A new Godunov-type numerical code with a non-linear Riemann solver for equations of relativistic hydrodynamics

TL;DR

This paper introduces a second-order upwind numerical scheme for relativistic hydrodynamics that employs a novel non-linear Riemann solver, capable of accurately handling shocks and rarefactions in multiple dimensions.

Contribution

It develops a new 'exact' Riemann solver for relativistic hydrodynamics equations, improving accuracy and efficiency in numerical simulations.

Findings

Effective handling of strong shocks and rarefactions

Good performance demonstrated in 1D and 3D tests

Solver simplifies complex equations for non-zero tangential velocities

Abstract

We present a second-order upwind numerical scheme for equations of relativistic hydrodynamics with a source term. A new non-linear Riemann solver is constructed. Solution of a Riemann problem on a cells boundary is based on exact relations in case of zero tangential velocities. In this sense our solver is "exact". In case of non-zero tangential velocities a reasonable approximation is made that allows to avoid solution of very complicated exact equations. The scheme is tested on several one- and three-dimensional solutions demonstrating a good performance for both strong shocks and strong rarefactions.