Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer—Meshkov Instability

Abstract

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. 90 (2010) 54003]. We discuss the reason why the Gram—Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka—Tsutahara model [Phys. Rev. E 69 (2004) 035701 (R)] is only valid in subsonic flows. The von Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer—Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang—Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.