Verifying the CRASH code: procedures and testing

1. 10x time resolution θH θC XH θH XC Hyades 2D CRASH 3D HP YH YHP YC YS CP PH MC MH PC T (eV) R (cm) x (cm) SPATIAL: LUMPED PWLD t = 10–14 s 1.2 1.0 analytic Cr-Nicol trap BDF2 fully impl. 0.8 0.6 Intensity 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 x (cm) t = 0.05 tCFL-rad Erad (erg cm-3) x (cm) 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 Verifying new code features 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 • 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 • 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 • 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 Su-Olson Tests Graziani Radiating Sphere: Multigroup FLD Test in development… Software architecture and modeling schema The “V” model CRASH t = 10-11 s Light-Front Propagation Test(FLD) operational code (field testing!) solution requirements VALIDATION 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 • 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 Data reduction problem specs. full system testing VERIFICATION AND VALIDATION Flat file: (,u,p,Te,m)(x,r) IMPLEMENTATION TESTING high-level design code integration testing Parallel comm.: (Sre, Srm)(x,y,z) Parallel comm.: (,u,p,Te,m)(x,y,z) VERIFICATION low-level design component testing PDT Multi-group radiation transfer 2D or 3D adaptive grid Discrete ordinates SN Implicit time stepping VERIFICATION Swesty & Myra, 2009 coding unit testing VERIFICATION • 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 Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook) Note: blue indicates components in development “Waterfall” process for quality Verification tests Light-Front Propagation Test (transport) Problem specification (physical processes, regimes,...) 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 MULTI-MATERIAL ADVECTION Mihalas Radiative Damping of Acoustic Waves: Fully coupled radiation hydro test in development… HEAT CONDUCTION Solution and algorithm design (equations, solutions, numerical approaches,…) • 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 Coding (implementation) LOWRIE TESTS DEFECT PREVENTION Testing (verification and “real” problems) Release and support Swesty & Myra, 2009 DEFECT REMOVAL LIGHT FRONT RADIOGRAPHY DEFECT CONTAINMENT Adapted from Jeff Tian (http://www.engr.smu.edu/~tian/SQEbook) • 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