSITY(WATTS/CC)(2)

322003

.76254D-07

.O1935D-O6

.89991D-06

.64958D-07

.0

.0

.01935D-06

PEAK TO AVG.POWER DENSITY

6.1.1.8.0.0.5.

I2676D+0056012D+OO91223D+OO17431D+OO0052991D+00

1542001

POWERFRACTION

.35848D-02

.25986D-01

.38244D-01

.21849D-02

.0

.0

.OOOOOD+00

(1) INTEGRATION WEIGHT FACTOR - (2/B)*SIN(B*H) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT(2) THE PEAK POWER DENSITY IS CALCULATED BY SAMPLING THE AVERAGE FLUX ON THE CELL SURFACES AND WITHIN THE CELL.

REGION ZOtfE ZONENO. NAME NO. NAME

123456

AB1COCRBCFCRTOTALS

412365

M4MlM2M3M6M5

PEAK INDEX'X'

1.OOOOOD+001.OOOOOD+001.00000D+011.40000D+010.00.01.OOOOOD+00

PEAK INDEX•Y.

1.OOOOOD+001.OOOOOD+005. OOOOOD+007. OOOOOD+000.00.01.OOOOOD+00

81

11001

PEAK INDEX'Z'

.OOOOOD+00

.80000D+01

.70000D+01

.70000D+01

.0

.0

.80000D+01

G.5-1

G.5 Sample Problem (selected pages)

i i i i i i i i i

RREFLCREFL

RFUELlCFUELl

RFUE2RCFUE2R

: RFUEL2CFUEL2

i \ \ i i i i i i

RFUE2RCF.UE.vR.

BRCK3R

1 1 1 1 1 1 1 f 1 1

CBflCKG :

1 S 1 1 1 1 1 1 1

'•

'•

;

m

GNIP4C Generated Calcomp 780 Plot of 2D IAEA Benchmark Model

G.5-2

DIF3R 4.0 7/83 . » » • SAMPLE 5 « • • • IAEA 2D BENCHMARK - 2 . CM MESH 1 / 0 5 / 8 4 1 6 1 6 . 3 0 0 PAiiE 14

« • • D1F3D STORAGE ALUWTION • • •

NbMBFR OF WORDS IN DATA STORAGE CONTAINER


WITH ALL DATA FOR I GROUP IN CORE



FCM

200

790

790

790

ECH

102000

61464

6S689

97639

LOCATION OF SCRATCH FILES DURING STEADY STATE r/UCULATION

FILE CONTENTS

f,_U FISSION SOURCE

OLD FISSIOII SRC. 1

OLD FISSION SRC. 2

TOTAL SOURCE

COMPOSITION MAP

FLUX ITERATE

CROSS SECTIONS

F1NITEDIFF. COEFS.

NO. OFRECORDS

1

1

1

1

1

2

2

2

RECORDLENGTH

7225

7225

7225

7225

3613

7225

50

21675

FILELENGTH

7225

7225

7225

7225

3613

14450

100

4 3350

LOCATION

CORE

CORE

CORE

CORE

CORE

CORE

CORL

CORE

RECORDSIN CORE

1

1

1

1

1

2

2

2

TOTAL NUMBER OP WORDS USED FOR THIS PROBLEM

DIF3D 4.0 7/B3 *«*• SAMPLE 5 •••• IAEA 2D BENCHMARK - 2. CH MESH

OUTER ITERATION SUKMARtf REAL SOLUTION K-EFF. PROBLEM


1/05/84 1616.400 PAGE 25

GROUPNO.

1 1

OUTERI T . NO.

1

2

3

4

5

6

7

8

9

10

11

12

13

i i

IS

16

17

18

19

20

21

22

23


.566200+00 14

REL. POINTERROR

3.686295D-O1

1.O87O9OD-O1

5.5414150-02

3.5r.0(-66D-02

2.726305D-O2

2.324552D-O2

1.954620D-02

1.6031850-02

1.118446D-O2

9.360O04D-O3

8.528902D-O3

6.I83622D-O3

5.174504O-03

4.992O1BD-O3

3.613O34O-03

3.187787O-O3

3.I37347D-O3

2.267487O-O3

2.O1O7O6D-O3

1.8555*40-03

1.3*26310-03

1.279728D-O3

1.O9OI73D-O3

GROUP

NO.

2 1 .

REL . SUM

ERROR

8.812177D-02

4.075031D-O2

2.3B0535D-O2

1.769028D-O2

1.2747O9D-O2

9.655415D-O3

8.190440D-03

7.1O98B6D-O3

5.623376D-O3

4.863033D-O3

4.58023OD-O3

3.634297D-O3

2.940846O-03

2.944204D-03

2.318619D-O3

1.740132D-O3

1.8I1439D-O3

1.398910D-O3

9.98O777D-O4

1.06OO73O-O1

8.I23937D-O4

5.653021D-O4

6.0938801X14


41751D+OO 9

EIGENVALUECHANGE

1.224134D-O2

1.235995D-O2

I.0S4773D-O3

6.7O72b7D-O4

6.574164D-O4

5.22496OD-O4

3.320O14D-O4

2.622962D-O4

3.391927D-O4

2.1432S5D-O4

1.056055D-04

2.077926O-04

1.4B2553D-O4

3.461179D-O5

9.8O3535D-O5

7.516984D-OS

1.251830D-O5

4.055590D-O5

3.3O2212D-O5

7.41632VO-O6

1.6I201ID-O5

1.32373*0-05

4.70J061D-O6

POLY.ORDER

0

0

0

1

2

3

1

2

3

1

2

3

1

2

3

I

2

3

1

2

3

1

2


DOM. RATIOUSED

0.0

0.0

0 .0

5.9 I2010D-O1

5.9I2010D-O1

5.912O10D-O1

8.363244D-O1

8.363244D-O1

8.363244D-O1

9.287O23D-O1

9.287O23D-O1

9.287023D-O1

9.564793D-O1

9.564793D-O1

9.564793D-O1

9.673322D-OI

9.673322D-OI

9.673322O-O1

9.710263D-O1

9.710263D-OI

9.710263D-0I

9.729O18D-O1

9.7290I8D-O1

DOM. RATIOESTIMATED

0.0

4.695831D-O1

5.912O1OD-O1

5.912O1OD-O1

8.O50748D-O1

8.363244D-O1

8.363244D-O1

9.241546D-O1

9.287O23D-O1

9.2B7O23D-O1

9.694433D-O1

9.564793D-O1

9.564793D-O1

1.001017D+00

9.673322O-O1

9.673322D-O1

1.O21432D+OO

9.71O263D-O1

9.71O263D-O1

I.O32139D+OO

9.7290180-01

9.729OI8O-O1

1.O4O157D+OO

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1,

1,

1.

1 .

1 .


K-EFFECTIVE

.012241340+00

.02460129D+00

.02565606D+O0

.O2632678D+OO

.026984200+00

.O2750669D+0O

.O2783870D+OO

.02810099D+00

.028440180+00

.028654510+00

.O28760I2D+OO

.028967910+00

.029116160+00

.O2915O7BD+OO

.029248810+00

.029323980+00

.029336500+00

.O29377O5D+OO

.G294IO08O+O0

.029417490+00

,029433610+00

02944685O+O0

029*51560+00

G.5-3

DIF3D 4.0 7/83 **** SAMPLE 5 **** IAEA 2D BENCHMARK - 2. CM MESH 1/05/84 1617.200 PAGE 26

OUTER ITERATION SUMMARY REAL SOLUTION K-EFF. PROBLEM

OUTERIT. NO.

24

25

26

27

28

29

30

31

32

33

34

35

36

37

REL. POINTERROR

REL. SUMERROR

EIGENVALUE POLY. DOM. RATIOCHANGE ORDER USED

DOM. RATIOESTIMATED

7.869962D-04 4.639558D-04 6.597291D-06

7.57O648D-O4 3.2O2154D-O4 5.286035D-O6

6.211472D-04 3.447927D-04 2.756975D-06

4.495778D-O4 2.624991D-O4

4.981576D-04

2.378958D-04

1.5476O8D-04

2.867366D-O6

1.793089D-04 2.1682O7D-O6

1.218137D-04 3.231O51D-O6

6.771766D-05 1.876176D-06

9.740612D-O1

1.12144OD-04 4.944923D-05 1.483748D-O6

5.678522D-05 2.690326D-05 1.1O1921D-06

3.O575O8D-O5 2.255934D-05 4.90l3'i6D-07

1.619595D-O5 1.594660D-05 2.568945D-07

1.375732D-05 1.287818D-O5 1.301539D-O7

1.186071D-05 1.12O915D-O5 1.520512D-08

9.942655D-06 8.34O138D-06 -3.135238D-O8


K-EPFECTIVE - 1.02947978522


DOMINANCE RATIO (SIGBAR) - 9.727808648906D-01


3

1

2

3

4

5

6

7

8

9

10

11

12

13

9.729018D-G1 9.74O612D-O1

9.74O612D-O1 9.740612D-O1

9.740612D-O1

9.740612D-01

9.740612D-01

9.740612D-01

1.039436D+00

9.740058D-01

9.656760D-O1

9.661532D-O1

9.740612D-01 9.647719D-01

9.74O612D-01

9.740612D-01

9.675397D-O1

9.675678D-O1

9.696837D-01

9.740612D-01 9.7O52O3D-O1

9.740612D-01 9.715116D-01

9.74O612D-O1 9.724532D-01

9.74O612D-O1 9.727809D-O1

K-EFFECTIVE

1.02945815D+O0

1.02946344D+00

1.02946620D+O0

1.02946906D+OO

1.O2947123D+OO

1.02947446D+OO

1.02947634D+O0

1.02947782D+00

1.02947892D+O0

1.02947941D+O0

1.02947967D+O0

1.02947980D+O0

1.02947982D+00

1.02947979D+O0

GROUPNO.

NO.1 1

OPTIMUMOMEGA

OMEGA.56620D+O0

GROUPNO.

OPTIMUMOMEGA

GROUPNO.

OPTIMUMOMEGA

GROUPNO.

OPTIMUMOMEGA

GROUP OPTIMUM

1.41751D+00

DIF3D 4.0 7/83 **** SAMPLE 5 **** IAEA 2D BENCHMARK - 2. CM MESH 1/05/84 1617.200 PAGE 27

MAXIMUM POWER DENSITY 8.67H9D-05 OCCURS AT MESH CELL (I.J.K) - ( 16, 16, 1)


G.5-4

IHF3D 4.0 7/83 **** SAMPLE 5 **** IAEA 2D BENCHMARK - 2. CM MESH 1/05/84 1627.100 PACE 28

REGION AND AREA POWER INTEGRALS FOR K-EFF PROBLEM WITH ENERGY RANGE (EV) "(0.0 .1.000D+07)

REGIONNO. NAME

12345

AREANO.

1

RREKLRFUEL1RFUEL2RFUE2RBACKGRTOTALS

AREANAME

TFUEL

ZONENO.

41235

ZONENAME

CREFLCFUEL1CFUEL2CFUE2RCBACKG

VOLUME(CC)

6.40000D+035.60OO0D+O31.12OOOD+O49.000000+0?4.80000D+032.89000D+O4

VOLUME(CC)

1.68000D+04

INTEGRATION(l)WEIGHT FACTOR

1.00000D+O01.00000D+001.00000D+001.00000D+00l.OOOOOD+000.0

INTEGRATIONO )WEIGHT FACTOR

0.0

POWES(WATTS)

0 . 02.29781D-017.41689D-012.853O1D-O20 . 0l.OOOOOD+00

POWER(WATTS)

9.7147OD-O1


0 . 04.10324D-056.62222D-053.17001D-050.03.46021D-05


5.78256D-05

PEAK DENSITY(WATTS/CCK2)

0.08.6O665D-O58.67119D-O55.89426D-050.08.67119D-05

PEAK DENSITY(WATTS/CCK2)

8.67119D-05

PEAK TO AVG.POWF.R DENSITY

0.02.O9753D«.O1.30941D+0O1.85939D+000.02.50597D+00

PEAK TO AVG.POWER DENSITY

1.49954D+00

POWERFRACTION

0.02.29781D-O17.41689D-O12.85301D-020.0l.OOOOOD+00

POWERFRACTION

9.71470D-01

(1) INTEGRATION WEIGHT FACTOR - (2/B)*SIN(B*H) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT(2) THE PEAK POWER DENSITY IS CALCULATED BY SAMPLING THE AVERAGE FLUX ON THE CELL SURFACES AND WITHIN THE CELL.

REGIONNO.

i

2345

NAME

RREFLRFUEL1RFUEL2RFUE2RBACKGRTOTALS

ZONENO.

412

5

ZONENAME

CREFLCFUEL1CFUEL2CFUE2RCBACKG

02150

PEAK INDEX

•x.

.0

.80000D+01

.60000D+01

.OOOOOD+OC

.01.60000D+01

06150i

PEAK INDEX•Y,

.0

.50000D+01

.60000D+01

.OOOOOD+00

.0

. 6 0 0 0 0 D + 0 I

PEAK INDEX•z.

0.0l.OOOOOD+00l.OOOOOD+00l.OOOOOD+000.0l.OOOOOD+00

AREA AREANO. NAME

I TFUEL

PEAK INDEX•X

,

PEAK INDEXIγ,

PEAK INDEX'Z

,

I.60000D+01 1.60000D+01 l.OOOOOD+00

G.6-1


GN1P4C 11/83 ***• BENCHMARK 1'ROBl.KM 6 *••* IAEA 3D BENCHMARK 10. CM MESH 1/05/84 1628.000 PACE 44

REACTOR COMPOSITION MAP

Z-DIM MAP FOR PLANES 29 - 36

Y -DIM /X -DIM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

17

16

15

14

13

12

11

10

A 4

* 1

• I

* 2

* 2

• 2

* 2

* 3A

• 3

• 2

* 2

* 2

* 2

* 2

• 2

A 3 I

1

4

1

1

2

2

I

2

* 2

» 2

•>

2

2

2

2

2

2

2

4

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

3

A

A

A

A

AA

4

1

1

1

1

2

2

2

2

2

2

3

3

2

2

2

4

4

1

I

1

1

2

2

2

2

2

2

3

3

2

2

2

A

A

A

A

AA

4

1

1

2

2

2

2

2

2

2

2

2

2

2

6

4

1

1

2

2 <

2

2 '

2

2

2

2

2

2

2 «

7

A

* 6

1

1

* 1

1 1

' 3

3

2

2

2

2

2

2

3

8

6

1

1

1

1

3

3

2

2

2

2

2

2

3

9

AA*

AAA

A

6

6

4

1

1

I

1

2

2

2

2

2

2

2

10

6

4

1

1

1

1

2

2

2

2

2

2

2

11

6

6

A

A 6

4

• 4

* 4

1

1

» 1

* 1

> 1

> 1

2

2

2

12

6

6

6

4

4

4

1

1

1

1

I

1

2 '

2 <

2 '

13

6

6

6

A

* 6

4

4

* 4

k 4

> 4

» 4

1

1

> 1

> 1

1

14

6

6

6

6

6

4

4

4

4

4

4

1

1

1 '

1 *

1 '

IS

6

6

6

6

6

6

A 6

* 6

* 6

* 6

4

4

» 4

» 4

> 4

' 4

4

16

6

6

6

6

6

6

6 '

6 *

6 *

l> *

4 '

4 s

4 *

4 *

£ 1

4 *

17

» 17

* !6

• 15

* 14

* 13

» 12

• 11

• 10

9

8

7

6

5

4

3

2

1

DIF3D 4.0 7/83 AAAA BENCHMARK PROBLEM 6 **** IAEA 3D BENCHMARK 10. CM MESH 1/17/84 1044.700 PAGE 51

*** DIF3D STORAGE ALLOCATION ***




WITH ALL DATA FOR 1 GROUP IN CORE



FCM

8000

390

390

390

390

ECM

166000

7142

93697

104679

159649

LOCATION OF SCRATCH FILES DURING STEADY STATE CALCULATION

FILE CONTENTS

NEW FISSION SOURCE

OLD FISSION SRC. 1

OLD FISSION SRC. 2

TOTAL SOURCE

COMPOSITION MAP

FLUX ITERATE

CROSS SECTIONS

FINITEDIFF. COEFS.

NO. OFRECORDS

1

1

1

1

1

2

2

2

RECORDLENGTH

10982

10982

10982

10982

5491

I09B2

60

43928

FILELENGTH

10932

10982

10982

10982

5491

21964

120

87856

LOCATION

CORE

cr •

CORE

CORE

CORE

CORE

CORE

CORE

RECORDSIN CORE

1

1

1

1

1

1

1

1

TOTAL NUMBER OF WORDS USED FOR THIS PROBLEM 390 159649

G.6-2

• • • • BENCHMARK PROBLEM 6 * * • • IAEA ID HKNCHHARK I f ) , CM HKSH

OUTER ITERATION SIIKKARY REAL SOLUTION K-EFF. PROBLEM

I / 1 7 / B 4 J 04. <V. H00 PACE 63

OPTIMIJEKD INNER ITERATION STf f T

GROUPNO.

1

OUTERI T . NO,

OPTIMUMOMEGA

1 .165650+00

R E L

NO. OPINKERS

5

POINTERROR

CROUPNO.

2 1

REL. SUMERRllK

OPTL.JM HO. OFOMKCA INNERS

.0B039D+O0 4

EIGENVALUE POLY.CHANGE ORDER

CROUPNO.

OPTIMUMOMEGA

HO. OP

INNERSCROUP

NO.OPTIMUM NO. OF

OMEGA INNERS

1 2.771832D-O1 I.O24438D-OI 3.8309690-03

2 1.76O958U-O1 5.8068h5D-O2 1.04O214D-O2

3 1.I98757D-O1 3.941B84D-02 3.O10733D-O3

4 9.499101D-02 3.O8B157D-O2 I.957533D-O3

5 6.8^843BD-02 2.328266D-O2 2.O19555D-O3

6 4.9244 79D-O2 1.7B4 312D-O2 I.744825D-O3

7 4.094458D-02 1.525653D-O2 1.071401D-03

8 3.579333D-O2 1.357514D-O2 7.4B6434O-O4

9 2.692639D-O2 I.O98765D-O2 1.O34374D-O3

10 2.1097280-02 9.372968D-O3 7.24198 7O-O4

I 1 2.OI992 7D-O2 8. /89 725D-O3 3.37B6OBD-O4

12 I .7394T D-02 7.2450O2D-O3 5.7O5062D-O'i

13 I.417O54D-O2 5.86I44 2D-O3 4.926338D-O4

14 I.33 72180-02 5.642111D-03 1,6751430-04

15 1.095615D-O2 4.6581830-01 2.4413 3BO-O4

16 8.621393D-03 3.5968O2O-O3 2.38O2O9D-O4

17 8.442859D-O3 3.506622D-O3 fl.5984590-05

IB 7.234 7OOD-O3 2.876 7IBD-OT B.8206951-05

19 5.BO4683D-O3 2.170280D-O3 9.339572D-O5

20 5.543135D-O3 2.124218D-O3 4.543612O-O5

?l 4.485072D-O3 1.737412D-O3 2.830801D-05

22 3.474716D-O3 K305627D-O3 3.38O435D-O5

23 2.604693D-O3 9.4247O5O-O4 2.B1I5O8D-O5

DOM. RATIOUSED

0.0

0.0

0.0

6.8921150-01

6.8921I5D-01

DOM. RATIOESI I MATED

0.0

5.729916D-0I

6.892115D-0J

6.892115D-01

8.443129D-O1

6 .8921I5D-01 8.72O990D-O1

8.72O99OD-OI 8.72O990D-O1

8.7 2O99OD-OI 9.4108 500-01

8.72O990D-OI 9.445983D-O1

9.4.

3 9.445983D-01 9.649009i>-OI

1 9.649009R-O1 9.6490O9D-01

2 9.649009D-OI 9.B23 799D-O1

3 9.649009D-O1 9.7O5796D-O1

1 9.7O5796O-O1 9.7O5716D-nl

2 9.7O5796D-O1 9.883136D-O1

3 9.7O5796D-O1 9.71599 3D-O1

1 9.715993D-OI 9.7I5993D-O1

2 9.715993O-OI 9.898949D-O1

3 9.7I5993D-OI 9.714718D-0I

4 9.715993D-OI 9.69O72RO-O1

5 9.7I5993D-O1 9.6903680-01

K-EFFECT1VE

1.0O383097D+O0

1.014233I1DH1O

1 .017243840+00

1.01920138D+OO

I.O2122093D+OO

I.O2296576D+OO

I.O2403716D+O0

1.0247B580D+O0

1.02587017D+00

1.02654437D+O0

1.026B82230+O0

I.O2745274O+O0

1.027945^*^+00

1.O2811289D+OO

1.02835702D+O0

1.02B59504D+O0

1.02B68103D+O0

1.02B76923D+O0

1.02886263O+O0

I.O289O8O7D+O0

I.02893637D+O0

I.O2897O18D+OO

1 .02899829D+O0

D1F3D 4.0 7/83

OUTERI T . NO.

**** BENCHMARK PROBLEM 6 *'


• • IAEA 3D BENCHMARK 10 . CH MESH 1 / 1 7 / 8 4 1044 .900 PAGE 64

REAL SOLUTION K-EFF. PROBLEH

REL. POINTERROR

REL. SUMERROR

24 1.93 7O53O-O3 6.607192D-O4

25 1 .41 I882D-03 4.7b9696O-O4

26 9.602456D-04 3.5O9338D-O4

2 7 6.60?ROBn-O4 1.807-1 78/1-04

28 5.O9O272O-O4 2.340O0ID-O4

29 5.10B61S 50-04 2.410647D-O4

30 4.8 I9845D-O4 2,155923D-O4

31 4.476779D-04 I .8987B8D-04

32 4.472955D-O4 I.9O53B6D-04

33 3.86O226D-O4 I.7O7BO6D-O4

34 3.3656500-04 I.444J65D-04

35 2.9O5289O-O4 1.19O343D-O4

36 2.333374D-O4 9.5O5S540-05

37 1.86532BD-O4 7.59199.'.D-O5

38 I.4O2I65D-04 6.036084D-O5

39 1.O10335D-04 4.793465D-15

40 8.I3O474D-O5 3.8193840-05

41 6.432B67D-05 2.976832D-O5

42 4.754541D-05 2.34133OD-O5

43 3.5532I4D-O5 1.7267O4D-O5

44 2.655172D-O5 :.3O0379D-O'

45 1.836076D-O5 9.O43O78D-O6

46 1.348597D-O5 6.435247D-O6

47 1.O2B656D-O5 4.436357O-O6

4S 8.778839O-06 3.019638D-O6

EIGENVALUECHANGE

I.991767D-O5

I.31OO00D-O5

B.562595D-O6

5.6000650-1)6

3.640009D-06

2.8553O7D-O6

8.12B949O-O7

7.H23396D-O7

-I .4694850-07

7.51O760D-O7

B.173546D-O7

7.129103D-O7

5.25O085D-O7

3.52I4I2D-O7

2.1590310-07

1.020P97D-O7

2.I32365D-O8

-3.46699ID-08

-/.725147D-O8

-1.0O5624D-O7

-I.092027D-O7

-I.1O4239D-O7

-1.O328O8D-O7

-9.063790D-08

-7.653597D-OB

POLY. DOM. RATIOORDER 115EP

9.7159930-01

9.715993D-O1

9.7I5993D-O1

9.715993D-OI

9.7I7O33D-OI

9.717033D-OI

9.717O33D-O1

9.BL7233D-01

9.887233D-OI

9.887231D-O1

9.8B/233D-O1

9.887233D-O1

9.B87233D-O1

9.B87233D-OI

9.887233O-OI

9.887233D-01

•J.887233D-O1

9.887233D-OI

9.8B7233D-OI

9.887233D-OI

9.687233D-OI

9.8B7233D-OI

9.B87233D-OI

9.887233D-O1

9.8B7233D-OI

DOM. RATIO

LSTIMATED K-EFFECTIVE

9.692OO4D-01 1.02yO1821D*O0

9.699473D-01 1.029O3I31D+OO

9.706347D-O1 1.O2903987D+O0

9.717O33D-O1 1.029O4547D+O0

9.717O33D-O1 I.02904911D+O0

1.O15566D+OO I.O2905197D+O0

9.887233D-O1 1.02905278D+O0

9.887233D-OI 1.02905356D+O0

l.O0!790D*O0 1.029053421HO0

9.865745D-01 I.02905417D+00

9.843B49D-O1 1.02905499D+GO

9.846O99D-O1 1.O29O557OD+OO

9.849260D-O1 I.02905622O+O0

9.855I28D-OI I.02905658D+O0

9.B6O203D-OI 1.02.-05679D+OO

9.86442OD-OI 1.O2905689D+O0

9.868250D-01 1.O29O5692D*OO

9.87OOO9D-O1 1.02905688D+O0

9.872028D-O1 I.02905680D+O0

9.872144D-OI I.O2905670D+OO

9.872958RHDI 1.O2905659D+O0

9.672579D-OI 1.O290564BD+O0

9.872922D-OI I.O29O563BD+<IO

9,87'148D-O1 1.02905629D+OO

9.8735O1D-O) 1.029056210+00

G.2-5

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 2 **** 2D SNR BENCHMARK - RODS IN - NODAL


1/05/84 2222.600 PAGE 58

.1.O5OD+O7)

REGIONNO. NAME

ZONE ZONENO. NAME

1COCRBCRCFTOTALS

MlM2M3M5M6

VOLUME(CC)

1.43O43D+O31.52096D+031.95552D+032.17280D+021.08640D+02

INTEGRATION I) POWERWEIGHT FACTOR (WATTS)

1.00000D+001.00000D+001.O00OOD+OO1.00000D+001.00000D+00

5.23283D+O3 0.0

2.87O42D-O12.03857D-019.1O133D-030.00.05.000000-01

POWER DENSITY PEAK DENSITY PEAK TO AVG. POWER(WATTS/CC) (WATTS/CCX2) POWER DENSITY FRACTION

2.00668D-041.34032D-044.65419D-O6

o.o0.09.55506D-05

2.69358D-042.26678D-O41.82823D-O50.00.02.69358D-04

1.34230D+O01.69123D+O03.92814D+O00.00.02.819O1D+O0

5.74O83D-014.O7714D-O11.82O27D-O20.0

o.c1.00000D+00

AREANO.

123

AREANAME

TCORETRODTOTAL

VOLUME(CC)

2 . 9 5 1 3 9 D + O 33.25920D+025.23283D+03


0.00.00.0

POWER(WATTS)

4.90899D-010.05.O0000D-01


1.66328D-O40.09.555O6D-O5

PEAK DENSITY PEAK TO AVG.(WATTS/CCX2) POWER DENSITY

2.69358D-O40.02.69358D-O4

1.61944D+000.02.81901D+O0

POWERFRACTION

9.81797D-O10.0l.OOOOOD+00

( 1 ) INTEGRATION WEIGHT FACTOR - ( ? / B ) * S I N ( B * H ) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT

REGIONNO. NAME

! 1C2 OC3 RB4 CR 5

CF 6TOTALS

ZONE ZONENO. NAME

1 Ml2 M23 M3

M5M6

PEAK INDEX•X,

1.00000D+006.00000D+008.00000D+000.00.01.00000D+00

PEAK INDEX•Y,

1.00000D+001.00000D+001.00000D+000.00.01.00000D+OO

PEAK INDEX'Z'

1.00000D+001.00000D+001.00000D+000.00.01.00000D+O0

AREA AREANO. NAME


PEAK INDEX'X,

1.00000D+000.01.00000D+00

PEAK INDEX

1.00000D+000.0l.OOOOODfOO

PEAK INDEX•z,

l.OOOOOD+000.0l.OOOOOD+00

DIF3D 4.0 7/83 **** SAMPLE PROBLEM 2 **** 2D SNR BENCHMARK - RODS IN - NODAL 1/05/84 2222.600 PAGE 59

MAXIMUM TOTAL FLUX 3.53887D+09 OCCURS AT: RING NO. 1POSITION NO. 1SURFACE NO. 0

Z-COORDINATE - 0.0

G.6-3

DIF3D 4.0 7/83 **** BENCHMARK PROBLEM 6 **** IAEA 3D BENCHMARK 10. CM MESH


K-EFFECT1VE - 1.O29O5621257


DOMINANCE RATIO (S1GBAR) - 9.873501094068D-01

1/17/84 1044.900 PAGE 65

GROUPNO.1

OPTIMUMOMEGA

1.165650+00

OPTIMIZED OVER-RELAXATION FACTORSGROUP OPTIMUM GROUP OPTIMUMNO. OMEGA NO. OMEGA

2 1.08039D+00

GROUPNO.

OPTIMUMOMEGA

GROUPNO.

OPTIMUMOMEGA

MAXIMUM POWER DENSITY 4.29119D-07 OCCURS AT MESH CELL (I.J.K) - ( 4, 3, 18)


DIF3D 4.0 7/83 **** BENCHMARK PROBLEM 6 **** IAEA 3D BENCHMARK 10. CM MESH


1/17/84 1046.300 PAGE 66

,1.000D+07)

REGIONNO. NAME

ZONE ZONENO. NAME

VOLUME( C O


POWER(WATTS)

POWER DENSITY PEAK DENSITY PEAK TO AVG. POWER(WATTS/CC) (WATTS/CCX2) POWER DENSITY FRACTION

RREFLRFUEL1RFUEL2RFUE2RRREFLRBACKGRTOTALS

4 CREFL1 CFUEll2 CFUEL23 CFUE2R5 CREFLR6 CBACKG

3.11400D+O61.9O4OOD+O63.776O0D+O63.38000D+052.60000D-KI41.824O0D+061.09820D+07

1.00000D+00l.OOOOOD+001.00000D+00l.OOOOOD+00l.OOOOOD+00l.OOOOOD+000.0

0.02.06648D-017.64862D-012.84906D-020.00.0l.OOOOOD+00

0.01.O8534D-O72.O2559D-O78.42918D-080.00.09.10581D-08

0.03.45221D-074.29119D-O72.77697D-070.00.04.29119D-07

0.03.18O78D+O02.11849D+003.29447D+000.00.04.71258D+00

0.02.06648D-017.64862D-012.84906D-020.00.0l.OOOOOD+00

AREA AREANO. NAME

1 TFUEL

VOLUME INTEGRATION 1) POWER POWER DENSITY(CC) WEIGHT FACTOR (WATTS) (WATTS/CC)

5.68000D+06 0.0 9.715O9D-01 1.71O4OD-O7

PEAK DENSITY PEAK TO AVG. POWER(WATTS/CCH2) POWER DENSITY FRACTION4.29119D-07 2.50887D+00 9.71509D-01

(1) INTEGRATION WEIGHT FACTOR - (2/B)*SIN(B*H) H-UNEXTRAPOLATED HALF HEIGHT, B-BUCKLING COEFFICIENT(2) THE PEAX POWER DENSITY IS CALCULATED BY SAMPLING THE AVERAGE FLUX ON THE CELL SURFACES AND WITHIN THE CELL.

REGIONNO. NAME

ZONE ZONENO. NAME

PEAK INDEX•X ,

PEAK INDEX

•rPEAK INDEX

•Z'

1 RREFL2 RFUEL13 RFUEL24 RFUE2R5 RREFLR6 BACKGR

TOTALS

4 CREFL1 CFUEL12 CFUEL23 CFIJE2R5 CREFLR6 CBACKG

0.01.30000D+014.00000D+00l.OOOOOD+000.00.04.00000D+00

0.06.00000D+003.00000D+O0l.OOOOOD+000.00.03.00000D+00

0.01.80000D+011.80000D+0]1.80000D+010.00.01.80000D+01

AREA AREANO. NAME

PEAK INDEX'X,

PEAK INDEXlyt

PEAK INDEX POWER DENSITY PEAK TO AVG.•Z, AXIAL (3) P.D. AXIAL (3)

1 TFIIEL 4.00000D+00 3.00000D+00 1.80000D+01 2.64605D-07 1.62174D+O0

(3) DERIVED FROM DATA IN THE AXIAL COLUMN OF MESH CELLS THAT INTERSECTS THE REACTOR PEAK POWER DENSITY LOCATION

Distribution for ANL-82-64

Internal:

C. B. AdamsC. L. BeckE. S. BeckjordJ. C. BeitelS. K. BhattacharyyaH. BigelowR. N. BlomquistM. M. BretscherS. B. BrumbachJ. E. CahalanS. G. CarpenterB. R. ChandlerY. I. ChangP. J. CollinsR. J. CorneliaD. C. CutforthT. A. DalyJ. °.. DeenK. L. Derstine (10)D. R. FergusonK. E. FreeseE. K. FujitaP. J. GarnerJ. M. GasidloE. M. GelbardG. L. GrasseschiG. M. GreenmanH. HenrysonR. Hosteny

External.

H. H. HummelR. N. HwangR. E. KaiserH. KhalilT. KraftR. D. LawrenceW. K. LehtoR. M. LellL. G. LeSageJ. R. LiawM. J. LineberryD. J. MalloyJ. E. MatosH. F. McFarlaneR. D. McKnightD. MeneghettiL. E. MeyerF. MoszurA. OlsonY. OrechwaE. M. PenningtonP. J. PersianiP. A. PizzicaR. B. PondJ. R. RossR. R. RudolphG. K. RuschR. W. SchaeferJ. E. Schofield

D. ShaftmanD. M. SmithK. S. SmithJ. L. SnelgroveC. G. StenbergW. J. SturmS. F. SuB. J. ToppelA. TravelliR. B. TurskiA. J. UlrichR. VilimD. C. WadeD. P. WeberW. L. WoodruffS. T. YangB. S. YarlagaddaANL Patent Dept.ANL Contract FileANL Libraries (2)TIS Files (6)AP Division File (10)

DOE-TIC, for distribution per UC-79d (117)Manager, Chicago Operations Office, DOEDirector, Technology Management, DOE-CHDirector, DOE-BRP (2)Applied Physics Division Review Committee:

l>. W. Dickson, Jr., Clinch River Breeder Reactor Project, Oak RidgeW. E. Kastenberg, University of CaliforniaK. D. Lathrop, Los Alamos National LaboratoryN. J. McCormick, University of WashingtonD. A. Meneley, Ontario HydroJ. E. Meyer, Massachusetts Inst. TechnologyA. E. Wilson, Idaho State University

H. Alter, Office of Breeder Technology, DOEAdvanced Reactor Library, Westinghouse Electric Co., Madison, PaM. Becker, Rensselaer Polytechnic Inst.R. A. Bennett, Wer L i.nghouse Hanford Co.F. W. Brinkley, Los Alamos National LaboratoryS. P. Congdon, General Electric Co.

C. Cowan, General Electric Co.H. L. Dodds, Technology for Energy Corp.R. Doncals, Westinghouse Electric Corp.J. J. Doming, University of IllinoisM. J. Driscoll, MITC. Durston, Combustion EngineeringR. Ehrlich, General Electric Co.H. Farrar IV, Atomics InternationalFast Breeder Dept. Library, General Electric Co.Y. C. Feng, General Electric Co., San JoseG. F. Flanagan, Oak Ridge National LaboratoryN. M. Greene, Oak Ridge National LaboratoryD. R. Harris, Rensselaer Polytechnic Inst.A. Hartman, General Electric Co., SunnyvaleP. B. Hemmig, Reactor Development and Demonstration, DOEA. F. Henry, MITJ. Kallfelz, Georgia Institute of TechnologyR. Karam, Georgia Institute of TechnologyW. Y. Kato, Brookhaven National LaboratoryR. J. LaBauve, Los Alamos National LaboratoryJ. Lewellen, Reactor Development and Demonstration, DOEE. E. Lewis, Northwestern UniversityM. D. Libby, NUSCOR. MacFarlane, Los Alamos National LaboratoryF. C. Maienschein, Oak Ridge National LaboratoryD. R. Marr, Los Alamos National LaboratoryD. R. Mathews, GA TechnologiesD. R. McCoy, Los Alamos National Laboratory (3)H. A. Morowitz, Tarzana, CAD. Moses, Oak Ridge National LaboratoryJ. Naser, Electric Power Research Inst.National Energy Software Center, ANL (10)R. J. Neuhold, Reactor Development and Demonstration, DOER. D. O'Dell, Los Alamos National LaboratoryD. Okrent, University of CaliforniaK. Ott, Purdue University0. Ozer, Electric Power Research Inst.A. M. Perry, Oak Ridge National LaboratoryC. Porter, Westinghouse Electric Corp.J. Prabulos, Combustion EngineeringR. Protsik, General Electric Co.A. B. Reynolds, University of VirginiaW. A. Rhoades, Oak Ridge National LaboratoryP. Rose, Brookhaven National LaboratoryD. H. Roy, Babcock and Wilcox Co.R. Schenter, Westinghouse Hanford Co.P. Soran, Los Alamos National LaboratoryE. R. Specht, Atomics InternationalS. Stewart, General Electric, Co.L. E. Strawbridge, Westinghouse Electric Corp.R. J. Tuttle, Atomics InternationalD. R. Vondy, Oak Ridge National LaboratoryJ. E. Vossahlik, GRP Consulting, Inc.C. WeisWn, Oak Ridge National LaboratoryJ. White, University of Lowell

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