Final Meeting held in conjunction with M&C-2009 The Saratoga …€¦ · - Participants submit...

NEA/NSC/DOC(2009)8

1

OECD Nuclear Energy Agency

"Benchmarking the Accuracy of Solution of 3-Dimensional Transport Codes and Methods

over a Range in Parameter Space"

Final Meeting held in conjunction with M&C-2009 The Saratoga Hilton Hotel

Saratoga Springs, New York

Room: Broadway 1

6 May 2009, 6:30 to 8:30 pm

Chair: Prof. Yousry Azmy

Summary

1. Welcome, Introduction of participants

Yousry Azmy welcomed participants to this last meeting, aiming at presenting the

most recent results, some of which had been presented also at the M&C-2009

conference sessions, and to decide the next steps to complete the benchmark work and

publish it.

The meeting was attended by 14 participants, who introduced themselves (see Annex).

2. Status of benchmark

a. New reference solution

Kursat B. Bekar presented the “Reference Solution Set for the NEA Suite of

Benchmarks for 3 D Transport Methods and Codes over a Range in Parameter Space”.

First the preliminary MCNP reference solution set was presented obtained with 2 billion

particle histories. Of the 729 different configurations (each having 23 different quantities)

computed by MCNP5 (with multi-group option, 1 group calculation) and using no biasing,

72 quantities were not computed (0-tally scoring for some benchmark quantities for some

benchmark cases), more than 500 quantities have a statistical error larger than 5 % (poor

statistics for many cases), 159 cases have unreliable results.

An improved MCNP reference solution set using ADVANTG/MCNP5 with FW-CADIS

(John C. Wagner, Radiation Transport & Criticality Group, ORNL) was produced.

ADVANTG uses TORT driven cell-averaged scalar flux distributions to generate Monte

Carlo weight windows parameters by implementing FW-CADIS methodology. Then,

MCNP5 computes the benchmark quantities for all benchmark cases using the generated

weight windows parameters. With this procedure the new reference solution set was

produced. The use of ADVANTG/MCNP5 code sequence improved the reference solution

NEA/NSC/DOC(2009)8

2

set. In fact this removed the 0-tally scoring problem, and reduced the statistical errors for

most quantities that had unreliable values without variance reduction.

An additional effort to obtain the reference solution set had been provided by Alan P.

Copestake, Rolls-Royce plc, using MCBEND results for a few sample cases. For these

cases MCBEND and ADVANTG/MCNP results are consistent with each other for most

quantities for these sample cases. Some quantities (e.g. 2.e,…,2.h) with net leakage across

internal faces show larger discrepancies between the two codes. In fact, the leakage term

was not calculated in the same way as with MCNP5. These cases will be recalculated and

resubmitted.

In conclusion the latest reference solution set computed by ADVANTG/MCNP is

more reliable than the preliminary reference solution set. This set can be used by the

participants to evaluate the solution of their 3D deterministic code to this benchmark.

b. Results from participants

Presentations from some participants followed

- Yi Ce presented the results obtained with TITAN,

- Nicolas Martin presented the results obtained with DRAGON,

- Armin Seubert presented a TORT solution using very strict convergence criteria (10–7

),

- Dave Barrett presented orally his results.

3. Publication of Benchmark report

The results will be published in a special issue of Progress in Nuclear Energy (PNE)

within a year or so. Enrico Sartori will distribute a form to participants for them to provide the

relevant information on the code used, including, name, references, method used, assumptions

made in the calculations and convergence criteria used. A synthesis of this will be added as an

Appendix to the summary report.

A report to be published by OECD/NEA summarizing the benchmark and the results

obtained, including conclusions, recommendations and lessons learned, will be prepared. The

benchmark specification, the reference solutions and the results provided by the participants

will be „packaged‟ at the NEA Data Bank for distribution to participants and to others who

wish to use the benchmark for testing their codes or to learn how to solve difficult cases.

The PNE issue will contain

1. The description of the benchmark and the synthesis of the results.

2. The reference solutions.

3. The individual solutions compared with reference solutions. This part will

consist of individual articles written by participants describing in detail the

methodology used and assumptions made.

NEA/NSC/DOC(2009)8

3

a. Schedule

- Y. Azmy sends out an e-mail asking participants to vote on how they wish the data

to be presented and condensed, norms to be used for absolute and relative errors,

RMS? Issues of monotonicity etc. (week of 11 May 2009)

- Participants indicate their preferences (by 21 May 2009). In case of lack of

consensus, the chairman will make the choice.

- Participants submit their paper for PNE by September 1st 2009.

- Participants submit their final results by September 1st 2009 to Kursat Bekar.

- A copy of the collected files will be submitted to the NEA Data Bank by Kursat

Bekar for „packaging‟ and distribution. Distribution will be done also by RSICC.

4. Proposal for Further Benchmarks

It was proposed to continue this activity by proposing new benchmarks. One proposal was made

by David Barrett, entitled “Benchmark to Assess the Accuracy of the Various Methods Used by

Transport Codes to Model Material Interfaces”. Transport codes use many different spatial meshing or

grid generation techniques. When faced with a configuration with curved interfaces between distinct

materials codes may model these interfaces using different approximations. The idea behind this

benchmark proposal is to provide a single test problem that quantifies and qualifies the effects of the

different approximations. A Monte Carlo based „reference solution‟ would be used as a reference

solution. This proposal will be submitted at the forthcoming OECD/NEA Data Bank meeting. A draft

version of the specification will be distributed to potential participants for comments. A final version

and a schedule for completing the benchmark will be provided. Results could be presented at the

M&C-2011 conference.

NEA/NSC/DOC(2009)8

4

Annex

List of participants

CANADA

MARLEAU, Guy Tel: +1 514 340 4711 ext 4204

Institut de genie nucleaire Fax: +1 514 340 4192

Ecole Polytechnique de Montreal Eml: [email protected]

Case Postale 6079

succ. Centre-Ville

MONTREAL, QUEBEC H3C 3A7

MARTIN, Nicolas Tel: +1 514 340 4192

Ecole Polytechnique de Montreal Fax:

Institut de Genie Nucleaire Eml: [email protected]

PO Box 6079, Station Centre-Ville

2900 boul. Edouard-Montpetit

Montreal H3T 1J4

GERMANY

SEUBERT, Armin Tel: +49 89 32004 469

Gesellschaft fuer Anlagen- Fax: +49 89 32004 10599

und Reaktorsicherheit (GRS) mbH Eml: [email protected]

Forschungsinstitute

D-85748 GARCHING b. Muenchen

UNITED KINGDOM

BARRETT, David Tel: +44 118 9826398

AWE Aldermaston Fax: +44 118 9824820

Building E3 Eml: [email protected]

READING RG7 4PR

COPESTAKE, Alan Tel: +44 1 332 667124

Rolls Royce Marine Power Fax +44 1 332 622 939

P.O. Box 2000 Eml: [email protected]

Derby DE21 7XX

SMEDLEY-STEVENSON, Richard P. Tel: +44 1 18 9824173

AWE Aldermaston Fax: +44 1 18 9824820

Building E3.1, Room 206 Eml:[email protected]

READING, RG7 4PR

UNITED STATES OF AMERICA

AZMY, Yousry Tel: +1 919 515 3385

Head, Department of Nuclear Engineering Fax: +1 919 515 5115

North Carolina State University Eml: [email protected]

Campus Box 7909

1110 Burlington Laboratories

Raleigh, NC, 27695-7909

BEKAR, Kursat B. Tel: +1 865 241 2437

OAK RIDGE NATIONAL LABORATORY Fax: +1 865 576 3513

PO Box 2008 MS6170 Eml: [email protected]

OAK RIDGE TN 37831-6170

DAHL, Jon A. Tel: +1 505 665 3972

Los Alamos National Laboratory Fax: +1 505 665 5538

LOS ALAMOS, NM 87544 Eml: [email protected]

HAGHIGHAT, Alireza Tel: +1 352 392 1401 x306

Nuclear and Radiological Engineering Fax: +1 352 392 3380

202 Nuclear Sciences Building Eml: [email protected]

University of Florida

Gainesville, FL 32611

NEA/NSC/DOC(2009)8

5

KIRK, Bernadette L. Tel: +1 865 574 6176

Director Fax: +1 8652414046

RSICC/ORNL Eml: [email protected]

PO Box 2008

Bldg. 5700, MS 6171

Oak Ridge, TN 37831-6171

ROSA, Massimiliano Tel: +1 505 667 0869

Computational Physics (CCS-2) Fax: +1 505 665 4972

Los Alamos National Laboratory Eml: [email protected]

P.O. Box 1663, MS K784

Los Alamos, NM 87545

YI, Ce Tel:

Nuclear and Radiological Engineering Fax:

202 Nuclear Sciences Building Eml: [email protected]

University of Florida

Gainesville, FL 32608

International Organisations

SARTORI, Enrico Tel: +33 1 45 24 10 72 / 78

OECD/NEA Data Bank Fax: +33 1 45 24 11 10 / 28

Le Seine-Saint Germain Eml: [email protected]

12 boulevard des Iles

F-92130 Issy-les-Moulineaux

France

Kursat B. Bekar Radiation Transport & Criticality Group

Oak Ridge National Laboratory

Yousry Y. Azmy Department of Nuclear Engineering

North Carolina State University

M&C 2009, Saratoga Springs, NY May 6, 2009

2 Managed by UT-Battelle for the Department of Energy

Preliminary TORT Solutions

•  4 level model refinement,

  Uniform mesh in each dimension, 40,80,120 and 160

  Initially started with fully-symmetric quadrature sets

  Square Legendre-Chebyshev Quadratures (S10, S14,

S18, S20)

  Angular quadrature rising order concurrent with the

mesh refinement

  θ-weighted method


Preliminary TORT Solutions

•  4 level model refinement,   At the earlier blind stage, three coarser model were

compared to the finest model to test asymptoticity of the solutions

  After obtaining “Reference solution set”, all four

models compared to the reference solutions   For most quantities for most cases accurate TORT solutions

  For some cases iteration convergence problem

  For some cases TORT failed

  Possible reason ray effects, not using cubic mesh, using SP TORT

  Problems in the reference solution set (0-tallies, significant

relative errors)


Improved TORT Solutions

•  Primary ray effects to mitigate by defining a computational sequence with GRTUNCLD (first

collision source generator)

•  Re-meshing to obtain unit cubic meshes to resolve TORT failures

•  64-bit arithmetic operations DP TORT and DP GRTUNCL3D


Improved TORT Solutions

•  A TORT solution set was obtained for the benchmark

cases with γ=0.9 (small source region, small flux sub-volumes

•  TORT Solutions to the benchmark cases γ=0.5 has not obtained yet

•  For most cases, primary ray effects was reduced TORT results were improved

•  Some benchmark quantities for some benchmark cases still has problem (large discrepancies when comparing to

the reference solution)


Conclusions

•  For most cases, TORT computes the benchmark

quantities accurately

•  For most cases, TORT solutions are in the asymptotic

regime


Thank You!

Questions


Error Calculations

•  Root Mean Square(RMS) of Errors:

•  Error in RMS calculation (propagated by the error in MCNP reference results)

•  Absolute and Relative Errors, (i=1,..,729)

€

RMS = (AE i)2i=1

729

∑ /729

€

σRMS =1/RMS × [ ((σmcnpi

i=1

729

∑ )2 × AE i)]1/ 2

€

AE i = Rmcnpi − RTORT

i

€

RE i = AE i /Rmcnpi

Kursat B. Bekar Radiation Transport & Criticality Group

Oak Ridge National Laboratory

Yousry Y. Azmy Department of Nuclear Engineering

North Carolina State University

M&C 2009, Saratoga Springs, NY May 4, 2009


Outline •  Overview of the Benchmark

  Description of Benchmark Problems

  Suite Specification

  Benchmark Quantities

  Reference Solutions

•  TORT Models and Preliminary Solutions

•  Improved TORT Solutions

•  Conclusions


Overview of the Benchmark •  The participants are required to illustrate their

software’s performance in view of the following three criteria:

  Dependence of conclusions for given method/code on specifics of benchmark configuration → suite of benchmarks

  Dependence of method/code accuracy on model refinement level → verify that reported solution is in asymptotic regime

  Dependence of code/algorithm performance on optional settings → report all deviations from default/standard options


Description of Benchmark Problems

•  Outer/inner parallelepiped index 1/2:   Square base, γ-scaled   Vacuum BCs   Scattering ratios: c1 & c2

•  Unit source

)0,0,0(‏

1

L

1

γ L

γ

γ

y x

z

)0,0,0(‏

x

z

(0,0,0) (0,0,0)


Suite Specification and Sample Geometries

•  Suite constructed by independently varying 6 parameters (comprised of a total of 36 = 729 cases)

1.0 0.8 0.5 c2

5.0 1.0 0.1 σ2

1.0 0.8 0.5 c1

5.0 1.0 0.1 σ1

0.9 0.5 0.1 γ 5.0 1.0 0.1 L

Range Parameter

L=0.1, γ=0.5 L=1.0, γ=0.9 L=5.0, γ=0.1

Inner region (green)

Outer region (gray/blue)

Source region (yellow)


Benchmark Quantities •  Set of 23 Benchmark quantities per configuration:

  Region-averaged scalar flux: Over regions 1 & 2   Net leakage out of 4 internal & 4 external faces   Scalar flux averaged over 13 sub volumes

3.a 3.b 3.g 3.h 3.i

Sub volume (red)


Reference Solutions •  Preliminary reference solutions computed by MCNP5

  No biasing, NPS = 109 & NPS = 2 x 109   0-tally scoring for some benchmark quantities for some

benchmark cases   Poor statistics for many cases

  With NPS = 1011 (no-biasing) → still 0-tallies for some of the benchmark cases

•  Improved reference solutions computed by ADVANTG/MCNP

  FW-CADIS methodology

  TORT driven cell-averaged fluxes → generates MC mesh-based WW parameters

  No 0-tallies, (NPS = 107 & NPS = 108 ), poor statistics for few cases

  Will be presented in detail soon.


TORT Models and Preliminary Solutions •  Four Computational Models;

  Uniform mesh: I x I x I, with I = 40, 80, 120, 160   refinement order 1,2,3 and 4   64 thousands to ~ 4.1 million cells)

  Square Legendre-Chebychev (SLC) angular quadrature:   Number of non-zero-weight angles 200, 392, 648, 800

  Angular quadrature rising order concurrent with the mesh refinement

  θ - weighted method (θ = 0.9), 10–4 convergence criterion, 100 inners

•  Started as a blind study, then compared to the provided MCNP reference results   Some cases (oblique cells) converged only to 2× 10–3

  Solutions of most cases in the suite of benchmark in the asymptotic regime


Sample Quantities

Benchmark quantity 1.a

(Region-averaged scalar flux for region 1)

Benchmark quantity 2.e

(Net-leakage, internal face, bottom)

€


i

€

RE i = AE i /Rmcnpi



Sample Quantities

Quantity 3.a

(Volume averaged scalar flux)

Quantity 3.i (Volume averaged scalar flux)


Problems Reported for the Preliminary Tort Solutions

•  When the aspect ratio is different from 1, some cases failed for some of the benchmark quantities

•  Iterative convergence problems

•  Produced errors that do not decrease monotonically with model refinement


Methodology to Mitigate ray effects

•  Using the standard approach: split the solution to the

transport equation into an uncollided and fully collided

flux

•  GRTUNCL3D

  Generates uncollided fluxes (semi analytic method) and first

collision source

  Does not compute the uncollided fluxes at the cell boundaries

(8 benchmark quantities, 2.a,…,2.h cannot be computed)

  Latest GRTUNCL3D was modified to compute the uncollided

flux at the cell boundaries


GTort Computation Sequence


GTort Solution for a Sample Case

Coarsest model (40x40x40, SLC-10) for L=5.0, γ=0.9

•  GTORT sequence

mitigates the primary ray effects

in the solutions

•  It's semi-analytic methodology is

poor in the source region


MGTort Computation Sequence •  GRTUNCL3D produces unacceptable results due to its inability to

accurately perform ray-tracing within a source cell


Improved TORT Solutions (40x40x40, SLC-10)‏


TORT Solutions with MGTORT Computational Sequence

Coarsest model (40x40x40, SLC-10)


TORT Solutions with MGTORT Computational Sequence

Benchmark Quantity 3.e for Four Models


Resolving Convergence Problem

•  Modify the mesh so as to use cubic cells (unit aspect ratio)

 Non-linear θ-weighted method works well if the cell aspect ratio is

close to 1

 Using 400x400x40, 40x40x40, and 40x40x200 mesh structures (cubic

cells) for the benchmark cases L=0.1, 1.0, and, 5.0 solved the

convergence problem for straight TORT calculations (except five cases

for L=5.0)

 Did not help for the calculation performed by MGTORT sequence.

Why?


TORT Convergence Problem in MGTORT Sequence

•  Convergence problem becomes evident for the TORT calculations in MGTORT sequence

  Dominant part of the flux is uncollided flux   The collided flux comprises too small numbers

•  Using cubic cells is not always a realistic option   The finest computational model needs an extremely large amount of memory and disk space (for both TORT and GRTUNCL3D)

•  Solution: Using 64-bit arithmetic operations in MGTORT sequence

  Longer computation time and almost 2 times larger disk/memory space requirement   All cases converged


Change in Convergence Rate for Two TORT Executables

€

L = 5.0,γ = 0.5,σ1,2 = 5.0,c1 = 0.5,c2 =1.0


Execution Times for Two TORT Executables

Calculations with Model-2 for all benchmark cases


Conclusion •  Solutions for most cases in the suite of benchmarks as

computed by TORT are reasonably accurate

•  Generating the first collision source and supplying this source to drive the TORT calculations of the fully collided flux yields more accurate results

•  Introducing double-precision versions of TORT and GRTUNCL3D completely resolved the convergence problem

•  Improved TORT solutions and ADVANTG/MCNP reference results are in good agreement except some cases;

  MGTORT sequence only mitigates the primary ray effects

  Secondary ray effects evident for some cases.


Thank You!

Questions


Error Calculations

•  Root Mean Square(RMS) of Errors:

•  Error in RMS calculation (propagated by the error in MCNP reference results)


€

RMS = (AE i)2i=1

729

∑ /729

€

σRMS =1/RMS × [ ((σmcnpi

i=1

729

∑ )2 × AE i)]1/ 2

€


i

€

RE i = AE i /Rmcnpi

1

Preliminary TORT Results on the

3-D Transport Accuracy Benchmark over a Range in

Parameter Space

A. Seubert

Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH

Forschungsinstitute

D-85748 Garching

M&C 2009 – 6 May 2009

TORT calculation details Considered cases model refinement:

Equal mesh sizes in each spatial dimension

Chebychev-Legendre quadrature

– Number of ordinates with non-zero weights: 4608 for S48,12800 for S80

80x80x80-S48 calculation: 512.000 spatial meshes

– Taken as preliminary reference for model refinement studies until S80 calculationhas finished

Convergence criteria (TORT-64):

– Fission rate pointwise: 5.010-7

– Flux pointwise: 1.010-7

2

nx = ny = nz S8 S16 S32 S48 S80

40

80 (ref.) ()

120

160

3

Geometrical configurations L = 0.1 cm

= 0.1 = 0.5 = 0.9

outer parallelepiped

inner parallelepiped

source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

4


= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

5


= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

3.a

3.b 3.j 3.k

3.f

3.e

3.l 3.m 3.c

3.d

3.g 3.h 3.i

General findings

6

Items = 0.1 = 0.5 = 0.9

1 reasonable reasonable reasonable

2 reasonable reasonable reasonable

3 reasonable c-f, h, i, k c-f, h-i

Items = 0.1 = 0.5 = 0.9

1 very good very good good

2 very good very good good

3 very good very good e-h

Items = 0.1 = 0.5 = 0.9

1 good good good

2 good good reasonable

3 good good d-i

L = 0.1cm

L = 1.0cm

L = 5.0cm

7

TORT 80x80x80 S48 Item 1.a



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1

8

TORT 80x80x80 S48 Item 2.a



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1

Dependence on model refinement: Quadrature order

9

Items 1.a-b Items 2.a-h

Items 3.a-f Items 3.g-m

Dependence on model refinement: Spatial meshing

Dependence on angular refinement more pronounced than on spatial refinement 10

Items 1.a-b Items 2.a-h

Items 3.a-f Items 3.g-m

11

TORT 80x80x80 S48 Item 3.c



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1

12

TORT 80x80x80 S48 Item 3.e



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1

= 0.9 = 0.5 = 0.1

13

TORT 80x80x80 S48 Item 3.i



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1

= 0.9 = 0.5 = 0.1

= 0.9 = 0.5 = 0.1

14

MCNP Item 3.i Errors



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m



source volume

3.a

3.b

3.c

3.d

3.e

3.f

3.g

3.h

3.i

3.j

3.k

3.l

3.m

= 0.1 = 0.5 = 0.9

L = 0.1 cm L = 1.0 cm L = 5.0 cm

= 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1 = 0.9 = 0.5 = 0.1

Dependence on inner parallelepiped material properties

Consider item 3.i for the case with L = 5.0 cm, = 0.9, 1 = 0.1 cm-1

15

c1 = 0.5 c1 = 0.8 c1 = 1.0

Dependence on inner parallelepiped material properties

Consider item 3.i for the case with L = 5.0 cm, = 0.9, 1 = 1.0 cm-1

16

c1 = 0.5 c1 = 0.8 c1 = 1.0

DRAGON solutions to the 3D transportbenchmark over a range in parameter

spaceNicolas Martin, Alain Hebert, Guy Marleau

Institut de Genie Nucleaire

Ecole Polytechnique de Montreal

3D Transport Benchmark meeting, M&C 2009 DRAGON solutions to the 3D transport benchmark over a range in parameter space – 1/10

Status of DRAGON results 1

Comparative study of MoC and SN solutions to be published inANE.

Results are displayed using the methodology proposed byBekar and Azmy:

The average relative error by region for all the 729 cases.The RMS error per quantity (with propapaged MCNPuncertainty.

Results are encouraging, relative errors seem to be similar tothose of TORT results (as published in ANE paper by Bekarand Azmy).


Computational models 1

Spatial discretization:

Basic mesh is[

0, 1−γ4 , 1−γ

2 , 12 , 1+γ

2 , 3+γ4 , 1

]

and for the z axis,[

0,L(1−γ)

4 ,L(1−γ)

2 , L2 ,

L(1+γ)2 ,

L(3+γ)4 , L

]

.

Relies on the optical thickness of the medias, i.e., refined by1

N × Σi

, N = {2, 3, 4}.

Angular quadrature:

Fully symmetric, Legendre Chebyshev and Quadruple rangequadratures were tested.

For the MoC calculations : 500 tracks cm−2.


SN computational model 1

1.1

2 × Σi

discretization (maximum of 22400 regions), S16 fully

symmetric quadrature,

2.1

3 × Σi


symmetric quadrature,

3.1

4 × Σi


symmetric quadrature.

2 additional runs performed to test different angular quadratures:

N = 2 and S44 Pn − Tn quadrature,

N = 2 and S54 QRn (Quadruple Range) quadrature.

Parabolic Diamond Differencing scheme by default: 32moments of the flux per computational cell.


MoC computational model 1

1 A discretization of the geometry by a factor of1

2 × Σi

with track

density of 5 × 102 integration lines in cm−2, and an angular

quadrature of type Pn-Tn with n=16.


3 × Σi

with a

track density of 5 × 102 integration lines in cm−2, and an

angular quadrature of type Pn-Tn with n=24.


4 × Σi

with a

track density of 1 × 103 integration lines in cm−2, and an

angular quadrature of type Pn-Tn with n=32.


SN relative error 1

Benchmark quantity 1.a Benchmark quantity 1.b

Benchmark quantity 3.a Benchmark quantity 3.m3D Transport Benchmark meeting, M&C 2009 DRAGON solutions to the 3D transport benchmark over a range in parameter space – 6/10

MoC relative error 1



SN RMS error 1



MoC RMS error 1



Conclusions 1

MoC and SN results exhibit similar behavior

Scalar fluxes for sub volumes close to the source aregenerally well computed.Relative errors grow when the sub volume dimension isreduced and when the distance from the source isimportant in term of mean free path.

Difficult for both methods to obtain spatially uniformconvergence

Model refinement fails for some sub regions.

A possible solution can be the use of ξ - biased angularquadratures.

Use of 64-bit arithmetic precision to encompass memorylimitations.


C. Yi and A. Haghighat

Accuracy of TITAN Based on a New OECD-NEA

Benchmark over a Range in Parameter Space

ANS M&C 2009

Contents

Description of the TITAN code1

g Introduction on Benchmark2

Calculation results and Comparison3

Conclusions4

Hybrid approach

Hybrid Discrete Ordinate and Characteristics Method

- Discrete Ordinates (Sn)

Method in regular regions

- Characteristics method in

low-scattering regions

Benefit:

To solve problems that

contain regions of low-

scattering materials more

efficiently

Coarse-mesh-oriented approach

Sn or characteristics solver

can be assigned to different

coarse meshes

TITAN code

1. Written from scratch in Fortran 90 with some features

in Fortran 2003 features.

2. object oriented programming, dynamic memory

allocation, and layered code structure

3. Benchmarked on a number of problems:

a) C5G7 MOX problem

b) Kobayashi problems

c) SPECT and CT models

TITAN Deterministic Code

Characteristic Solver

Hybrid Approach Localized meshing

and quadrature set

Coarse Mesh-oriented Paradigm

Sn Solver

High computational Efficiency

TITAN

Benchmarking the Accuracy of Solution of 3-D

Transport Codes and Methods over a Range in

Parameter Space

“The geometric configuration and xs

data are intentionally simple and

unsophisticated to avoid diverting the

participants’ attention and efforts

toward modeling details”

•Number of cases : 729

•Calculating targets

•Pure scattering

Easy points:

Hard points:

Benchmark Geometry

Parameter Range

L 0.1 1.0 5.0

γ 0.1 0.5 0.9

σ1 0.1 1.0 5.0

c1 0.5 0.8 1.0

σ2 0.1 1.0 5.0

c2 0.5 0.8 1.0

Total cases: 36=729

Case Numbering: 111111 to 333333

e.g. Case 123123 will be:

L=0.1, γ=0.5 σ1=5.0

c1=0.5 σ2=1.0 c2=1.0

Calculating Targets

There are 23 benchmark

quantities to be calculated:

Set 1: Scalar fluxes in

material regions (2 values)

Set 2: Net leakages (8 values)

Set 3: Scalar fluxes in some

small boxes (13 values)

Most of the difficult values are in Set 3.

Reference solutions are provided with

the benchmark (MCNP)

TITAN model

3x3x3 coarse meshes

Fine meshing is automatically adjusted

case by case

A Python script to drive all the cases

Added subroutines to calculate required

quantities

Batch Run Quadrature Meshing

1 Serial S50 from 1,728 for Case 111111 to 22,400

for Case 333333

2 Parallel S60 from 5,832 for Case 111111 to 75,600

for Case 333333

S50 and S60 Quadrature Set

S50 Quadrature set:

~2500 directionS60 Quadrature set:

~3600 direction

Quantity 1.a -averaged flux in outside box

Second BatchFirst Batch

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

0 100 200 300 400 500 600 700 800

Quantity 2.a – net leakage at left boundary


-1.00%

-0.80%

-0.60%

-0.40%

-0.20%

0.00%

0.20%

0.40%

0.60%

0 100 200 300 400 500 600 700 800

3a

Quantity 3.a – Avg. Flux over part of the source box


-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0 100 200 300 400 500 600 700 800

Case 33333 quantities

0.20%

0.39%

0.78%

1.56%

3.13%

6.25%

12.50%

25.00%

50.00%

100.00%

1.a 1.b 2.a 2.b 2.c 2.d 2.e 2.f 2.g 2.h 3.a 3.b 3.c 3.d 3.e 3.f 3.g 3.h 3.i 3.j 3.k 3.l 3.m

Conclusions

• Some quantities are usually less than 1% difference. Including: 1.a 2.a 2.c 2.d 2.g 3.a 3.g

• Most of the rest quantities are within 5% difference. Some quantities for low scattering cases are up to 10% different, including 3.c and 3.m

• The most difficult quantities to calculate are 3.f and 3.i.

• Running time

Batch Run Quadrature Time

1 Serial S50 30 hrs

2 Parallel 20 CPU S60 5 hrs

Thank You!

Final Meeting held in conjunction with M&C-2009 The Saratoga …€¦ · - Participants submit...

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