Validation of SPHC and CRASH codes in modeling of linear and non-linear Richtmyer-Meshkov instabilities

Abstract

Richtmyer-Meshkov instability (RMI) plays an important role in a broad variety of phenomena in nature and technology and is of special interest in the fields of shockturbulence interaction, supersonic aerodynamic flows, and inertial and magneto-inertial fusion. The instability develops when a shock refracts an interface between two fluids with different values of the acoustic impedance, and RMI dynamics is defined primarily by the flow Mach number and the Atwood number for the two fluids. For continuous fluid dynamic (CFD) codes, numerical modeling of RMI is a severe task, which imposes high requirements on the resolution, accuracy and spatio-temporal dynamic range of the simulations. Modeling of high-Atwood and high-Mach flows, which are of interest in practical applications, is even more challenging, as it requires shock capturing, interface tracking and accurate accounting for the dissipation processes. We used Smooth Particle Hydrodynamics Code (SPHC) and Center for RAdiative Shock Hydrodynamics (CRASH) codes to mutually evaluate the codes and compare their results against the analytical RMI theory. The numerical and theoretical results are in good qualitative and quantitative agreement with one another. These results indicate that at large scales the nonlinear dynamics of RMI is a multi-scale processes; at small scale the flow field is heterogeneous and is characterized by appearance of local microscopic structures; the coupling between the scales has a complicated character.