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A High Order Kinetic Flux-Splitting Method for the Relativistic Magnetohydrodynamics

by Qamar, S., Warnecke, G..

Series: 2004-09, Preprints

65M99 None of the above, but in this section
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
85A30 Hydrodynamic and hydromagnetic problems

In this article we extend the special relativistic hydrodynamic (SRHD) equations
[Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] and as a limiting case the ultra-relativistic hydrodynamic equations
[Kunik, Qamar and Warnecke, {\em J. Comput. Phys}., 187 (2003) pp. 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 one dimensional 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.