An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
New algorithms for ultra-relativistic numerical hydrodynamics
Journal of Computational Physics
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Numerical simulation of the MHD equations by a kinetic-type method
Journal of Scientific Computing
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
Gas-kinetic theory-based flux splitting method for ideal magnetohydrodynamics
Journal of Computational Physics
A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Kinetic schemes for the ultra-relativistic Euler equations
Journal of Computational Physics
Kinetic schemes for the relativistic gas dynamics
Numerische Mathematik
A BGK-Type Flux-Vector Splitting Scheme for the Ultrarelativistic Euler Equations
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Finite element form of FDV for widely varying flowfields
Journal of Computational Physics
On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
Applied Numerical Mathematics
Journal of Computational Physics
Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics
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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.