Corrugation instabilities of the Riemann problem in relativistic hydrodynamics

TL;DR

This paper investigates the stability of solutions to the Riemann problem in relativistic hydrodynamics, revealing that perturbations mainly affect contact discontinuities while shocks and rarefactions remain stable.

Contribution

It provides a numerical analysis of corrugation instabilities in relativistic Riemann problems with various equations of state and velocities.

Findings

Instabilities are localized around contact discontinuities.

Shock and rarefaction waves are stable under perturbations.

Results apply to moderately relativistic velocities.

Abstract

Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations both for ultrarelativistic and perfect gas equations of state. We focus on a set of problems with moderately relativistic velocities but exhausting all possible wave patterns of solutions. Perturbations are applied to the shape of the initial discontinuity. Instabilities that develop are only restricted to a region around a contact discontinuity. Both shock and rarefaction waves appear to be stable.