A subgrid-scale model based on singular values for LES in complex geometries

An eddy-viscosity based, subgrid-scale model for Large Eddy Simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. It is shown that the proposed σ-model has the property to automatically vanish as soon as the resolved field is two-dimensional, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results obtained for different physical configurations (isotropic turbulence, channel flows, and periodic jet) are presented to illustrate the potential of the model. A dynamic version based on a volume averaged procedure is also proposed.