A Tensor-Diffusivity Subgrid Model for Large-Eddy Simulation

Subgrid-scale models for large-eddy simulation that are based on exact series expansions for filtered products are considered. In particular, if the first two terms are retained, the result is a diffusive subgrid term with a tensor diffusivity. This tensor is proportional to the rate-of-strain tensor of the large-scale velocity field. This leads to negative diffusion in the stretching directions. Implications of this result are considered for the filtered scalar advection-diffusion equation and for the momentum equation for incompressible fluid flow. When coupled with a dynamic Smagorinsky term to form a mixed model, very encouraging results are shown for turbulent, isotropic decay and for turbulent channel flow. In addition, it is shown that the model, mixed or not, transforms appropriately when differing frames of reference are considered. Modifications to the model are suggested for the case in which the unfiltered field(s) has discontinuities.