Large eddy simulation of the Richtmyer-Meshkov instability using dynamic eddy viscosity

Large eddy simulation (LES) is a useful framework for reducing the computational cost of turbulent flows. By solving the spatially-filtered Navier-Stokes equations, the smallest flow scales do not need to be resolved; many models exist for closing these subgrid scale terms. One such model, dynamic subgrid scale eddy viscosity, derives from relating subgrid scale stresses at the "grid filter" scale to those at a larger "test filter" scale. This work investigates the use of the dynamic subgrid scale eddy viscosity model for variable density mixing. The subgrid scale model's application to the Richtmyer-Meshkov instability presents additional numerical challenges. Adaptive mesh refinement (AMR) is beneficial for maintaining fine resolution around the shock and mixing layer, allowing for coarser resolution elsewhere. While necessary for practical large scale simulations, an adaptive mesh results in local grid and test filter scales that evolve during the simulation. In addition, the dynamic eddy viscosity is sensitive to velocity gradients, and thus easily triggered by the initial and reflected shock waves. Two approaches for computing the dynamic eddy viscosity are assessed: first, by using an explicit test filter operation, and second, by leveraging the AMR hierarchy directly. The inclusion of a sensor to deactivate the model in the vicinity of shocks is found to improve the stability of simulations. Demonstrated for the Richtmyer-Meshkov instability, the dynamic LES captures the evolution of key quantities including mixing zone width and turbulent kinetic energy.