Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics
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[1] Paul R. Woodward,et al. An approximate Riemann solver for ideal magnetohydrodynamics , 1994 .
[2] J. Flaherty,et al. Parallel, adaptive finite element methods for conservation laws , 1994 .
[3] Phillip Colella,et al. A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics , 1994, SIAM J. Sci. Comput..
[4] P. Woodward,et al. The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .
[5] P. Londrillo,et al. High-Order Upwind Schemes for Multidimensional Magnetohydrodynamics , 1999, astro-ph/9910086.
[6] C. Munz,et al. Hyperbolic divergence cleaning for the MHD equations , 2002 .
[7] Chi-Wang Shu,et al. Efficient Implementation of Weighted ENO Schemes , 1995 .
[8] Equation of State in Numerical Relativistic Hydrodynamics , 2006, astro-ph/0605550.
[9] The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics , 2000, Journal of Fluid Mechanics.
[10] G. Tóth. The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes , 2000 .
[12] R. Blandford,et al. Fluid dynamics of relativistic blast waves , 1976 .
[13] E. Müller,et al. Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics , 2015, Living reviews in computational astrophysics.
[14] W. H. Reed,et al. Triangular mesh methods for the neutron transport equation , 1973 .
[15] J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .
[16] Angelo Marcello Anile,et al. Relativistic fluids and magneto-fluids , 2005 .
[17] Chi-Wang Shu,et al. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .
[18] Chi-Wang Shu,et al. Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..
[19] J. Brackbill,et al. The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations☆ , 1980 .
[20] Michael Dumbser,et al. A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement , 2013, Comput. Phys. Commun..
[21] L. Rezzolla,et al. THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics , 2012, 1206.6502.
[22] J. Gibbs. Fourier's Series , 1898, Nature.
[23] R. Courant,et al. Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .
[24] Ewald Müller,et al. Extension of the Piecewise Parabolic Method to One-Dimensional Relativistic Hydrodynamics , 1996 .
[25] Z. Wang. High-order methods for the Euler and Navier–Stokes equations on unstructured grids , 2007 .
[26] John H. Kolias,et al. A CONSERVATIVE STAGGERED-GRID CHEBYSHEV MULTIDOMAIN METHOD FOR COMPRESSIBLE FLOWS , 1995 .
[27] T. A. Zang,et al. Spectral Methods: Fundamentals in Single Domains , 2010 .
[28] J. Hawley,et al. Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .
[29] Claus-Dieter Munz,et al. Maxwell's equations when the charge conservation is not satisfied , 1999 .
[30] Steven J. Ruuth,et al. A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods , 2002, SIAM J. Numer. Anal..
[31] N. Bucciantini,et al. An efficient shock-capturing central-type scheme for multidimensional relativistic flows , 2002 .
[32] James M. Stone,et al. MOCCT: A numerical technique for astrophysical MHD , 1995 .
[33] K. Powell. An Approximate Riemann Solver for Magnetohydrodynamics , 1997 .
[34] Dongsu Ryu,et al. Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow , 1995 .
[35] Claus-Dieter Munz,et al. Explicit Discontinuous Galerkin methods for unsteady problems , 2012 .
[36] Rosa Donat,et al. A Flux-Split Algorithm applied to Relativistic Flows , 1998 .
[37] L. Rezzolla,et al. An improved exact Riemann solver for relativistic hydrodynamics , 2001, Journal of Fluid Mechanics.
[38] Claus-Dieter Munz,et al. New Algorithms for Ultra-relativistic Numerical Hydrodynamics , 1993 .
[39] Chi-Wang Shu,et al. Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters , 2005, SIAM J. Sci. Comput..
[40] Paul R. Woodward,et al. On the Divergence-free Condition and Conservation Laws in Numerical Simulations for Supersonic Magnetohydrodynamical Flows , 1998 .
[41] James M. Stone,et al. A SECOND-ORDER GODUNOV METHOD FOR MULTI-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMICS , 2011, 1101.3573.
[42] David A. Kopriva,et al. Implementing Spectral Methods for Partial Differential Equations , 2009 .
[43] Jun Zhu,et al. Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes , 2013, J. Comput. Phys..
[44] W. F. Noh. Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .
[45] A. Love,et al. Fourier's Series , 1898, Nature.
[46] Luciano Rezzolla,et al. Numerical Relativistic Hydrodynamics: HRSC Methods , 2013 .
[47] Philip A. Hughes,et al. Simulations of Relativistic Extragalactic Jets , 1994 .
[48] Ewald Müller,et al. The analytical solution of the Riemann problem in relativistic hydrodynamics , 1994, Journal of Fluid Mechanics.
[49] Paul R. Woodward,et al. Extension of the Piecewise Parabolic Method to Multidimensional Ideal Magnetohydrodynamics , 1994 .
[50] Huazhong Tang,et al. An Adaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics , 2012 .
[51] Claus-Dieter Munz,et al. Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Subcells , 2014 .
[52] Luciano Rezzolla,et al. Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes , 2011, 1103.2426.
[53] P. Teuben,et al. Athena: A New Code for Astrophysical MHD , 2008, 0804.0402.
[54] Lilia Krivodonova,et al. Limiters for high-order discontinuous Galerkin methods , 2007, J. Comput. Phys..
[55] A. Harten. High Resolution Schemes for Hyperbolic Conservation Laws , 2017 .
[56] Weiqun Zhang,et al. RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code , 2005, astro-ph/0505481.
[57] Guang-Shan Jiang,et al. A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics , 1999 .
[58] D. Balsara,et al. A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations , 1999 .
[59] Jonathan C. McKinney,et al. WHAM : a WENO-based general relativistic numerical scheme -I. Hydrodynamics , 2007, 0704.2608.
[60] Michael Dumbser,et al. Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters , 2005, SIAM J. Sci. Comput..
[61] Manuel Torrilhon,et al. Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics , 2003 .
[62] M. Brio,et al. An upwind differencing scheme for the equations of ideal magnetohydrodynamics , 1988 .
[63] G. Bodo,et al. The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics , 2005, astro-ph/0505200.
[64] Jonatan Núñez-de la Rosa. High-order methods for computational astrophysics , 2015 .
[65] Chi-Wang Shu. Total-variation-diminishing time discretizations , 1988 .
[66] A. Ferrari,et al. PLUTO: A Numerical Code for Computational Astrophysics , 2007, astro-ph/0701854.
[67] E. Müller,et al. Numerical Hydrodynamics in Special Relativity , 1999, Living reviews in relativity.
[68] Claus-Dieter Munz,et al. xtroem-fv: a new code for computational astrophysics based on very high order finite-volume methods – II. Relativistic hydro- and magnetohydrodynamics , 2016 .
[69] Michael Dumbser,et al. A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes , 2016, J. Comput. Phys..
[70] S. Orszag,et al. Small-scale structure of two-dimensional magnetohydrodynamic turbulence , 1979, Journal of Fluid Mechanics.
[71] Chi-Wang Shu,et al. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems , 1989 .
[72] Chi-Wang Shu,et al. The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V , 1998 .
[73] W. Schiesser. The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .
[74] Andrea Mignone,et al. High-order conservative finite difference GLM-MHD schemes for cell-centered MHD , 2010, J. Comput. Phys..
[75] B. M. Fulk. MATH , 1992 .
[76] Michael Dumbser,et al. A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws , 2014, J. Comput. Phys..
[77] E. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .
[78] S. Osher,et al. Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .
[79] S. Osher,et al. Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .
[80] Claus-Dieter Munz,et al. xtroem-fv: a new code for computational astrophysics based on very high order finite-volume methods – I. Magnetohydrodynamics , 2016 .
[81] Chi-Wang Shu,et al. TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .
[82] Andrew G. Glen,et al. APPL , 2001 .
[83] Chi-Wang Shu,et al. High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems , 2009, SIAM Rev..
[84] Claus-Dieter Munz,et al. Efficient Parallelization of a Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Sub-cells , 2017, J. Sci. Comput..
[85] Antonio Huerta,et al. One‐dimensional shock‐capturing for high‐order discontinuous Galerkin methods , 2013 .
[86] Hans De Sterck,et al. High-order central ENO finite-volume scheme for ideal MHD , 2013 .
[87] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[88] D. Kopriva. A Conservative Staggered-Grid Chebyshev Multidomain Method for Compressible Flows. II. A Semi-Structured Method , 1996 .