Analytic solutions of the Riemann problem in relativistic hydrodynamics and their numerical applications

TL;DR

This paper derives an analytic solution for the Riemann problem in relativistic hydrodynamics with specific conditions and demonstrates its application through a 3D numerical code tested against the solution.

Contribution

It provides the first analytic solution for the Riemann problem in relativistic hydrodynamics with ultra-relativistic equation of state and tangential velocities.

Findings

Analytic solution matches numerical code results

Code accurately simulates relativistic hydrodynamics scenarios

Enhances understanding of relativistic shock waves

Abstract

We present an analytic solution of the Riemann problem for the equations of relativistic hydrodynamics with the ultra-relativistic equation of state and non-zero tangential velocities. A 3-dimensional numerical code solving such equations is described and then tested against the analytic solution.