Numerical simulation of Richtmyer–Meshkov instabilities

Abstract

The results of detailed numerical simulations of the Richtmyer–Meshkov instability of the interface between layers of air and either helium or SF6 in a shock tube are reported. Two- and three-dimensional simulations based on both the Euler and Navier–Stokes equations were obtained by a finite difference method that employs a front-tracking technique to keep the interface sharp. The nature of the flow patterns induced by the instability is discussed. The results of a numerical resolution study and a demonstration of the influence of boundary layers are presented also. Agreement with experimental data is found to be satisfactory, with the exception of the initial instability growth rate.

An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems

“…We note that as far as the global wave structure is concerned the results presented here are reasonable ones as compared to those appearing in the literature [11,32]. A more careful study of the solutions that covers results from the theoretical prediction of a nonlinear theory developed by Zhang and Sohn [76] and the laboratory experiments [27,73] will be reported elsewhere [66].…”

“…Since the derivation of the volumefraction model comes closely out of the γ -based model, it can be shown that this model is as effective as the γ -based model. But for general multicomponent problems, the γ -based model is the preferred one to use, because the basic equations for the model stay as five, see (11), irrespective of the number of components involved in the problem.…”

Hydrodynamic Instabilities in Gaseous Detonations: Comparison of Euler, Navier–Stokes, and Large-Eddy Simulation

“…Hence, their 2-D and 3-D simulations showed very similar results. The behavior of RM instability has been isolated and studied by many authors (e.g., [63,[71][72][73]). The numerical study of RM instability by Anuchina et al [74] showed that the growth rate of perturbations in a 3D case was higher than that in a 2D case at the identical initial amplitudes of perturbation and wavelengths.…”

Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks

“…Meanwhile, many experiments have been designed to study the RM instability [7,8,13,[20][21][22][23]. In recent years, with the aid of modern computers, numerical simulation has become a very helpful and powerful tool for the investigation of RM instability [3,7,13,19,[24][25][26][27][28][29][30].…”