On linking the filter width to the boundary layer thickness in explicitly filtered large eddy simulations of wall bounded flows

Abstract

Obtaining grid independent large eddy simulations (LES) can be elusive. The filtering technique, along with the subgrid scale (SGS) model, plays an important role in reducing grid sensitivity and improving the accuracy of LES. It is known that grid sensitive simulations present a major problem with implicitly filtered LES and this can lead to poor convergence. In the last two decades, explicit filtering schemes have appeared that offer a promising solution, where the model (essentially the filter width) is maintained constant while the numerical error is reduced by refining the grid. In this study, a systematic approach is proposed to obtain grid independence by combining an explicit filtering scheme for LES with a damped Smagorinsky subgrid model. In this approach, emphasis is given to the selection of the filter width as a function of a physical parameter, namely boundary layer thickness (BLT). An analysis of the energy spectrum ensures that grid converged solutions are consistent with LES principles by accurately capturing the energy containing eddies. This approach is successfully applied to two benchmark cases at two different Reynolds numbers. A high Reynolds number flow (Reλ=115) over a backward facing step and a low Reynolds number, buoyancy driven flow (Reλ=25) inside a differentially heated cavity. The proposed approach provides a novel way of selecting an explicit LES filter in the absence of DNS as a reference case. This study also provides guidelines on the selection of filter width to grid spacing ratio (ultimately BLT to grid spacing ratio) for the proposed numerical scheme for resolving turbulent flows.