Spherical Richtmyer-Meshkov instability for axisymmetric flow

Front tracking has proved to be an accurate and efficient algorithm in the sense that tracking the interface can reduce the error significantly [9,10]. By applying this algorithm, we conduct numerical simulations of Richtmyer-Meshkov (RM) instabilities in spherical geometry for axisymmetric flow. We demonstrate scaling invariance with respect to shock Mach number for fluid mixing statistics, such as growth rate and volume fraction. Here the mixing is related to bulk transport rather than molecular mixing. Our results are validated by convergence under both mesh refinement and statistical ensemble averaging. We also show that the spherical geometry will converge to planar geometry when the number of modes of interface perturbation goes to infinity.