Mach number effect on the high-amplitude Richtmyer–Meshkov instability using the DSMC method

Abstract

This study conducts a numerical investigation of the Richtmyer–Meshkov instability (RMI) at microscale Helium/Argon interfaces using the Direct Simulation Monte Carlo (DSMC) method. The hydrodynamic behaviour and evolutionary mechanisms governing the single-mode RMI with high-amplitude are discussed, with the consideration of different Mach numbers (Ma) ranging from 1.5 to 6.0. Key findings reveal two distinct evolutionary pathways. In the high-Mach regime (Ma ≥ 3), complex shock configurations form through the establishment of Mach stem, accompanied by sustained positive vorticity deposition along the slipstream. This persistent process drives cavity initiation at spike apices. In the low-Mach regime (Ma ≤ 2), gradual degradation of Mach stem to regular reflection configurations occurs, wherein viscous dissipation extinguishes the vorticity accumulation and suppresses cavity formation. Quantitative comparison with DSMC data demonstrates that the Zhang and Guo (ZG) theoretical model has a prediction error of less than 20% for the overall amplitude growth of RMI across different Ma numbers, yet overestimates the bubble amplitude growth with a prediction error of approximately 50%, particularly in the late nonlinear stage. A dedicated discussion on gas species is also presented, revealing that the ZG theoretical model aligns well with the DSMC-calculated overall amplitude growth at high Ma numbers, with relative errors below 20%. Furthermore, the influence of Ma on the discrepancy between ZG model predictions and DSMC data diminishes as the Atwood number increases.