A High Order Kinetic Flux-Splitting Method for the Special Relativistic Hydrodynamics

by Qamar, S.; Warnecke, G.


Preprint series: 04-08, Preprints

The paper is published: Accepted in International Journal of Computational Methods (IJCM)

65M99 None of the above but in this section
76Y05 Quantum hydrodynamics and relativistic hydrodynamics, See also {83C55, 85A30}
85A30 Hydrodynamic and hydromagnetic problems, See also {76Y05}


Abstract: In this article we present a flux splitting method based on gas-kinetic theory for the special relativistic hydrodynamics (SRHD) [Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] in one and two space dimensions. This kinetic method is based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle ``collisions\'\' are implemented in the free transport process to reduce numerical dissipation. Due to the nonlinear relations between conservative and primitive variables and the consequent complexity of the Jacobian matrix, the multi-dimensional shock-capturing numerical schemes for SRHD are computationally more expensive. All the previous methods presented for the solution of these equations were based on the macroscopic continuum description. These upwind high-resolution shock-capturing (HRSC) schemes, which were originally made for non-relativistic flows, were extended to SRHD. However our method, which is based on kinetic theory is more related to the physics of these equations and is very efficient, robust, and easy to implement. In order to get high order accuracy in space, we use a third order central weighted essentially non-oscillatory (CWENO) finite difference interpolation routine. To achieve high order accuracy in time we use a Runge-Kutta time stepping method. The one- and two-dimensional computations reported in this paper show the desired accuracy, high resolution, and robustness of the method.

Keywords: Special relativistic hydrodynamics, kinetic flux splitting method, high order reconstruction, conservation laws, hyperbolic systems, discontinuous solutions.

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