Genuinely Multidimensional Physical-Constraints-Preserving Finite Volume Schemes for the Special Relativistic Hydrodynamics

Abstract

This paper develops the genuinely multidimensional HLL Riemann solver for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving (PCP) property. Based on the resulting HLL solver, the first- and high-order accurate PCP finite volume schemes are proposed. In the high-order scheme, the WENO reconstruction, the third-order accurate strong-stability-preserving time discretizations and the PCP flux limiter are used. Several numerical results are given to demonstrate the accuracy, performance and resolution of the shock waves and the genuinely multi-dimensional wave structures etc. of our PCP finite volume schemes.