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A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics. (English) Zbl 1087.76090
Summary: We extend the special relativistic hydrodynamic (SRHD) equations [L. D. Landau, E. M. Lifshitz, Fluid mechanics, Pergamon, New York (1987; Zbl 0655.76001)] and as a limiting case the ultra-relativistic hydrodynamic equations [M. Kunik, S. Qamar, G. Warnecke, J. Comput. Phys. 187, No. 2, 572–596 (2003; Zbl 1061.76068 )] 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.

MSC:
76M28 Particle methods and lattice-gas methods
76W05 Magnetohydrodynamics and electrohydrodynamics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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