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Parallel, grid-adaptive approaches for relativistic hydro- and magnetohydrodynamics. (English) Zbl 1426.76385
Summary: Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed of light. Significant progress in its numerical modeling emerged in the last two decades, and we highlight specifically the need for grid-adaptive, shock-capturing treatments found in several contemporary codes in active use and development. Our discussion highlights one such code, MPI-AMRVAC (Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code), but includes generic strategies for allowing massively parallel, block-tree adaptive simulations in any dimensionality. We provide implementation details reflecting the underlying data structures as used in MPI-AMRVAC. Parallelization strategies and scaling efficiencies are discussed for representative applications, along with guidelines for data formats suitable for parallel I/O. Refinement strategies available in MPI-AMRVAC are presented, which cover error estimators in use in many modern AMR frameworks. A test suite for relativistic hydro and magnetohydrodynamics is provided, chosen to cover all aspects encountered in high-resolution, shock-governed astrophysical applications. This test suite provides ample examples highlighting the advantages of AMR in relativistic flow problems.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76W05 Magnetohydrodynamics and electrohydrodynamics
76L05 Shock waves and blast waves in fluid mechanics
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[1] Aloy, M.A.; Ibáñez, J.M.; Martí, J.M.; Müller, E., GENESIS: a high-resolution code for three-dimensional relativistic hydrodynamics, Apjs, 122, 151, (1999)
[2] Aloy, M.A.; Rezzolla, L., A powerful hydrodynamic booster for relativistic jets, Astrophys. J., 640, L115, (2006)
[3] Anderson, M.; Hirschmann, E.W.; Liebling, S.L.; Neilsen, D., Relativistic MHD with adaptive mesh refinement, Cqgra, 23, 6503, (2006) · Zbl 1133.83343
[4] Anninos, P.; Fragile, P.C.; Salmonson, J.D., Cosmos++: relativistic magnetohydrodynamics on unstructured grids with local adaptive refinement, Apj, 635, 723, (2005)
[5] Antón, L.; Miralles, J.A.; Martí, J.M.; Ibáñez, J.M.; Aloy, M.A.; Mimica, P., Relativistic magnetohydrodynamics: renormalized eigenvectors and full wave decomposition Riemann solver, Apjs, 188, 1, (2010)
[6] Balsara, D.S., Total variation diminishing scheme for relativistic magnetohydrodynamics, Astrophys. J. suppl. ser., 132, 83, (2001)
[7] Balsara, D.S.; Kim, J., A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics, Astrophys. J., 602, 1079, (2004)
[8] Berger, M.J., Data structures for adaptive grid generation, SIAM J. sci. stat. comput., 7, 904, (1986) · Zbl 0625.65116
[9] Berger, M.J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. comput. phys., 82, 64, (1989) · Zbl 0665.76070
[10] J. Bergmans, R. Keppens, D.E.A. van Odyck, A. Achterberg, Simulations of relativistic astrophysical flows, in: T. Plewa, T. Linde, V.G. Weirs (Eds.), Adaptive Mesh Refinement - Theory and Applications, Lecture Notes in Computational Science and Engineering, vol. 41, 2005, p. 223. · Zbl 1065.85502
[11] Cactus toolkit at <http://cactuscode.org>.
[12] Cada, M.; Torrilhon, M., Compact third-order limiter functions for finite volume methods, J. comput. phys., 228, 4118, (2009) · Zbl 1273.76286
[13] Calder, A.C.; Fryxell, B.; Plewa, T.; Rosner, R.; Dursi, L.J.; Weirs, V.G.; Dupont, T.; Robey, H.F.; Kane, J.O.; Remington, B.A.; Drake, R.P.; Dimonte, G.; Zingale, M.; Timmes, F.X.; Olson, K.; Ricker, P.; MacNeice, P.; Tufo, H.M., On validating an astrophysical simulation code, Astrophys. J. suppl. ser., 143, 201, (2002)
[14] Chombo library at <http://seesar.lbl.gov/ANAG/chombo/>.
[15] Colella, P.; Woodward, P.R., The piecewise parabolic method (PPM) for gas dynamical simulations, J. comput. phys., 54, 174, (1984) · Zbl 0531.76082
[16] Dedner, A.; Kemm, F.; Kröner, D.; Munz, C.-D.; Schnitzer, T.; Wesenberg, M., Hyperbolic divergence cleaning for the MHD equations, J. comput. phys., 175, 645, (2002) · Zbl 1059.76040
[17] Dellar, P.J., A note on magnetic monopoles and the one-dimensional MHD Riemann problems, J. comput. phys., 172, 392, (2001) · Zbl 1065.35523
[18] Delmont, P.; Keppens, R.; van der Holst, B., An exact Riemann-solver-based solution for regular shock refraction, J. fluid mech., 627, 33, (2009) · Zbl 1171.76409
[19] Del Zanna, L.; Bucciantini, N., An efficient shock-capturing central-type scheme for multidimensional relativistic flows. I. hydrodynamics, Astron. astrophys., 390, 1177, (2002) · Zbl 1209.76022
[20] Del Zanna, L.; Bucciantini, N.; Londrillo, P., An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. magnetohydrodynamics, Astron. astrophys., 400, 397, (2003) · Zbl 1222.76122
[21] Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P., ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics, Astron. astrophys., 473, 11, (2007)
[22] Dubal, M.R., Numerical simulations of special relativistic, magnetic gas flows, Comput. phys. commun., 64, 221, (1991)
[23] Evans, C.R.; Hawley, J.F., Simulation of magnetohydrodynamic flows – a constrained transport method, Astrophys. J., 332, 659, (1988)
[24] FLASH3 user guide at <http://flash.uchicago.edu>.
[25] Font, J.A.; Ibáñez, J.M.; Marquina, A.; Martí, J.M., Multidimensional relativistic hydrodynamics: characteristic fields and modern high-resolution shock-capturing schemes, Astron. astrophys., 282, 304, (1994)
[26] Font, J.A., Numerical hydrodynamics and magnetohydrodynamics in general relativity, Living rev. relat., 11, 7, (2008) · Zbl 1166.83003
[27] Gammie, C.F.; McKinney, J.C.; Tóth, G., HARM: a numerical scheme for general relativistic magnetohydrodynamics, Astrophys. J., 589, 444, (2003)
[28] Gardiner, T.A.; Stone, J., An unsplit Godunov method for ideal MHD via constrained transport in three dimensions, J. comput. phys., 227, 4123, (2008) · Zbl 1317.76057
[29] Giacomazzo, B.; Rezzolla, L., The exact solution of the Riemann problem in relativistic MHD, J. fluid mech., 562, 223, (2006) · Zbl 1097.76073
[30] Giacomazzo, B.; Rezzolla, L., Whiskymhd: a new numerical code for general relativistic magnetohydrodynamics, Cqgra, 24, S235, (2007) · Zbl 1117.83002
[31] Goedbloed, J.P.; Keppens, R.; Poedts, S., Advanced MHD. with application to laboratory and astrophysical plasmas, (2010), Cambridge University Press Cambridge
[32] Harten, A.; Lax, P.D.; van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM rev., 25, 35, (1983) · Zbl 0565.65051
[33] Honkkila, V.; Janhunen, P., HLLC solver for ideal relativistic MHD, J. comput. phys., 223, 643, (2007) · Zbl 1111.76036
[34] Hughes, P.A.; Miller, M.A.; Duncan, G.C., Three-dimensional hydrodynamic simulations of relativistic extragalactic jets, Astrophys. J., 572, 713, (2002)
[35] is a product of <http://www.ittvis.com>.
[36] Janhunen, P., A positive conservative method for magnetohydrodynamics based on HLL and roe methods’, J. comput. phys., 160, 649, (2000) · Zbl 0967.76061
[37] Keppens, R.; Meliani, Z., Linear wave propagation in relativistic magnetohydrodynamics, Phys. plasmas, 15, 102103, (2008)
[38] Keppens, R.; Meliani, Z., Grid-adaptive simulations of relativistic flows, () · Zbl 1197.76085
[39] Keppens, R.; Meliani, Z.; van der Holst, B.; Casse, F., Extragalactic jets with helical magnetic fields: relativistic MHD simulations, Astron. astrophys., 486, 663, (2008)
[40] Keppens, R.; Nool, M.; Tóth, G.; Goedbloed, J.P., Adaptive mesh refinement for conservative systems: multi-dimensional efficiency evaluation, Comput. phys. commun., 153, 317, (2003) · Zbl 1196.76055
[41] Keppens, R.; Tóth, G., Openmp parallelism for multi-dimensional grid-adaptive magnetohydrodynamic simulations, Lect. notes comput. sci., 2329, 940, (2002) · Zbl 1053.76526
[42] Koldoba, A.V.; Kuznetsov, O.A.; Ustyugova, G.V., An approximate Riemann solver for relativistic magnetohydrodynamics, Mnras, 333, 932, (2002)
[43] Komissarov, S.S., A Godunov-type scheme for relativistic magnetohydrodynamics, Mnras, 303, 343, (1999)
[44] Komissarov, S.S., Multi-dimensional numerical scheme for resistive relativistic MHD, Mnras, 382, 995, (2007)
[45] Koren, B., A robust upwind discretization method for advection, diffusion and source terms, (), 117 · Zbl 0805.76051
[46] Kurganov, A.; Tadmor, E., New high-resolution central schemes for nonlinear conservation laws and convection – diffusion equations, J. comput. phys., 160, 241, (2000) · Zbl 0987.65085
[47] Leismann, T.; Antón, L.; Aloy, M.A.; Müller, E.; Martí, J.M.; Miralles, J.A.; Ibáñez, J.M., Relativistic MHD simulations of extragalactic jets, Astron. astrophys., 436, 503, (2005)
[48] Löhner, R., An adaptive finite element scheme for transient problems in CFD, Comput. methods appl. mech. eng., 61, 323, (1987) · Zbl 0611.73079
[49] MacNeice, P.; Olson, K.M.; Mobarry, C.; deFainchtein, R.; Packer, C., PARAMESH: a parallel adaptive mesh refinement community toolkit, Comput. phys. commun., 126, 330, (2000) · Zbl 0953.65088
[50] Mathews, W.G., The hydromagnetic free expansion of a relativistic gas, Astrophys. J., 165, 147, (1971)
[51] Marder, B., A method for incorporating gauss’ law into electromagnetic PIC codes, J. comput. phys., 68, 48, (1987) · Zbl 0603.65079
[52] Martí, J.M.; Müller, E.; Font, J.A.; Ibáñez, J.M.; Marquina, A., Morphology and dynamics of relativistic jets, Astrophys. J., 479, 151, (1997)
[53] Martí, J.M.; Müller, E., Numerical hydrodynamics in special relativity, Living rev. relat., 6, 7, (2003) · Zbl 1068.83502
[54] Meliani, Z.; Sauty, C.; Tsinganos, K.; Vlahakis, N., Relativistic parker winds with variable effective polytropic index, Astron. astrophys., 425, 773, (2004)
[55] Meliani, Z.; Keppens, R.; Casse, F.; Giannios, D., AMRVAC and relativistic hydrodynamic simulations for gamma-ray burst afterglow phases, Mnras, 376, 1189, (2007)
[56] Meliani, Z.; Keppens, R.; Giacomazzo, B., Fanaroff-riley type I jet deceleration at density discontinuities, Astron. astrophys., 491, 321, (2008)
[57] Meliani, Z.; Keppens, R., Decelerating relativistic two-component jets, Astrophys. J., 705, 1594, (2009)
[58] Meliani, Z.; Keppens, R., Dynamics and stability of relativistic GRB blast waves, Astron. astrophys., 520, L3, (2010)
[59] Mignone, A.; Plewa, T.; Bodo, G., The piecewise parabolic method for multidimensional relativistic fluid dynamics, Astrophys. J. suppl. ser., 160, 199, (2005)
[60] Mignone, A.; Bodo, G., An HLLC Riemann solver for relativistic flows - I. hydrodynamics, Mnras, 364, 126, (2005)
[61] Mignone, A.; Bodo, G., An HLLC Riemann solver for relativistic flows - II. magnetohydrodynamics, Mnras, 368, 1040, (2006)
[62] Mignone, A.; Bodo, G.; Massaglia, S.; Matsakos, T.; Tesileanu, O.; Zanni, C.; Ferrari, A., PLUTO: a numerical code for computational astrophysics, Astrophys. J. suppl. ser., 170, 228, (2007)
[63] Mignone, A.; McKinney, J.C., Equation of state in relativistic magnetohydrodynamics: variable versus constant adiabatic index, Mnras, 378, 1118, (2007)
[64] Mignone, A.; Rossi, P.; Bodo, G.; Ferrari, A.; Massaglia, S., High resolution 3D relativistic MHD simulations of jets, Mnras, 402, 7, (2010)
[65] Mignone, A.; Tzeferacos, P., A second-order unsplit Godunov scheme for cell-centered MHD: the CTU-GLM scheme, J. comput. phys., 229, 2117, (2010) · Zbl 1303.76142
[66] Mignone, A.; Ugliano, M.; Bodo, G., A five-wave harten – lax – van leer Riemann solver for relativistic magnetohydrodynamics, Mnras, 393, 1141, (2009)
[67] Miller, G.H.; Colella, P., A conservative three-dimensional Eulerian method for coupled solid – fluid shock capturing, J. comput. phys., 183, 26, (2002) · Zbl 1057.76558
[68] Mizuno, Y.; Hardee, P.; Nishikawa, K.I., Three-dimensional relativistic magnetohydrodynamic simulations of magnetized spine-sheath relativistic jets, Astrophys. J., 662, 835, (2007)
[69] Noble, S.C.; Gammie, C.F.; McKinney, J.C.; del Zanna, L., Primitive variable solvers for conservative general relativistic magnetohydrodynamics, Astrophys. J., 641, 626, (2006)
[70] OpenDX is an open source tool available at <http://www.opendx.org>.
[71] Paraview is an open source tool available at <http://www.paraview.org>.
[72] Perucho, M.; Martí, J.M., A numerical simulation of the evolution and fate of a fanaroff-riley type I jet, Mnras, 382, 526, (2007)
[73] Pons, J.A.; Martí, J.M.; Müller, E., The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics, J. fluid mech., 422, 125, (2000) · Zbl 0994.76104
[74] K.G. Powell, An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More than One Dimension), ICASE Report No. 94-24, Langley VA, 1994.
[75] Rossi, P.; Mignone, A.; Bodo, G.; Massaglia, S.; Ferrari, A., Formation of dynamical structures in relativistic jets: the FRI case, Astron. astrophys., 488, 795, (2008)
[76] Rusanov, V.V., The calculation of the interaction of non-stationary shock waves and obstacles, USSR comput. math. math. phys., 1, 304, (1961)
[77] Ryu, D.; Chattopadhyay, I.; Choi, E., Equation of state in numerical relativistic hydrodynamics, Astrophys. J. suppl. ser., 166, 410, (2006)
[78] Sokolov, I.V.; Zhang, H.-M.; Sakai, J.I., Simple and efficient Godunov scheme for computational relativistic gas dynamics, J. comput. phys., 172, 209, (2001) · Zbl 1065.76585
[79] is a product of , see <http://www.tecplot.com>.
[80] Synge, J.L., The relativistic gas, (1957), North Holland Amsterdam · Zbl 0077.41706
[81] Toro, E.F., Riemann solvers and numerical methods for fluid dynamics, (1997), Springer-Verlag Berlin · Zbl 0888.76001
[82] Tóth, G., The LASY preprocessor and its application to general multi-dimensional codes, J. comput. phys., 138, 981, (1997) · Zbl 0903.76077
[83] Tóth, G., A general code for modeling MHD flows on parallel computers: versatile advection code, Astrophys. lett. commun., 34, 245, (1996), See <http://www.phys.uu.nl/∼toth>
[84] Tóth, G.; Odstrčil, D., Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems, J. comput. phys., 128, 82, (1996) · Zbl 0860.76061
[85] Tóth, G., The ∇·B=0 constraint in shock-capturing magnetohydrodynamics codes, J. comput. phys., 161, 605, (2000) · Zbl 0980.76051
[86] van der Holst, B.; Keppens, R., Hybrid block-AMR in Cartesian and curvilinear coordinates: MHD applications, J. comput. phys., 226, 925, (2007) · Zbl 1310.76133
[87] van der Holst, B.; Keppens, R.; Meliani, Z., A multidimensional grid-adaptive relativistic magnetofluid code, Comput. phys. commun., 179, 617, (2008) · Zbl 1197.76085
[88] A.J. van Marle, R. Keppens, Radiative cooling in numerical astrophysics: the need for adaptive mesh refinement, Comput. Fluids, in press, doi:10.1016/j.compfluid.2010.10.022. · Zbl 1271.76202
[89] van Leer, B., Towards the ultimate conservative difference scheme. V. A second-order sequel to godunov’s method, J. comput. phys., 32, 101, (1979) · Zbl 1364.65223
[90] Visit is available at <https://wci.llnl.gov/codes/visit/home.html>.
[91] Wang, P.; Abel, T.; Zhang, W., Relativistic hydrodynamic flows using spatial and temporal adaptive structured mesh refinement, Astrophys. J. suppl. ser., 176, 467, (2008)
[92] T. Wen, J. Su, P. Colella, K. Yelick, N. Koen, An adaptive mesh refinement benchmark for modern parallel programming languages, in: SC’07 Proceedings of the 2007 ACM/IEEE Conference on Supercomputing, doi:10.1145/1362622.1362676.
[93] H.C. Yee, A class of high-resolution explicit and implicit shock-capturing methods, NASA TM-101088, 1989.
[94] Zenitani, S.; Hesse, M.; Klimas, A., Scaling of the anomalous boost in relativistic jet boundary layer, Astrophys. J., 712, 951, (2010)
[95] Zhang, W.; MacFadyen, A.I., RAM: a relativistic adaptive mesh refinement hydrodynamics code, Astrophys. J. suppl. ser., 164, 255, (2006)
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