Modal Discontinuous Galerkin Simulations of Richtmyer–Meshkov Instability at Backward-Triangular Bubbles: Insights and Analysis

This paper investigates the dynamics of Richtmyer–Meshkov instability (RMI) in shocked
backward-triangular bubbles through numerical simulations. Two distinct gases, He and SF6, are
used within the backward-triangular bubble, surrounded by N2 gas. Simulations are conducted
at two distinct strengths of incident shock wave, including Ms = 1.25 and 1.50. A third-order
modal discontinuous Galerkin (DG) scheme is applied to simulate a physical conservation laws
of two-component gas flows in compressible inviscid framework. Hierarchical Legendre modal
polynomials are employed for spatial discretization in the DG platform. This scheme reduces the
conservation laws into a semi-discrete set of ODEs in time, which is then solved using an explicit
3rd-order SSP Runge–Kutta scheme. The results reveal significant effects of bubble density and
Mach numbers on the growth of RMI in the shocked backward-triangular bubble, a phenomenon
not previously reported. These effects greatly influence flow patterns, leading to intricate wave
formations, shock focusing, jet generation, and interface distortion. Additionally, a detailed analysis
elucidates the mechanisms driving vorticity formation during the interaction process. The study
also thoroughly examines these effects on the flow fields based on various integral quantities and
interface characteristics.