Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

Abstract

The single-mode Richtmyer-Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier-Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models.

Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

“…The HOTS has been validated to be stable and reasonably accurate for DNS of RMI at M S ≤ 1.6 (Liu & Xiao 2016;Peng et al 2021), and M S can be further increased (e.g. M S ≥ 2) by using the shock-resolved technique to solve the NS equations (see Kramer et al 2010).…”

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

“…Various definitions exist for mixing layer amplitude. 11,50 We define amplitude by a position weighted integral of the initial volume fraction for solids modeled by isotropic Mie-Grüneisen equations of state and mass fraction for perfect gases. Before roll up occurs, we define the interfaces centerline as y cd ðx; tÞ ¼ Ð 1 À1 ywðx; y; tÞð1 À wðx; y; tÞÞdy Ð 1 À1 wðx; y; tÞð1 À wðx; y; tÞÞdy ; (49) where w is the initial volume fraction.…”

“…A great deal of research has been performed on Richtmyer-Meshkov instability since its introduction. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] A common component of most previously performed experimental and computational work has been the use of gases at conditions close to room temperature and pressure. In light of this, the current investigation is focused on exploring the role of the equation of state in RichtmyerMeshkov instability specifically in relation to commonly studied perfect gas cases.…”