A comparative numerical study of the Richtmyer-Meshkov instability with nonlinear analysis in two and three dimensions

A shock driven inter-facial instability, known as the Richtmyer-Meshkov instability, is studied numerically in two and three dimensions and in the nonlinear regime. The numerical solution is tested for convergence under computational mesh refinement and is compared with the predictions of a recently developed nonlinear theory based on the Padé approximation and asymptotic matching. Good agreement has been found between numerical solutions and predictions of the nonlinear theory in both two and three dimensions and for both the reflected shock and the reflected rarefaction wave cases. The numerical study is extended to the re-shock experiment in which the fluid interface interacts initially with the incident shock. Later, as the transmitted shock bounces back from the wall, the fluid interface is re-shocked.