A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector

Journal of Computational Physics - Tập 312 - Trang 357-384 - 2016
Dinshaw S. Balsara1, Jinho Kim1
1Physics Department, University of Notre Dame, USA

Tài liệu tham khảo

Abgrall, 1994, Approximation du problème de Riemann vraiment multidimensionnel des équations d'Euler par une méthode de type Roe, I: la linéarisation, C.R. Acad. Sci. Ser. I, 319, 499 Abgrall, 1994, Approximation du problème de Riemann vraiment multidimensionnel des équations d'Euler par une méthode de type Roe, II: solution du problème de Riemann approché, C.R. Acad. Sci. Ser. I, 319, 625 Aloy, 1999, GENESIS: a high resolution code for three-dimensional general relativistic hydrodynamics, Astrophys. J. Suppl., 166, 122 Anton, 2010, Relativistic MHD: renormalized eigenvectors and full wave decomposition Riemann solver, Astrophys. J. Suppl., 188, 1, 10.1088/0067-0049/188/1/1 Balsara, 1999, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations, J. Comput. Phys., 149, 270, 10.1006/jcph.1998.6153 Balsara, 2000, Monotonicity preserving weighted non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys., 160, 405, 10.1006/jcph.2000.6443 Balsara, 2001, Total variation diminishing scheme for relativistic magnetohydrodynamics, Astrophys. J. Suppl., 132, 83, 10.1086/318941 Balsara, 2001, Divergence-free adaptive mesh refinement for magnetohydrodynamics, J. Comput. Phys., 174, 614, 10.1006/jcph.2001.6917 Balsara, 2004, Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction, Astrophys. J. Suppl., 151, 149, 10.1086/381377 Balsara, 2009, Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics, J. Comput. Phys., 228, 5040, 10.1016/j.jcp.2009.03.038 Balsara, 2009, Efficient, high-accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics, J. Comput. Phys., 228, 2480, 10.1016/j.jcp.2008.12.003 Balsara, 2010, Multidimensional HLLE Riemann solver, application to Euler and magnetohydrodynamic flows, J. Comput. Phys., 229, 1970, 10.1016/j.jcp.2009.11.018 Balsara, 2012, Self-Adjusting positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, J. Comput. Phys., 231, 7504, 10.1016/j.jcp.2012.01.032 Balsara, 2012, A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows, J. Comput. Phys., 231, 7476, 10.1016/j.jcp.2011.12.025 Balsara, 2013, Efficient implementation of ADER schemes for Euler and magnetohydrodynamic flow on structured meshes – comparison with Runge–Kutta methods, J. Comput. Phys., 235, 934, 10.1016/j.jcp.2012.04.051 Balsara, 2014, Multidimensional HLL and HLLC Riemann solvers for unstructured meshes – with application to Euler and MHD flows, J. Comput. Phys., 261, 172, 10.1016/j.jcp.2013.12.029 Balsara, 2014, Multidimensional Riemann problem with self-similar internal structure – Part I – application to hyperbolic conservation laws on structured meshes, J. Comput. Phys., 277, 163, 10.1016/j.jcp.2014.07.053 Balsara, 2015, Multidimensional Riemann problem with self-similar internal structure – Part II – application to hyperbolic conservation laws on unstructured meshes, J. Comput. Phys., 287, 269, 10.1016/j.jcp.2014.11.004 Balsara, 2015, Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers, J. Comput. Phys., 299, 687, 10.1016/j.jcp.2015.07.012 Balsara, 2015, Three dimensional HLL Riemann solver for structured meshes; application to Euler and MHD flow, J. Comput. Phys., 295, 1, 10.1016/j.jcp.2015.03.056 Balsara, 2016, A two-dimensional Riemann solver with self-similar sub-structure – alternative formulation based on least squares projection, J. Comput. Phys., 304, 138, 10.1016/j.jcp.2015.10.013 Balsara, 2016, High order accuracy divergence-free scheme for the electrodynamics of relativistic plasmas with multidimensional Riemann solvers, J. Comput. Phys., 10.1016/j.jcp.2016.05.006 Balsara, 2016, Formulating multidimensional Riemann solvers in similarity variables – part III: a multidimensional analogue of the HLLEM Riemann solver for conservative hyperbolic systems, J. Comput. Phys. Barth, 1990, Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction Batten, 1997, On the choice of wavespeeds for the HLLC Riemann solver, SIAM J. Sci. Comput., 18, 1553, 10.1137/S1064827593260140 Boscheri, 2014, Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers, J. Comput. Phys., 267, 112, 10.1016/j.jcp.2014.02.023 Boscheri, 2014, High order Lagrangian ADER-WENO schemes on unstructured meshes – application of several node solvers to hydrodynamics and magnetohydrodynamics, Int. J. Numer. Methods Fluids, 76, 737, 10.1002/fld.3947 Brio, 2001, Two-dimensional Riemann solver for Euler equations of gas dynamics, J. Comput. Phys., 167, 177, 10.1006/jcph.2000.6666 Colella, 1984, The piecewise parabolic method (PPM) for gas dynamical simulations, J. Comput. Phys., 54, 174, 10.1016/0021-9991(84)90143-8 Colella, 2008, A limiter for PPM that preserves accuracy at smooth extrema, J. Comput. Phys., 227, 7069, 10.1016/j.jcp.2008.03.034 Del Zanna, 2003, An efficient shock-capturing central-type scheme for multidimensional relativistic flows, Astron. Astrophys., 400, 397, 10.1051/0004-6361:20021641 Del Zanna, 2007, ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics, Astron. Astrophys., 473, 11, 10.1051/0004-6361:20077093 Dumbser, 2008, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes, J. Comput. Phys., 227, 8209, 10.1016/j.jcp.2008.05.025 Dumbser, 2009, ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows, Comput. Fluids, 38, 1731, 10.1016/j.compfluid.2009.03.008 Dumbser, 2011, A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems, J. Sci. Comput., 48, 88 Dumbser, 2016, A new, efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems, J. Comput. Phys., 304, 275, 10.1016/j.jcp.2015.10.014 Einfeldt, 1988, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25, 294, 10.1137/0725021 Einfeldt, 1991, On Godunov-type methods near low densities, J. Comput. Phys., 92, 273, 10.1016/0021-9991(91)90211-3 Etienne, 2015, IllinoisGRMHD: an open-source, user-friendly GRMHD code for dynamical spacetimes, Class. Quantum Gravity, 32, 10.1088/0264-9381/32/17/175009 Fey, 1998, Multidimensional upwinding 1. The method of transport for solving the Euler equations, J. Comput. Phys., 143, 159, 10.1006/jcph.1998.5958 Fey, 1998, Multidimensional upwinding 2. Decomposition of the Euler equation into advection equation, J. Comput. Phys., 143, 181, 10.1006/jcph.1998.5959 Gammie, 2003, HARM: a numerical scheme for general relativistic magnetohydrodynamics, Astrophys. J., 589, 444, 10.1086/374594 Gardiner, 2005, An unsplit Godunov method for ideal MHD via constrained transport, J. Comput. Phys., 205, 509, 10.1016/j.jcp.2004.11.016 Gardiner, 2008, An unsplit Godunov method for ideal MHD via constrained transport in three dimensions, J. Comput. Phys., 227, 4123, 10.1016/j.jcp.2007.12.017 Giacomazzo, 2007, WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics, Class. Quantum Gravity, 24, S235, 10.1088/0264-9381/24/12/S16 Giacomazzo, 2006, The exact solution of the Riemann problem in relativistic magnetohydrodynamics, J. Fluid Mech., 562, 223, 10.1017/S0022112006001145 Gilquin, 1993, Multidimensional Riemann problems for linear hyperbolic systems, Notes Numer. Fluid Mech., 43, 284 Gurski, 2004, An HLLC-type approximate Riemann solver for ideal magnetohydrodynamics, SIAM J. Sci. Comput., 25, 2165, 10.1137/S1064827502407962 Honkkila, 2007, HLLC solver for relativistic MHD, J. Comput. Phys., 223, 643, 10.1016/j.jcp.2006.09.027 Jiang, 1996, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126, 202, 10.1006/jcph.1996.0130 Kim, 2014, A stable HLLC Riemann solver for relativistic magnetohydrodynamics, J. Comput. Phys., 270, 634, 10.1016/j.jcp.2014.04.023 Komissarov, 1999, A Godunov-type scheme for relativistic MHD, Mon. Not. R. Astron. Soc., 303, 343, 10.1046/j.1365-8711.1999.02244.x Komissarov, 2006, On some recent developments in numerical methods for relativistic MHD, AIP Conf. Proc., 856, 129, 10.1063/1.2356388 Li, 2005, An HLLC Riemann solver for magnetohydrodynamics, J. Comput. Phys., 203, 344, 10.1016/j.jcp.2004.08.020 Meadows, 1989 McCorquodale, 2011, A high order finite volume method for conservation laws on locally refined grids, Commun. Appl. Math. Comput. Sci., 6, 1, 10.2140/camcos.2011.6.1 McKinney, 2014, Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure, Mon. Not. R. Astron. Soc., 441, 3177, 10.1093/mnras/stu762 Mignone, 2006, An HLLC Riemann solver for relativistic flows II – magnetohydrodynamics, Mon. Not. R. Astron. Soc., 368, 1040, 10.1111/j.1365-2966.2006.10162.x Mignone, 2009, A five-wave HLL Riemann solver for relativistic MHD, Mon. Not. R. Astron. Soc., 393, 1141, 10.1111/j.1365-2966.2008.14221.x Miyoshi, 2005, A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics, J. Comput. Phys., 208, 315, 10.1016/j.jcp.2005.02.017 Osher, 1982, Upwind difference schemes for hyperbolic systems of conservation laws, Math. Comput., 38, 339, 10.1090/S0025-5718-1982-0645656-0 Pao, 1981 Roe, 1981, Approximate Riemann solver, parameter vectors and difference schemes, J. Comput. Phys., 43, 357, 10.1016/0021-9991(81)90128-5 Ryu, 2006, Equation of state in numerical relativistic hydrodynamics, Astrophys. J. Suppl., 166, 410, 10.1086/505937 Schulz-Rinne, 1993, Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput., 14, 1394, 10.1137/0914082 Tchekhovskoy, 2007, WHAM: a WENO-based general relativistic numerical scheme – I. Hydrodynamics, Mon. Not. R. Astron. Soc., 379, 469, 10.1111/j.1365-2966.2007.11876.x Titarev, 2002, ADER: arbitrary high order Godunov approach, J. Sci. Comput., 17, 609, 10.1023/A:1015126814947 Titarev, 2005, ADER schemes for three-dimensional nonlinear hyperbolic systems, J. Comput. Phys., 204, 715, 10.1016/j.jcp.2004.10.028 Toro, 2002, Solution of the generalized Riemann problem for advection reaction equations, Proc. R. Soc. Lond. Ser. A, 458, 271, 10.1098/rspa.2001.0926 Toro, 1994, Restoration of the contact surface in the Harten–Lax–van Leer Riemann solver, Shock Waves, 4, 25, 10.1007/BF01414629 Vides, 2015, A simple two-dimensional extension of the HLL Riemann solver for hyperbolic conservation laws, J. Comput. Phys., 280, 643, 10.1016/j.jcp.2014.10.013 Wendroff, 1999, A two-dimensional HLLE Riemann solver and associated Godunov-type difference scheme for gas dynamics, Comput. Math. Appl., 38, 175, 10.1016/S0898-1221(99)00296-5 Zanotti, 2016, Efficient conservative ADER schemes based on WENO reconstruction and space–time predictor in primitive variables, Comput. Astrophys. Cosmol., 3, 1, 10.1186/s40668-015-0014-x