High-fidelity simulations of Richtmyer–Meshkov flows triggered by a forward-pentagonal bubble with different Atwood numbers

Abstract

In fluid dynamics, the Atwood number is a dimensionless parameter that quantifies the density difference between two fluids. It is calculated as $At=({\rho }_1-{\rho }_2)/({\rho }_1+{\rho }_2)$, where ${\rho }_1$ and ${\rho }_2$ represent the densities of the respective fluids. This research employs high-fidelity numerical simulations to examine the Atwood number impacts on Richtmyer–Meshkov (RM) flows triggered by a shocked forward-pentagonal bubble. Five distinct gases — ${\text{SF}}_6$, Kr, Ar, Ne, and He — are considered within the forward-pentagonal bubble, encompassed by ${\text{N}}_2$ gas. In these simulations, a third-order discontinuous Galerkin approach is applied to solve a two-dimensional set of compressible Navier–Stokes-Fourier (NSF) equations for two-component gas flows. To discretize space, hierarchical modal basis functions based on orthogonal-scaled Legendre polynomials are employed. This approach simplifies the NSF equations into a set of ordinary differential equations over time, which are solved using an explicit third-order SSP Runge–Kutta algorithm. The numerical results highlight the notable impact of the Atwood number on the evolution of RM flows in the shocked forward-pentagonal bubble, a phenomenon not previously reported in the literature. The Atwood number exerts a significant influence on the flow patterns, leading to intricate wave formations, shock focusing, jet generation, and interface distortion. Moreover, a comprehensive analysis of the these impact elucidates the mechanisms driving vorticity formation during the interaction process. Additionally, the study conducts a thorough quantitative examination of the Atwood number impacts on the flow fields based on integral quantities and interface features.