The RAGE radiation-hydrodynamic code

We describe RAGE, the 'radiation adaptive grid Eulerian' radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation?material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm.

[1]  F. Petrini,et al.  The Case of the Missing Supercomputer Performance: Achieving Optimal Performance on the 8,192 Processors of ASCI Q , 2003, ACM/IEEE SC 2003 Conference (SC'03).

[2]  A. Harten,et al.  The artificial compression method for computation of shocks and contact discontinuities. 3: Self-adjusting hybrid schemes , 1977 .

[3]  Phillip Colella,et al.  Efficient Solution Algorithms for the Riemann Problem for Real Gases , 1985 .

[4]  Huanan Yang,et al.  An artificial compression method for ENO schemes - The slope modification method. [essentially nonoscillatory , 1990 .

[5]  R. E. Marshak,et al.  Effect of Radiation on Shock Wave Behavior , 1958 .

[6]  Michael L. Gittings,et al.  SAGE CALCULATIONS OF THE TSUNAMI THREAT FROM LA PALMA , 2006 .

[7]  Mikhail Shashkov,et al.  Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes , 2004 .

[8]  Richard Sanders,et al.  High resolution staggered mesh approach for nonlinear hyperbolic systems of conser-vation laws , 1992 .

[9]  R. E. Williamson,et al.  THE PENETRATION OF RADIATION WITH CONSTANT DRIVING TEMPERATURE , 1960 .

[10]  G. C. Pomraning,et al.  Numerical transport and diffusion methods in radiative transfer , 1992 .

[11]  Michael L. Hall,et al.  Diffusion, P1, and other approximate forms of radiation transport , 2000 .

[12]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[13]  Michael S. Warren,et al.  The Fast Solution of Three-Dimensional Fluid Dynamical N-Body Problems Using Parallel Tree Codes: Vortex Element Method and Boundary Element Method , 1995, PPSC.

[14]  M. Edwards.  Elimination of Adaptive Grid Interface Errors in the Discrete Cell Centered Pressure Equation , 1996 .

[15]  L. H. Howell,et al.  Solving the radiation diffusion and energy balance equations using pseudo-transient continuation , 2004 .

[16]  A. Harten,et al.  The artificial compression method for computation of shocks and contact discontinuities: III. Self , 1978 .

[17]  S. Coggeshall.  Lie Group Invariance Properties of Radiation Hydrodynamics Equations , 1986 .

[18]  M. S. Warren,et al.  A parallel hashed Oct-Tree N-body algorithm , 1993, Supercomputing '93.

[19]  S. K. Godunov,et al.  Reminiscences about Difference Schemes , 1999 .

[20]  Robert F. Benjamin,et al.  Simulation of shock-generated instabilities , 1996 .

[21]  L. H. Howell,et al.  Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement , 2003 .

[22]  Paul F. Dubois,et al.  An implicit scheme for calculating time- and frequency-dependent flux limited radiation diffusion in one dimension , 1984 .

[23]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[24]  G. Rodriguez,et al.  Using pulsed power for hydrodynamic code validation , 2001, PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference. Digest of Papers (Cat. No.01CH37251).

[25]  William J. Rider,et al.  Time Step Size Selection for Radiation Diffusion Calculations , 1999 .

[26]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[27]  G. Gisler,et al.  TWO-DIMENSIONAL SIMULATIONS OF EXPLOSIVE ERUPTIONS OF KICK-EM JENNY AND OTHER SUBMARINE VOLCANOS , 2006 .

[28]  Mikhail Shashkov,et al.  Solving Diffusion Equations with Rough Coefficients in Rough Grids , 1996 .

[29]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[30]  Michael Lang,et al.  A Performance and Scalability Analysis of the BlueGene/L Architecture , 2004, Proceedings of the ACM/IEEE SC2004 Conference.

[31]  Phillip Colella,et al.  Glimm's Method for Gas Dynamics , 1982 .

[32]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[33]  J. M. Foster,et al.  SUPERSONIC JET AND SHOCK INTERACTIONS , 2001 .

[34]  S. Penner.  Physics of shock waves and high-temperature hydrodynamic phenomena - Ya.B. Zeldovich and Yu.P. Raizer (translated from the Russian and then edited by Wallace D. Hayes and Ronald F. Probstein); Dover Publications, New York, 2002, 944 pp., $34. , 2003 .

[35]  Dimitri Mihalas,et al.  On laboratory-frame radiation hydrodynamics , 2001 .

[36]  Scott B. Baden,et al.  Dynamic Partitioning of Non-Uniform Structured Workloads with Spacefilling Curves , 1996, IEEE Trans. Parallel Distributed Syst..

[37]  Keh-Ming Shyue,et al.  A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state , 2001 .

[38]  A. M. Winslow.  Multifrequency-gray method for radiation diffusion with Compton scattering , 1995 .

[39]  Multimode flux-limited diffusion theory , 1992 .

[40]  S. V. Coggeshall.  Analytic solutions of hydrodynamics equations , 1991 .

[41]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[42]  G. C. Pomraning.  The non-equilibrium Marshak wave problem , 1979 .

[43]  Robert P. Weaver,et al.  Shock structuring due to fabrication joints in targets , 1999 .

[44]  Michael L. Norman,et al.  Beyond Flux-Limited Diffusion: Parallel Algorithms for Multidimensional Radiation Hydrodynamics , 2003 .

[45]  Michael S. Warren,et al.  Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems , 1994, Int. J. High Perform. Comput. Appl..

[46]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[47]  G. R. Magelssen,et al.  Validation of the radiation hydrocode RAGE against defect-driven mix experiments in a compressible, convergent, and miscible plasma system , 2006 .

[48]  Michael L. Gittings,et al.  Two- and Three-Dimensional Simulations of Asteroid Ocean Impacts , 2002 .

[49]  Gordon L. Olson,et al.  An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium , 1997 .

[50]  G. C. Pomraning,et al.  A flux-limited diffusion theory , 1981 .

[51]  Gordon L. Olson,et al.  BENCHMARK RESULTS FOR THE NON-EQUILIBRIUM MARSHAK DIFFUSION PROBLEM , 1996 .

[52]  C. A. Zoldi.  A Numerical and Experimental Study of a Shock-Accelerated Heavy Gas Cylinder , 2002 .

[53]  J. Quirk.  A Contribution to the Great Riemann Solver Debate , 1994 .

[54]  G. Strang.  On the Construction and Comparison of Difference Schemes , 1968 .

[55]  Two- and three-dimensional asteroid impact simulations , 2004 .

[56]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[57]  Marilyn Schneider,et al.  Richtmyer–Meshkov instability growth: experiment, simulation and theory , 1999, Journal of Fluid Mechanics.

[58]  Dana A. Knoll,et al.  Temporal Accuracy of the Nonequilibrium Radiation Diffusion Equations Applied to Two-Dimensional Multimaterial Simulations , 2006 .

[59]  William J. Rider,et al.  Physics-Based Preconditioning and the Newton-Krylov Method for Non-equilibrium Radiation Diffusion , 2000 .

[60]  Michael S. Warren,et al.  A parallel hashed oct-tree N-body algorithm , 1993, Supercomputing '93. Proceedings.

[61]  G. C. Pomraning,et al.  Flux-limited diffusion models in radiation hydrodynamics , 1993 .

[62]  J. H. Bolstad,et al.  An exact solution for the linearized multifrequency radiation diffusion equation , 2005 .

[63]  A. I. Shestakov.  Time-dependent simulations of point explosions with heat conduction , 1999 .

[64]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[65]  J. Meyer-ter-Vehn,et al.  The point explosion with heat conduction , 1991 .

[66]  Roger B. Lazarus,et al.  Self-Similar Solutions for Converging Shocks and Collapsing Cavities , 1981 .

[67]  M. Shashkov,et al.  A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes , 2001 .

[68]  K. A. Klare,et al.  Production of enhanced pressure regions due to inhomogeneities in inertial confinement fusion targets , 2000 .

[69]  William J. Rider,et al.  Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations , 2007, J. Comput. Phys..

[70]  D. P. Young,et al.  A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics , 1990 .

[71]  G. C. Pomraning,et al.  A family of flux-limited diffusion theories. , 1991 .

[72]  F. Douglas Swesty,et al.  A Comparison of Algorithms for the Efficient Solution of the Linear Systems Arising from Multigroup Flux-limited Diffusion Problems , 2004 .

[73]  William J. Rider,et al.  A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov , 2004 .

[74]  B. Vanleer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[75]  G. C. Pomraning,et al.  The non-equilibrium Marshak wave problem: A transport theory solution , 1983 .

[76]  Fabrizio Petrini,et al.  Predictive Performance and Scalability Modeling of a Large-Scale Application , 2001, ACM/IEEE SC 2001 Conference (SC'01).

[77]  William J. Rider,et al.  An efficient nonlinear solution method for non-equilibrium radiation diffusion , 1999 .

[78]  Steven L. Lee,et al.  Analyzing radiation diffusion using time-dependent sensitivity-based techniques , 2003 .

[79]  E. Lee,et al.  JWL equation of state coefficients for high explosives , 1973 .

[80]  Carol S. Woodward,et al.  Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration , 2005 .