A physical-constraints-preserving genuinely multidimensional HLL scheme for the special relativistic hydrodynamics

TL;DR

This paper introduces a new genuinely multidimensional HLL Riemann solver and finite volume scheme for 2D special relativistic hydrodynamics, ensuring physical constraints and improving shock wave resolution.

Contribution

It develops a novel multidimensional HLL scheme with PCP properties for relativistic hydrodynamics, enhancing accuracy and shock capturing capabilities.

Findings

Demonstrates high accuracy in numerical tests

Shows improved shock wave resolution

Validates physical-constraint-preserving property

Abstract

This paper develops the genuinely multidimensional HLL Riemann solver and finite volume scheme for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving (PCP) property. Several numerical results demonstrate the accuracy, the performance and the resolution of the shock waves and the genuinely multi-dimensional wave structures of the proposed PCP scheme.