Verifying the CRASH code: procedures and testing

E.S. Myra1a, M.L. Adams2, R.P. Drake1a, B. Fryxell1a, W.D. Hawkins2, J.P. Holloway1b, B. van der Holst1a, R.G. McClarren2, J.E. Morel2, K.G. Powell1c, I. Sokolov1a, Q.F. Stout1a,d, G. Toth1a

• University of Michigan: (a) Department of Atmospheric, Oceanic and Space Sciences; (b) Department of Nuclear Engineering and Radiological Sciences; (c) Department of Aerospace Engineering; (d) Department of Computer Science and Engineering

2. Department of Nuclear Engineering, Texas A&M University

Abstract

The CRASH project seeks to improve the predictive capability of models for shock waves produced in Xe or Ar when a laser is used to shock, ionize, and accelerate a Be plate into a gas-filled shock tube. These shocks, when driven above a threshold velocity of about 100 km/s, become strongly radiative and convert most of the incoming energy flux into radiation. The CRASH code, which is used to simulate these experiments, includes contributions from several existing and developing codebases: (i) BATSRUS (a 3D, adaptive, MHD code), (ii) PDT (a discrete-ordinates radiation-transport code), (iii) a flux-limited-diffusion implementation of radiation hydrodynamics, (iv) code for employing material-properties data (equations of state, opacities, etc.), and (v) a package for making simulated radiographs to compare to experimental data.

To ensure both accurate simulation and code implementation, extensive verification and validation is required. In this presentation, we outline key tests in our verification procedure and illustrate some of the more interesting test problems in greater detail.

We gratefully acknowledge the support of the U.S. Dept. of Energy NNSA under the Predictive Science Academic Alliance Program by grant DE-FC52-08NA28616, under the Stewardship Sciences Academic Alliances program by grant DE-FG52-04NA00064, and under the National Laser User Facility by grant DE-FG03–00SF22021.

Heat Conduction Tests

Su-Olson Tests

CRASH

Software architecture and modeling schema

HYADESMulti-material hydro with EOSMulti-group flux limited diffusionElectron heat conduction Laser heating1D or 2D Lagrangian

BATSRUSMulti-material hydro with EOS(Flux-limited) grey diffusionElectron heat conduction2D (cylindrical) or 3D block-AMR Explicit or implicit time stepping

PDTMulti-group radiation transfer2D or 3D adaptive gridDiscrete ordinates SNImplicit time stepping

Data reduction

Flat file: (,u,p,Te,m)(x,r)

Parallel comm.:(,u,p,Te,m)(x,y,z)

Parallel comm.:(Sre, Srm)(x,y,z)

Note: blue indicates components in development

Hyades2D

Hyades2D

CRASH

3D

CRASH

3D

θHθHXHXH

PHPH MHMH MC MC PCPC

θH

θC

θH

θCXCXC

HPHP CPCPYH YHP YC YS

“Waterfall” process for quality

Problem specification(physical processes,

regimes,...)

Solution and algorithm design(equations, solutions,numerical approaches,…)

Coding(implementation)

Testing(verification and “real” problems)

Releaseand

support

Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook)

DEFECT PREVENTION

DEFECT REMOVAL

DEFECTCONTAINMENT

The “V” model

solution requirements operational code (field testing!)

problem specs. full system testing

high-level design code integration testing

low-level design component testing

coding unit testing

VALIDATION

VERIFICATIONAND

VALIDATION

VERIFICATION

VERIFICATION

VERIFICATION

Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook)

IMPLEMENTATION

TESTING

Verification tests

Multiple classes of tests

• Hydrodynamics

• Radiation transport

– grey diffusion

– discrete ordinates

• Radiation hydrodynamics

– grey diffusion

– discrete ordinates

• Radiography

• Material properties

– EOS

– opacities

• Unit tests

• Component tests

• Full-system tests

HEAT CONDUCTION

LIGHT FRONT

MULTI-MATERIAL ADVECTION

LOWRIE TESTS

RADIOGRAPHY

Verifying new code features

Electron heat conduction• see also, the van der Holst poster

Gray FLD transport

Multigroup FLD transport

Discrete-ordinates transport• see also, the PDT poster

Testing interfaces• e.g., BATSRUS/transport

x (cm)

analyticCr-Nicoltrap BDF2fully impl.

SPATIAL: LUMPED PWLD t = 10–14 s

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.6

0.4

0.8

1.0

1.2

Intensity

Light-Front Propagation Test(FLD)

10x time resolution

Erad (erg cm-3)

x (cm)

t = 0.05 t CFL-rad

Light-Front Propagation Test (transport)

• Propagation of a free-streaming radiation front

• Boltzmann equation is hyperbolic.

• Challenge for flux-limited diffusion

• Models the propagation of a radiation front, from inner edge to a point halfway into the domain.

• Timescale for this process is x/c

• Backward Euler; 1st-order accuracy in time

• Lagged Knudsen number

• Propagation of a free-streaming radiation front

• Boltzmann equation is hyperbolic

• Uses beam quadrature

set (S2)

• Backward Euler smooths out step function

• 2nd-order methods (Crank-Nicolson and TBDF-2) have oscillations near the step

• Time-dependent heat conduction model

• 2 tests: 1D slab and 2D r-z geometry

• uniform heat conduction coefficient.

• 1D: Gaussian temperature profile.

• 2D: Gaussian temperature profile in the z-direction; J0 in the r-

direction.

• Crank-Nicolson used for 2nd-order time accuracy

• Analytic solution exists

• 1D, non-equilibrium Marshak wave; linearized problem: Cv T 3

• slab geometry; light-front, plus radiation-matter exchange• two semi-implicit schemes:

• (1) solving for Erad and setting Eint ; (2) solving for both Erad and Eint

QuickTime™ and a decompressor

are needed to see this picture.

Graziani Radiating Sphere: Multigroup FLD Testin development…

Mihalas Radiative Damping of Acoustic Waves:Fully coupled radiation hydro test

in development…

Swesty & Myra, 2009

x (cm)

T (eV)

R (cm)

QuickTime™ and a decompressor

are needed to see this picture.

Swesty & Myra, 2009

• Hot sphere (1.5 keV) in a cooler medium (50 eV)• Spectrum observed at radius r at various times t.• Analytic solution exists for pure diffusion• Monte Carlo solution for transport (Gentile)• True multigroup test—one of a class of such problems• One of the few multigroup problems with an analytic solution

t = 10-11 s

• Acoustic oscillations are driven at the left-hand edge (/x < 1)• Disturbance propagates to the right• Radiation damps oscillations as a function of and • Analytic solution exists for linearized RHD equations• One of the few coupled RHD problems with an analytic solution