High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

Abstract

The interaction of a Mach 1.45 shock wave with a perturbed planar interface between sulphur hexafluoride and air is studied through high-resolution two-dimensional (2D) and three-dimensional (3D) shock-capturing adaptive mesh refinement simulations of multi-species Navier-Stokes equations. The sensitivities of time-dependent statistics on grid resolution for 2D and 3D simulations are evaluated to ensure the accuracy of the results. The numerical results are used to examine the differences between the development of 2D and 3D Richtmyer-Meshkov instability during two different stages: (1) initial growth of hydrodynamic instability from multi-mode perturbations after first shock and (2) transition to chaotic or turbulent state after re-shock. The effects of the Reynolds number on the mixing in 3D simulations are also studied through varying the transport coefficients. * wongml@stanford.edu † livescu@lanl.gov ‡

Rayleigh–Taylor Instability With Varying Periods of Zero Acceleration

“…For the AZ case, as the acceleration is withdrawn, we observe that B 33 slowly decays towards 0.1 as the mixing layer becomes progressively less anisotropic. This observation is consistent with studies of RMI [35,36]. The AD case exhibits internal wave like behavior as the acceleration is reversed; the vertical component of the anisotropy tensor is observed to oscillate as shown in Fig.…”

Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer

“…They highlighted that the two methods agreed in their predictions of large-scale flow features, but differed in their predictions of gradient-sensitive quantities such as enstrophy. Recent computational studies of reshocked mixing were conducted by Li et al (2019) and Wong, Livescu & Lele (2019). Many of the simulations referenced here (Schilling & Latini 2010;Thornber et al 2010Thornber et al , 2011Grinstein et al 2011;Hahn et al 2011;Malamud et al 2014) were implicit large-eddy simulations that did not include physical mass diffusivity, viscosity or thermal conductivity.…”

“…Recent computational studies of reshocked mixing were conducted by Li et al. (2019) and Wong, Livescu & Lele (2019). Many of the simulations referenced here (Schilling & Latini 2010; Thornber et al.…”

Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows1

“…Estimates of the power law decay of variable density total enstrophy X total may be derived following Fig. 8 Narrowband 3D compared to 2D in a term-by-term comparison -note that for the three dimensional case the baroclinic terms is predominantly negative initially at At 5 0.9, and mostly negative and very small throughout for all 3D cases hence the cases are plotted separately to allow log axes for the 2D cases: (a) X dimensionless, (b) q 23 xÁ ($q3 $p) (2D only), and (c) q 23 xÁ ($q3 $p) (2D and 3D) the methodology of Skrbek and Stalp [134], assuming a model spectrum and self-similarity for a large eddy simulation where enstrophy is resolved only in a range given by k min k k max where k max ¼ 2p=Dx is the maximum wavenumber resolved on a given grid (assumed isotropic) and k min ¼ 2p=L. A model kinetic energy power spectrum is assumed consisting of two power law ranges which meet at k e ¼ 2p=l e , with l e being the integral length, of the form:…”

“…Broadband 3D compared to 2D in a term-by-term comparison: (a) X time scaled and (b) q23 xÁ ($q3 $p) Visualizations of the two-dimensional narrowband computations at s 5 13:2 for the 2dnb05lwn case (top) and s 5 9:3 for the 2dnb05hwn case (bottom). Note that the contour flood is logarithmic-a variation of four orders of magnitude is shown: (a) 2dnb05lwn X, (b) 2dnb05lwn X, (c) 2dnb05lwn z 1 , (d) 2dnb05hwn X, (e) 2dnb05hwn X, and (f) 2dnb05hwn z 1 .…”