On the justification and extension of mixed models in LES

Abstract

A reformulation of the large eddy simulation (LES) equations is presented, based on an alternative decomposition of the subgrid stress tensor leading to modified Leonard, cross, and Reynolds terms, which are all individually frame indifferent. The new Leonard tensor, identical to the scale similarity model proposed by Bardina et al(J. Bardina, J. H. Ferziger and W. C. Reynolds, 1980, AIAA Paper 80-1357), is computable and thus becomes an integral part of the LES equations, so this formulation clearly emphasizes the difference between Reynolds averaged Navier–Stokes (RANS) and LES. The remaining modified cross and Reynolds terms can be regrouped further into a reconstructable part and a true subgrid component, where we here use an approximate deconvolution model and a subgrid viscosity model for the respective parts. This structure justifies the use of a dissipative model term in mixed models based on, e.g., the scale similarity model. The reformulated LES model is tested on two basic flows, the Taylor Green flow and a fully developed turbulent channel flow at Reynolds numbers (Reτ) between 395 and 1800. The results are compared with direct numerical simulation and experimental data as well as other LES using other subgrid models. In both cases the predictions are improved by the more detailed modeling. Including the resolved, or scale similarity, tensor has larger effect than including the reconstructable tensor, but the latter is by no means negligible. The effects are larger for cases with lower resolution, where the subgrid model has to account for a larger amount of flow scales.