Numerical simulation of Richtmyer–Meshkov instabilities

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Abstract
The results of detailed numerical simulations of the Richtmyer–Meshkov instability of the interface between layers of air and either helium or SF6 in a shock tube are reported. Two- and three-dimensional simulations based on both the Euler and Navier–Stokes equations were obtained by a finite difference method that employs a front-tracking technique to keep the interface sharp. The nature of the flow patterns induced by the instability is discussed. The results of a numerical resolution study and a demonstration of the influence of boundary layers are presented also. Agreement with experimental data is found to be satisfactory, with the exception of the initial instability growth rate.