An autonomous LES method using eddy viscosity derived from the subgrid-scale similarity model

A previously developed method for large eddy simulations (LESs), based on spectral eddy viscosity models, is generalized to the physical space representation. The method estimates the subgrid scale (SGS) energy transfer using a similarity-type expression for the SGS tensor obtained using Gaussian filtering of velocity fields advanced in LESs. Subsequently, following steps for the spectral space representation, the SGS transfer in the physical space is used to obtain a spatially varying eddy viscosity at each time step in LESs. The eddy viscosity is then employed to model the SGS stress tensor in the familiar Boussinesq form for use in LESs. The method is autonomous in a sense that the functional form of the eddy viscosity is not postulated but is computed at each time step without adjustable constants from the resolved LES fields. The method is tested in LES of isotropic turbulence at high Reynolds numbers where the inertial range dynamics is expected and for lower Reynolds number decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments. In both cases the agreement with reference data is very good and the SGS transfer computed for the proposed eddy viscosity model is highly correlated with the transfer computed for the similarity model ($C approx 0.8$).