Comparative Study of the Predictions of Four-Equation Reynolds-Averaged Navier-Stokes Models Applied to Richtmyer-Meshkov Instability-Induced Mixing

A multicomponent, weighted essentially nonoscillatory implementation of several four-equation $K$-$\epsilon$ and $K$-$L$ based Reynolds-averaged Navier--Stokes models is used to simulate reshocked Richtmyer--Meshkov turbulent mixing at various Mach and Atwood numbers. One class of models is based on mechanical turbulence coupled to scalar variance and its dissipation rate, and the other is based on mechanical turbulence coupled to mass flux and the density--specific volume correlation. The predicted evolution of the mixing layer, molecular mixing and other quantities obtained from these models are systematically intercompared, as well as compared to experimental shock tube data. The relative advantages and disadvantages of the various models are discussed.