Total Variation Diminishing Scheme for Relativistic Magnetohydrodynamics
Open Access
- 1 January 2001
- journal article
- research article
- Published by American Astronomical Society in The Astrophysical Journal Supplement Series
- Vol. 132 (1) , 83-101
- https://doi.org/10.1086/318941
Abstract
In this paper we present a total variation diminishing (TVD) scheme for numerical relativistic magnetohydrodynamics (MHD). The eigenstructure of the equations of relativistic MHD has been cataloged here. We also describe a strategy for obtaining the physically relevant eigenvectors. These eigenvectors are then used to build an interpolation strategy that operates on the characteristic fields. The design of a linearized Riemann solver for relativistic MHD is also described. The resulting higher order Godunov scheme has been implemented in the author's RIEMANN code for astrophysical fluid dynamics. The resulting code is second-order accurate both in space and time. A number of design features have been used to make it a high-resolution scheme. It shows efficient and robust performance for several stringent test problems.Keywords
This publication has 35 references indexed in Scilit:
- Linearized formulation of the Riemann problem for radiation magnetohydrodynamicsJournal of Quantitative Spectroscopy and Radiative Transfer, 1999
- LINEARIZED FORMULATION OF THE RIEMANN PROBLEM FOR RADIATION HYDRODYNAMICSJournal of Quantitative Spectroscopy and Radiative Transfer, 1999
- AN ANALYSIS OF THE HYPERBOLIC NATURE OF THE EQUATIONS OF RADIATION HYDRODYNAMICSJournal of Quantitative Spectroscopy and Radiative Transfer, 1999
- THE EIGENSTRUCTURE OF THE EQUATIONS OF RADIATION MAGNETOHYDRODYNAMICSJournal of Quantitative Spectroscopy and Radiative Transfer, 1999
- A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic SimulationsJournal of Computational Physics, 1999
- Maintaining Pressure Positivity in Magnetohydrodynamic SimulationsJournal of Computational Physics, 1999
- Total Variation Diminishing Scheme for Adiabatic and Isothermal MagnetohydrodynamicsThe Astrophysical Journal Supplement Series, 1998
- Linearized Formulation of the Riemann Problem for Adiabatic and Isothermal MagnetohydrodynamicsThe Astrophysical Journal Supplement Series, 1998
- Riemann Solver for Relativistic HydrodynamicsJournal of Computational Physics, 1994
- Relativistic Fluids and Magneto-fluidsPublished by Cambridge University Press (CUP) ,1990