High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

Abstract

The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513 × 257 2 three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF 6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed flow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

“…Individual terms in VD transport equations such as (4.3) and (4.5) have heretofore not been measured experimentally: only high-resolution simulations have yielded estimates of terms in these types of model equations for VD flows. For example, high-resolution weighted essentially non-oscillatory (WENO) simulations have been used to examine amplification of turbulence through production of turbulence kinetic energy (TKE) after reshock (Schilling & Latini 2010). Also, in a reshocked RM flow, Moran-Lopez & Schilling (2013) examined mechanisms of the TKE evolution in a RANS framework, observing that shear production was balanced by molecular and turbulent diffusion of TKE as the dominant terms.…”

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

“…It is no surprise, therefore, that the characterization of the dissipative behavior of various WENO type schemes is an important area of interest in the computational fluid dynamics community [27][28][29]. Although the primary motivation for the development of non-oscillatory upwinding schemes was for the simulation of hyperbolic conservation laws with sharp discontinuities in the solution field [30][31][32][33][34], ILES has emerged as a popular alternative to the more formal techniques for subgrid scale modeling in turbulent flows [35][36][37][38][39] since it is convenient to let the numerical dissipation inherent to these schemes substitute the subgrid scale dissipation that would otherwise require artificial modeling [40][41][42][43]. We remark that controlling this numerical dissipation is not a trivial task, but the computational efficiency of this approach (as it does not require any explicit turbulence model) makes it attractive.…”

Reshocked Richtmyer-Meshkov instability: Numerical study and modeling of random multi-mode experiments

“…47,[50][51][52][53] However, the comparisons to experiments were done for a single given configuration (i.e., shock wave Mach number, shock tube dimensions, etc.). Moreover, these studies did not present a comprehensive parametric study of possible initial conditions, which could successfully reproduce the experiments.…”