A numerical method for the special relativistic hydrodynamics equations based on a symmetric-hyperbolic Godunov-type formalism
I.M. Kulikov
Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: computational astrophysics, relativistic hydrodynamics, numerical methods
Abstract
The hyperbolicity preserving numerical solving of equations is a fundamental problem of computational mathematics. In the presence of relativistic effects and a magnetic field, the problem becomes even more complicated. The construction of numerical methods for solving continuum mechanics problems that allow one to control the hyperbolicity of a system of equations in solving the equations is an important problem formulated by Sergey Konstantinovich Godunov. This paper proposes an approach to constructing a Godunov-type scheme using a method of formulating the equations in the form of symmetric hyperbolic systems. An important property of this formalism, in addition to hyperbolicity control, is the use of all waves in solving the Riemann problem, which allows one to reproduce the tangential discontinuities with the quality of the Roe and HLLC schemes. The use of an operator splitting into the pressure forces and the advective transfer in the Riemann problem makes it possible to eliminate the ``sonic point'' problem, which may occur in Roe-type schemes. The scheme is verified by using some classical tests on the breakdown of a discontinuity in one-dimensional and two-dimensional formulations.
|
