AstroPhi : a hydrodynamical code for complex modelling of astrophysical objects dynamics by means of hybrid architecture supercomputers on Intel Xeon Phi base

I. M. Kulikov   ; I. G. Chernykh   ; B. M. Glinsky

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 2 (2013) no. 4, pp. 57-79

Résumé

There is a new hydrodinamical code AstroPhi for modeling of astrophysical objects dynamics on hybrid supercomputer proposed. This software package is optimized for using with Intel Xeon Phi calculations accelerators. AstroPhi code is based on combination of Godunov and author’s FlIC numerical methods for solving of gas dynamics equations. Fast Fourier Transform was used for Poisson equation solution. AstroPhi was tested on gas dynamics problems, Poisson equation solution and classical gravitational gas dynamics problems. The results of this tests and results of gravitational collapse of astrophysical objects modeling proposed. The results of AstroPhi scalability based on Intel Xeon Phi runs are shown.

Détail

Keywords: numerical simulation, parallel computing, Intel Xeon Phi accelerated, computational astrophysics.

Bibliographie

[1] N. V. Ardeljan, G. S. Bisnovatyi-Kogan, S. G. Moiseenko, “An Implicit Lagrangian Code for the Treatment of Nonstationary Problems in Rotating Astrophysical Bodies”, Astronomy Astrophysics, 115 (1996), 573–594

[2] A. Tutukov, G. Lazareva, I. Kulikov, “Gas Dynamics of a Central Collision of Two Galaxies: Merger, Disruption, Passage, and the Formation of a New Galaxy”, Astronomy Reports, 55:9 (2011), 770–783

[3] R. A. Gingold, J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical Stars”, Monthly Notices of the Royal Astronomical Society, 181 (1977), 375–389

[4] L. B. Luci, “Numerical Approach to the Testing of the Fission Hypothesis”, The Astrophysical Journal, 82:12 (1977), 1013–1024

[5] P. Collela, P. R. Woodward, “The Piecewise Parabolic Method (PPM) for Gas-dynamical Simulations”, Journal of Computational Physics, 54 (1984), 174–201

[6] M. Norman, “The Impact of AMR in Numerical Astrophysics and Cosmology”, Lecture Notes in Computational Science and Engineering, 41 (2005), 413–430

[7] R. W. Hockney, J. W. Eastwood, Computer Simulation Using Particles, New York: McGraw-Hill, 1981, 540 pp.

[8] H. Couchman, F. Pearce, P. Thomas, Hydra Code Release } {\tt http://arxiv.org/abs/astro-ph/9603116

[9] J. Barnes, P. Hut, “O(N log N) Force-calculation Algorithm”, Nature, 324 (1986), 446–449

[10] J. Dubinski, J. Kim, C. Park, R. Humble, “O(N log N) Force-calculation Algorithm”, New Astronomy, 9 (2004), 111–126

[11] R. Fedorenko, “A Relaxation Method for Solving Elliptic Difference Equations”, U.S.S.R. Computational Mathematics and Mathematical Physics, 1 (1961), 1092–1096

[12] S. K. Godunov, “A Difference Scheme for Numerical Solution of Discontinuous Solution of Hydrodynamic Equations”, Matematicheskii Sbornik, 47 (1959), 271–306

[13] A. Kulikovskii, N. Pogorelov, A. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems, Fizmatlit, Moscow, 2001, 608 pp.

[14] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1999, 686 pp.

[15] R. Courant, E. Isaacson, M. Rees, “On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Difference”, Communications on Pure and Applied Mathematics, 5:3 (1952), 243–255

[16] P. Roe, “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes”, Journal of Computational Physics, 135:2 (1997), 250–258

[17] B. Engquist, S. J. Osher, “One-sided Difference Approximations for Nonlinear Conservation Laws”, Mathematics of Computation, 36:154 (1981), 321–351

[18] A. Harten, P. D. Lax, B. Van Leer, “On Upstream Differencing and Godunov-type Schemes for Hyperbolic Conservation Laws”, Society for Industrial and Applied Mathematics Review, 25:1 (1983), 35–61

[19] B. Einfeld, “On Godunov-type Methods for Gas Dynamics”, Society for Industrial and Applied Mathematics Journal on Numerical Analysis, 25:2 (1988), 294–318

[20] P. Batten, N. Clarke, C. Lambert, D. M. Causon, “On the Choice of Savespeeds for the HLLC Riemann Solver”, Society for Industrial and Applied Mathematics Journal on Computing, 18:6 (1997), 1553–1570

[21] B. Van Leer, “Towards the Ultimate Conservative Difference Scheme. V - A Second-order Sequel to Godunov’s Method”, Journal of Computational Physics, 32 (1979), 101–136

[22] J. W. Wadsley, J. Stadel, T. Quinn, “Gasoline: a Flexible, Parallel Implementation of TreeSPH”, New Astronomy, 9:2 (2004), 137–158

[23] S. Matthias, “GRAPESPH: Cosmological Smoothed Particle Hydrodynamics Simulations with the Special-purpose Hardware GRAPE”, Monthly Notices of the Royal Astronomical Society, 278:4 (1996), 1005–1017

[24] V. Springel, “The Cosmological Simulation Code GADGET-2”, Monthly Notices of the Royal Astronomical Society, 364:4 (2005), 1105–1134

[25] S. Jin, Z. Xin, “The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions”, Communications on Pure and Applied Mathematics, 48 (1995), 235–276

[26] S. K. Godunov, Yu. D. Manuzina, M. A. Nazareva, “Experimental Analysis of Convergence of the Numerical Solution to a Generalized Solution in Fluid Dynamics”, Computational Mathematics and Mathematical Physics, 51 (2011), 88–95

[27] U. Ziegler, “Self-gravitational Adaptive Mesh Magnetohydrodynamics with the NIRVANA Code”, Astronomy Astrophysics, 435 (2005), 385–395

[28] A. Mignone, T. Plewa, G. Bodo, “The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics”, The Astrophysical Journal, 160 (2005), 199–219

[29] J. Hayes, et al., “Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUSMP”, The Astrophysical Journal Supplement Series, 165 (2006), 188–228

[30] R. Teyssier, “Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUSMP”, Astronomy Astrophysics, 385 (2002), 337–364

[31] A. Kravtsov, A. Klypin, Y. Hoffman, “Constrained Simulations of the Real Universe. II. Observational Signatures of Intergalactic Gas in the Local Supercluster Region”, The Astrophysical Journal, 571 (2002), 563–575

[32] J. Stone, et al., “Athena: A New Code for Astrophysical MHD”, The Astrophysical Journal Supplement Series, 178 (2008), 137–177

[33] A. Brandenburg, W. Dobler, “A. Hydromagnetic Turbulence in Computer Simulations”, Computer Physics Communications, 147 (2002), 471–475

[34] H. Schive, Y. Tsai, T. Chiueh, “GAMER: a GPU-accelerated Adaptive-Mesh-Refinement Code for Astrophysics”, The Astrophysical Journal, 186 (2010), 457–484

[35] J. Murphy, A. Burrows, “BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multidimensional Hydrodynamics Code for Astrophysical Simulations”, The Astrophysical Journal Supplement Series, 179 (2008), 209–241

[36] V. Springel, “E Pur Si Muove: Galilean-invariant Cosmological Hydrodynamical Simulations on a Moving Mesh”, Monthly Notices of the Royal Astronomical Society, 401 (2010), 791–851

[37] S. Bruenn, et al., “2D and 3D Core-collapse Supernovae Simulation Results Obtained with the CHIMERA Code”, Journal of Physics, 180 (2009), 1–5

[38] V. Vshivkov, G. Lazareva, A. Snytnikov, I. Kulikov, A. Tutukov, “Hydrodynamical Code for Numerical Simulation of the Gas Components of Colliding Galaxies”, The Astrophysical Journal Supplement Series, 194:47 (2011), 1–12

[39] M. Gonzalez, E. Audit, P. Huynh, “HERACLES: a Three-dimensional Radiation Hydrodynamics Code”, Astronomy Astrophysics, 464 (2007), 429–435

[40] M. R. Krumholz, R. I. Klein, C. F. McKee, J. Bolstad, “Radiation-hydrodynamic Simulations of the Formation of Orion-like Star Clusters. I. Implications for the Origin of the Initial Mass Function”, The Astrophysical Journal, 667:74 (2007), 1–16

[41] A. Mignone, et al., “PLUTO: A Numerical Code for Computational Astrophysics”, The Astrophysical Journal Supplement Series, 170 (2007), 228–242

[42] A. Almgren, et al., “CASTRO: A New Compressible Astrophysical Solver. I. Hydrodynamics and Self-gravity”, The Astrophysical Journal, 715 (2010), 1221–1238

[43] Y. Feng, et al., “Terapixel Imaging of Cosmological Simulation”, The Astrophysical Journal Supplement Series, 197:18 (2011), 1–8

[44] Enzo-P: Petascale Enzo and the Cello Project } {\tt http://mngrid.ucsd.edu/projects/cello/

[45] PetaART: Toward Petascale Cosmological Simulations Using the Adaptive Refinement Tree (ART) Code } {\tt http://www.cs.iit.edu/zlan/petaart.html

[46] A. Ferrari, et al., “A New Parallel SPH Method for 3D Free Surface Flows”, High performance computing on vector systems 2009, 4 (2010), 179–188

[47] B. Van Straalen, J. Shalf, T. Ligocki, N. Keen, W. Yang, “Scalability Challenges for Massively Parallel AMR Applications”, IPDPS ’09 (Washington, DC, USA), Proceedings of the 2009 IEEE International Symposium on Parallel Distributed Processing, 1–12

[48] V. Vshivkov, G. Lazareva, I. Kulikov, “A Operator Approach for Numerical Simulation of Self-gravitation Gasdynamic Problem”, Computational Technologies, 11:3 (2006), 27–35

[49] V. Vshivkov, G. Lazareva, I. Kulikov, “A Modified Fluids-in-cell Method for Problems of Gravitational Gas Dynamics”, Optoelectronics, Instrumentation and Data Processing, 43:6 (2007), 530–537

[50] V. Vshivkov, G. Lazareva, A. Snytnikov, I. Kulikov, A. Tutukov, “Computational Methods for Ill-posed Problems of Gravitational Gasodynamics”, Journal of Inverse and Ill-posed Problems, 19:1 (2011), 151–166

[51] A. V. Aksenov, “Symmetries and Relations Between Solutions of a Class of Euler-PoissonDarboux Equations”, Reports of RAS, 381:2 (2001), 176–179

[52] V. Vshivkov, G. Lazareva, A. Snytnikov, I. Kulikov, “Supercomputer Simulation of an Astrophysical Object Collapse by the Fluidsin-Cell Method”, Lecture Notes in Computational Science, 5698 (2009), 414–422

[53] M. I. Petrov, P. P. Berczik, “Simulation of the Gravitational Collapse and Fragmentation of Rotating Molecular Clouds”, Astronomische Nachrichten, 326 (2005), 505–513