Efficient dynamic mixed subgrid-scale model

Abstract

It is well known that the scale-similarity class of subgrid models have a high correlation with the actual subgrid stresses in a priori tests. However, these models are typically underdissipative and not robust enough to be practically useful for large-eddy simulation. On the other hand, the dynamic Smagorinsky model (DSM), which is a popular subgrid model, is sufficiently dissipative and robust, but has a lower correlation with actual subgrid stresses in a priori tests. There have been many successful attempts to combine the two models into a “mixed” subgrid model that have typically retained the favorable properties of both. However, most dynamic mixed models require two or more levels of test filtering beyond the (often implicit) grid filtered quantities that are solved, in contrast to a single test filtering operation for the dynamic Smagorinsky model. The additional cost involved in test filtering has likely hindered the widespread use of dynamic mixed models in production codes. We propose an efficient dynamic mixed model that is constrained to have the same subgrid dissipation as the DSM model, and only requires a single level of test filtering. Thus, the additional computational cost is negligible compared to the DSM model. A posteriori simulations of the turbulent channel flow reveal that the proposed mixed model is as robust as the DSM model, and more accurate on coarser grids. Notably, smooth-body turbulent separation is better captured by the new model when combined with a standard wall model.