A Global Arbitrary Lagrangian-Eulerian Method for Stratified Richtmyer-Meshkov Instability

摘要

Richtmyer -- Meshkov (RM) instability arises when a material interface is accelerated impulsively by shock waves. In this work, an arbitrary Lagrangian-Eulerian method, global ALE method, was proposed for the simulation of stratified RM instability. In the global ALE method, an Eulerian diffusion interface model was implemented based on mass fraction function. Thus all the meshes can be remeshed arbitrarily no matter whether they are material interface or not. Some benchmark problems, such as shock tube problem with different specific ratio, RM instability with small initial perturbation, were computed with the global ALE method, and the numerical results agree well with exact solution or theoretical model. Also, we proposed some stratified RM instability model problems with two or more material interfaces in planar, cylindrical and spherical geometries. Then the stratified RM instabilities were simulated with global ALE method. The interface evolution process was studied and compared in different geometry cases based on simulation results. To overcome the spurious mesh distortion, a sub-zonal Riemann solver method was proposed in appendix part of the paper based on the analysis of the error source of 2D Lagrangian computation due to non-uniform multidimensional mesh.