High order numerical simulations of the Richtmyer Meshkov instability in a relativistic fluid

TL;DR

This paper presents high-order numerical simulations of the relativistic Richtmyer-Meshkov instability using advanced adaptive mesh refinement techniques, revealing how relativistic effects influence instability growth and fluid mixing.

Contribution

It introduces a third-order accurate numerical scheme with adaptive mesh refinement for simulating relativistic RM instability, highlighting relativistic effects absent in Newtonian models.

Findings

Relativistic effects weaken and can suppress the RM instability at high Lorentz factors.

The growth rate of the instability peaks at a critical Lorentz factor between 1.2 and 2.

Non-zero tangential velocity components significantly alter the instability dynamics.

Abstract

We study the Richtmyer--Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme adopts a finite volume Weighted Essentially Non-Oscillatory (WENO) reconstruction to increase accuracy in space, a local space-time discontinuous Galerkin predictor method to obtain high order of accuracy in time and a high order one-step time update scheme together with a "cell-by-cell" space-time AMR strategy with time-accurate local time stepping. In this way, third order accurate (both in space and in time) numerical simulations of the RM instability are performed, spanning a wide parameter space. We present results both for the case in which a light fluid penetrates into a higher density one (Atwood number $A>0$), and for the case in which a heavy fluid penetrates into a lower density one (Atwood number $A<0$). We find that, for large Lorentz factors \gamma_s of the incident shock wave, the relativistic RM instability is substantially weakened and ultimately suppressed. More specifically, the growth rate of the RM instability in the linear phase has a local maximum which occurs at a critical value of \gamma_s ~ [1.2,2]. Moreover, we have also revealed a genuine relativistic effect, absent in Newtonian hydrodynamics, which arises in three dimensional configurations with a non-zero velocity component tangent to the incident shock front. In this case, the RM instability is strongly affected, typically resulting in less efficient mixing of the fluid.