1. Verifying the CRASH code: procedures and testing E.S. Myra 1a, M.L. Adams 2, R.P. Drake 1a, B. Fryxell 1a, W.D. Hawkins 2, J.P. Holloway 1b, B. van der Holst 1a, R.G. McClarren 2, J.E. Morel 2, K.G. Powell 1c, I. Sokolov 1a, Q.F. Stout 1a,d, G. Toth 1a 1. 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 HYADES Multi-material hydro with EOS Multi-group flux limited diffusion Electron heat conduction Laser heating 1D or 2D Lagrangian BATSRUS Multi-material hydro with EOS (Flux-limited) grey diffusion Electron heat conduction 2D (cylindrical) or 3D block-AMR Explicit or implicit time stepping PDT Multi-group radiation transfer 2D or 3D adaptive grid Discrete ordinates SN Implicit time stepping Data reduction Flat file: ( ,u,p,T e,m)(x,r) Parallel comm.: ( ,u,p,T e,m)(x,y,z) Parallel comm.: (S re, S rm )(x,y,z) Note: blue indicates components in development Hyades 2D Hyades 2D CRASH 3D CRASH 3D θHθH θHθH XHXH XHXH PHPH PHPH MHMH MHMH MCMC MCMC PCPC PCPC θHθCθHθC θHθCθHθC XCXC XCXC HP CP YHYH Y HP YCYC YSYS “Waterfall” process for quality Problem specification (physical processes, regimes,...) Solution and algorithm design (equations, solutions, numerical approaches,…) Coding (implementation) Testing (verification and “real” problems) Release and support Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook) DEFECT PREVENTION DEFECT REMOVAL DEFECT CONTAINMENT The “V” model solution requirements operational code (field testing!) problem specs.full system testing high-level designcode integration testing low-level designcomponent testing codingunit testing VALIDATION VERIFICATION AND VALIDATION 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) analytic Cr-Nicol trap BDF2 fully impl. SPATIAL: LUMPED PWLD  t = 10 –14 s 0.00.20.40.60.81.0 0.0 0.2 0.6 0.4 0.8 1.0 1.2 Intensity Light-Front Propagation Test(FLD) 10x time resolution E rad (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; 1 st -order accuracy in time Lagged Knudsen number Propagation of a free- streaming radiation front Boltzmann equation is hyperbolic Uses beam quadrature set (S 2 ) Backward Euler smooths out step function 2 nd -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; J 0 in the r- direction. Crank-Nicolson used for 2 nd -order time accuracy Analytic solution exists 1D, non-equilibrium Marshak wave; linearized problem: C v  T 3 slab geometry; light-front, plus radiation-matter exchange two semi-implicit schemes: (1) solving for E rad and setting E int ; (2) solving for both E rad and E int Graziani Radiating Sphere: Multigroup FLD Test in development… Mihalas Radiative Damping of Acoustic Waves: Fully coupled radiation hydro test in development… Swesty & Myra, 2009 x (cm) T (eV) R (cm) 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