Richtmyer-Meshkov instability in a rarefied gas, results of continuum and kinetic numerical simulations

Abstract

The Richtmyer–Meshkov instability in a rarefied gas is numerically simulated using both continuum and kinetic approaches. Continuum simulations based on the Navier–Stokes equations are carried out for different Mach numbers of the incident shock wave Ms = 1.5, 4.0, 8.0; Reynolds numbers Re = 50÷1000 and density ratios across the contact discontinuity ρ2/ρ1 = 2, 3, and 10. The evolution of disturbance amplitude as a function of the problem parameters is investigated. It is obtained that the growth of disturbances is suppressed if the Reynolds number decreases below some critical value. Kinetic simulations are performed by directly solving the Bhatnagar–Gross–Krook (BGK) kinetic equation in the multidimensional phase space. The development of the Richtmyer–Meshkov instability is reproduced with the kinetic approach and close agreement between the results of continuum and kinetic simulations is observed.