A Numerical Study of the Richtmyer–Meshkov Instability in a Relativistic Fluid using Multi-Directional Riemann Solvers and High-Order WENO Schemes

The present work focuses on relativistic hydrodynamic (RHD) simulations of the Richtmyer–Meshkov (RM) instability in 2D and assesses the performance of different numerical schemes. The RM instability is known to occur in various high-energy phenomena such as supernovae detonations and relativistic jets. The RHD equations are solved using the finite volume method (FVM) via a third-order TVD Runge–Kutta scheme for time integration and WENO reconstructions for spatial discretization. The effect of the imposed Riemann solver is studied via the comparative use of a Rusanov, HLL, and HLLC Riemann solver. A novel multi-directional approach has been used in which all fluxes have been computed by taking into account information propagation from all spatial directions. In particular, we investigate the linear growth-rate of the instability under a parameter space consisting of positive and negative Atwood numbers and varying shock-speed for a perfect gas. The growth-rate in the linear regime has been reported to peak in the mildly relativistic limit. We aim to shed light on the numerical influence and predictive capability of computational modelling relativistic fluids.