Some remarks on approximation of subgrid scale modeling in Large Eddy Simulation

The Leonard expansion on the subgrid-scale (SGS) terms is exploited for SGS modeling, in which the first two terms are kept from the truncation. This leads to an approximation that is related to the corresponding viscous dissipation and with properties similar to a mixed SGS model. Furthermore, a heuristic hypothesis is employed. It is assumed that, with a certain spatial filtering, a SGS turbulent quantity should correspond harmonically in magnitude to its resolved, large-scale counterpart. The SGS quantity is then approximated in terms of the product of an appropriate SGS time scale and the net energy occurrence between the resolved and the subgrid scales, leading to implicit algebraic expressions for the unknown SGS terms.