Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics

TL;DR

This paper introduces a new genuinely multidimensional finite volume scheme for special relativistic hydrodynamics that preserves physical constraints and demonstrates high accuracy and shock resolution.

Contribution

It develops the first genuinely multidimensional PCP finite volume schemes for relativistic hydrodynamics using a novel HLL Riemann solver.

Findings

The schemes accurately resolve shock waves and wave structures.

The high-order scheme achieves third-order accuracy.

Numerical results confirm the physical-constraint preservation and effectiveness.

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 etc. as well as the genuinely multi-dimensional wave structures of our PCP finite volume schemes.