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

[1]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[2]  S. Osher,et al.  Upwind difference schemes for hyperbolic systems of conservation laws , 1982 .

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

[4]  Bernd Einfeld On Godunov-type methods for gas dynamics , 1988 .

[5]  P. Frederickson,et al.  Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction , 1990 .

[6]  Kristine R. Meadows,et al.  Computational Study on the Interaction Between a Vortex and a Shock Wave , 1991 .

[7]  P. Roe,et al.  On Godunov-type methods near low densities , 1991 .

[8]  Peter A. Jacobs Approximate Riemann solver for hypervelocity flows , 1991 .

[9]  R. LeVeque Approximate Riemann Solvers , 1992 .

[10]  James P. Collins,et al.  Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics , 1993, SIAM J. Sci. Comput..

[11]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[12]  Rémi Abgrall APPROXIMATION DU PROBLEME DE RIEMANN VRAIMENT MULTIDIMENSIONNEL DES EQUATIONS D'EULER PAR UNE METHODE DE TYPE ROE (I) : LA LINEARISATION , 1994 .

[13]  Carole Rosier,et al.  Multi-dimensional Riemann problems for linear hyperbolic systems , 1996 .

[14]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[15]  Derek M. Causon,et al.  On the Choice of Wavespeeds for the HLLC Riemann Solver , 1997, SIAM J. Sci. Comput..

[16]  Michael Fey,et al.  Multidimensional Upwinding. Part I. The Method of Transport for Solving the Euler Equations , 1998 .

[17]  Michael Fey,et al.  Multidimensional Upwinding. Part II. Decomposition of the Euler Equations into Advection Equations , 1998 .

[18]  E. Muller,et al.  GENESIS: A High-Resolution Code for Three-dimensional Relativistic Hydrodynamics , 1999, astro-ph/9903352.

[19]  S. Komissarov,et al.  A Godunov-type scheme for relativistic magnetohydrodynamics , 1999 .

[20]  D. Balsara,et al.  A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations , 1999 .

[21]  Burton Wendroff,et al.  A two-dimensional HLLE riemann solver and associated godunov-type difference scheme for gas dynamics☆ , 1999 .

[22]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[23]  Dinshaw Balsara,et al.  Divergence-free adaptive mesh refinement for Magnetohydrodynamics , 2001 .

[24]  Aramais R. Zakharian,et al.  Two-dimensional Riemann solver for Euler equations of gas dynamics , 2001 .

[25]  Dinshaw S. Balsara,et al.  Total Variation Diminishing Scheme for Relativistic Magnetohydrodynamics , 2001 .

[26]  P. Londrillo,et al.  An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. Magnetohydrodynamics , 2002 .

[27]  E. Toro,et al.  Solution of the generalized Riemann problem for advection–reaction equations , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  N. Bucciantini,et al.  An efficient shock-capturing central-type scheme for multidimensional relativistic flows , 2002 .

[29]  Eleuterio F. Toro,et al.  ADER: Arbitrary High Order Godunov Approach , 2002, J. Sci. Comput..

[30]  Charles F. Gammie,et al.  HARM: A NUMERICAL SCHEME FOR GENERAL RELATIVISTIC MAGNETOHYDRODYNAMICS , 2003 .

[31]  Dinshaw Balsara,et al.  Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction , 2003, astro-ph/0308249.

[32]  Katharine Gurski,et al.  An HLLC-Type Approximate Riemann Solver for Ideal Magnetohydrodynamics , 2001, SIAM J. Sci. Comput..

[33]  J. Stone,et al.  An unsplit Godunov method for ideal MHD via constrained transport , 2005, astro-ph/0501557.

[34]  K. Kusano,et al.  A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics , 2005 .

[35]  Eleuterio F. Toro,et al.  ADER schemes for three-dimensional non-linear hyperbolic systems , 2005 .

[36]  INFN,et al.  The exact solution of the Riemann problem in relativistic magnetohydrodynamics , 2005, Journal of Fluid Mechanics.

[37]  Equation of State in Numerical Relativistic Hydrodynamics , 2006, astro-ph/0605550.

[38]  S. Komissarov On Some Recent Developments in Numerical Methods for Relativistic MHD , 2006 .

[39]  G. Bodo,et al.  An HLLC Solver for Relativistic Flows – II . , 2006 .

[40]  G. Bodo,et al.  An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics , 2006 .

[41]  O. Zanotti,et al.  ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics , 2007, 0704.3206.

[42]  Jonathan C. McKinney,et al.  WHAM : a WENO-based general relativistic numerical scheme -I. Hydrodynamics , 2007, 0704.2608.

[43]  Pekka Janhunen,et al.  HLLC solver for ideal relativistic MHD , 2007, J. Comput. Phys..

[44]  Department of Physics,et al.  WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics , 2007, gr-qc/0701109.

[45]  G. Bodo,et al.  A five-wave HLL Riemann solver for relativistic MHD , 2008, 0811.1483.

[46]  Michael Dumbser,et al.  A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes , 2008, J. Comput. Phys..

[47]  Phillip Colella,et al.  A limiter for PPM that preserves accuracy at smooth extrema , 2008, J. Comput. Phys..

[48]  B R U N O G I A C O M A Z Z O,et al.  Under consideration for publication in J. Fluid Mech. 1 The Exact Solution of the Riemann Problem in Relativistic MHD , 2008 .

[49]  James M. Stone,et al.  An unsplit Godunov method for ideal MHD via constrained transport in three dimensions , 2007, J. Comput. Phys..

[50]  Michael Dumbser,et al.  Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics , 2008, Journal of Computational Physics.

[51]  Dinshaw S. Balsara Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics , 2009, J. Comput. Phys..

[52]  M. J. Castro,et al.  ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows , 2009 .

[53]  Andrea Mignone,et al.  A five‐wave Harten–Lax–van Leer Riemann solver for relativistic magnetohydrodynamics , 2009 .

[54]  Universitat d'Alacant,et al.  RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER , 2009, 0912.4692.

[55]  Dinshaw S. Balsara Multidimensional HLLE Riemann solver: Application to Euler and magnetohydrodynamic flows , 2010, J. Comput. Phys..

[56]  Michael Dumbser,et al.  A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems , 2011, J. Sci. Comput..

[57]  Phillip Colella,et al.  A HIGH-ORDER FINITE-VOLUME METHOD FOR CONSERVATION LAWS ON LOCALLY REFINED GRIDS , 2011 .

[58]  Dinshaw S. Balsara,et al.  Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics , 2012, J. Comput. Phys..

[59]  Dinshaw S. Balsara A two-dimensional HLLC Riemann solver for conservation laws: Application to Euler and magnetohydrodynamic flows , 2012, J. Comput. Phys..

[60]  Michael Dumbser,et al.  Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes - Speed comparisons with Runge-Kutta methods , 2013, J. Comput. Phys..

[61]  Harvard,et al.  Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure , 2013, 1312.6127.

[62]  Dinshaw S. Balsara,et al.  A stable HLLC Riemann solver for relativistic magnetohydrodynamics , 2014, J. Comput. Phys..

[63]  Rémi Abgrall,et al.  Multidimensional HLLC Riemann solver for unstructured meshes - With application to Euler and MHD flows , 2014, J. Comput. Phys..

[64]  Michael Dumbser,et al.  High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics , 2013, 1310.7256.

[65]  Dinshaw S. Balsara,et al.  Multidimensional Riemann problem with self-similar internal structure. Part I - Application to hyperbolic conservation laws on structured meshes , 2014, J. Comput. Phys..

[66]  Michael Dumbser,et al.  Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers , 2013, J. Comput. Phys..

[67]  Dinshaw S. Balsara,et al.  Three dimensional HLL Riemann solver for conservation laws on structured meshes; Application to Euler and magnetohydrodynamic flows , 2015, J. Comput. Phys..

[68]  Michael Dumbser,et al.  Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers , 2015, J. Comput. Phys..

[69]  Roland Haas,et al.  IllinoisGRMHD: an open-source, user-friendly GRMHD code for dynamical spacetimes , 2015, 1501.07276.

[70]  Michael Dumbser,et al.  Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes , 2015, J. Comput. Phys..

[71]  Edouard Audit,et al.  A simple two-dimensional extension of the HLL Riemann solver for hyperbolic systems of conservation laws , 2015, J. Comput. Phys..

[72]  Michael Dumbser,et al.  Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables , 2015, Computational astrophysics and cosmology.

[73]  Michael Dumbser,et al.  A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems , 2016, J. Comput. Phys..

[74]  Dinshaw S. Balsara,et al.  A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism , 2016, J. Comput. Phys..

[75]  Michael Dumbser,et al.  A two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection , 2016, J. Comput. Phys..

[76]  M. Aloy,et al.  An HLLC Riemann solver for resistive relativistic magnetohydrodynamics , 2017, 1711.06691.