Transcript Document

Verifying the CRASH code: procedures and testing
1a
Myra ,
2
Adams ,
1a
Drake ,
1a
Fryxell ,
2
Hawkins ,
E.S.
M.L.
R.P.
B.
W.D.
2
1c
1a
1a,d
1a
J.E. Morel , K.G. Powell , I. Sokolov , Q.F. Stout , G. Toth
1.
J.P.
1b
Holloway ,
B. van der
1a
Holst ,
R.G.
2
McClarren ,
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
Department of Nuclear Engineering, Texas A&M University
2.
Abstract
Verifying new code features
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.
Heat Conduction Tests
• Time-dependent heat conduction
model
Electron heat conduction
• see also, the van der Holst poster
• 2 tests: 1D slab and 2D r-z
geometry
T (eV)
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 discreteordinates 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.
• uniform heat conduction
coefficient.
Gray FLD transport
• 1D: Gaussian temperature profile.
• 2D: Gaussian temperature profile
in the z-direction; J0 in the rdirection.
Multigroup FLD transport
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.
Discrete-ordinates transport
• see also, the PDT poster
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.
Testing interfaces
• e.g., BATSRUS/transport
• Crank-Nicolson used for 2nd-order
time accuracy
• Analytic solution exists
Su-Olson Tests
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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
Graziani Radiating Sphere: Multigroup FLD Test
Software architecture and modeling schema
in development…
The “V” model
CRASH
solution requirements
BATSRUS
Multi-material hydro with EOS
Multi-group flux limited diffusion
Electron heat conduction
Laser heating
1D or 2D Lagrangian
Multi-material hydro with EOS
(Flux-limited) grey diffusion
Electron heat conduction
2D (cylindrical) or 3D block-AMR
Explicit or implicit time stepping
Flat file: (,u,p,Te,m)(x,r)
problem specs.
VERIFICATION
AND
VALIDATION
XH
θH
XC
Parallel comm.:
Parallel comm.:
(,u,p,Te,m)(x,y,z) (Sre, Srm)(x,y,z)
PH
YH
HP
MH
YHP
CRASH
3D
PC
YC
CP
MC
Note: blue indicates components
in development
coding
Swesty & Myra, 2009
unit testing
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Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook)
• Models the propagation of a
radiation front, from inner
edge to a point halfway into
the domain.
• Timescale for this process is
x/c
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
• Backward Euler; 1st-order
accuracy in time
HEAT CONDUCTION
Solution and algorithm design
(equations, solutions,
numerical approaches,…)
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Hydrodynamics
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Radiation transport
Light-Front Propagation Test (transport)
MULTI-MATERIAL ADVECTION
Mihalas Radiative Damping of Acoustic Waves:
Fully coupled radiation hydro test
– discrete ordinates
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DEFECT PREVENTION
LOWRIE TESTS
– discrete ordinates
DEFECT
CONTAINMENT
•
Radiography
•
Material properties
LIGHT FRONT
1.0
• Propagation of a freestreaming radiation front
0.8
• Boltzmann equation is
hyperbolic
Radiation hydrodynamics
– grey diffusion
Testing
(verification and
“real” problems)
SPATIAL: LUMPED PWLD
t = 10–14 s
1.2
in development…
– grey diffusion
Coding
(implementation)
• Lagged Knudsen number
x (cm)
Verification tests
Multiple classes of tests
Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook)
• Challenge for flux-limited
diffusion
VERIFICATION
Problem specification
(physical processes,
regimes,...)
DEFECT REMOVAL
t = 0.05 t CFL-rad
component testing
VERIFICATION
“Waterfall” process for quality
Release
and
support
• Boltzmann equation is
hyperbolic.
10x time resolution
code integration testing
low-level design
Multi-group radiation transfer
2D or 3D adaptive grid
Discrete ordinates SN
Implicit time stepping
YS
full system testing
VERIFICATION
PDT
Hyades
2D
• Propagation of a freestreaming radiation front
QuickTime™ and a
decompressor
are needed to see this picture.
high-level design
θH
θC
Light-Front Propagation Test (FLD)
– EOS
QuickTime™ and a
decompressor
are needed to see this picture.
Swesty & Myra, 2009
Intensity
Data reduction
operational code (field testing!)
VALIDATION
Erad (erg cm-3)
HYADES
t = 10-11 s
analytic
Cr-Nicol
trap BDF2
fully impl.
0.6
• Uses beam quadrature
set (S2)
• Backward Euler smooths
out step function
0.4
RADIOGRAPHY
– opacities
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Unit tests
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Component tests
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Full-system tests
0.2
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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
0.0
0.0
0.2
0.4
0.6
x (cm)
0.8
1.0
• 2nd-order methods
(Crank-Nicolson and
TBDF-2) have oscillations
near the step