A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics

Journal Article · Sun May 01 04:00:00 EDT 2005 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2004.11.004· OSTI ID:20687230

Qamar, Shamsul ^[1]; Warnecke, Gerald ^[1]

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1. Institute for Analysis and Numerics, Otto-von-Guericke University PSF 4120, D-39106 Magdeburg (Germany)

In this paper we extend the special relativistic hydrodynamic (SRHD) equations [L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, New York, 1987] and as a limiting case the ultra-relativistic hydrodynamic equations [M. Kunik, S. Qamar, G. Warnecke, J. Comput. Phys. 187 (2003) 572-596] to the special relativistic magnetohydrodynamics (SRMHD). We derive a flux splitting method based on gas-kinetic theory in order to solve these equations in one space dimension. The scheme is based on the direct splitting of macroscopic flux functions with consideration of particle transport. At the same time, particle 'collisions' are implemented in the free transport process to reduce numerical dissipation. To achieve high-order accuracy we use a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. For the direct comparison of the numerical results, we also solve the SRMHD equations with the well-developed second-order central schemes. The 1D computations reported in this paper have comparable accuracy to the already published results. The results verify the desired accuracy, high resolution, and robustness of the kinetic flux splitting method and central schemes.

• OSTI ID: 20687230
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 205; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
CHARGED-PARTICLE TRANSPORT
COMPARATIVE EVALUATIONS
CONSERVATION LAWS
EQUATIONS
HYDRODYNAMIC MODEL
MAGNETOHYDRODYNAMICS
MATHEMATICAL SOLUTIONS
RELATIVISTIC RANGE