A Family of Dynamic Models for Large-eddy Simulation

Since its rst application, the dynamic procedure has been recognized as an eeec-tive means to compute rather than prescribe the unknown coeecients that appear in a subgrid-scale model for Large-Eddy Simulation (LES). The dynamic procedure (Germano et al. 1991; Ghosal et al. 1995) is usually used to determine the non-dimensional coeecient in the Smagorinsky (1963) model. In reality the procedure is quite general and it is not limited to the Smagorinsky model by any theoretical or practical constraints. The purpose of this note is to consider a generalized family of dynamic eddy viscosity models that do not necessarily rely on the local equilibrium assumption built into the Smagorinsky model. By invoking an inertial range assumption, it will be shown that the coeecients in the new models need not be non-dimensional. This additional degree of freedom allows the use of models that are scaled on traditionally unknown quantities such as the dissipation rate. In certain cases, the dynamic models with dimensional coeecients are simpler to implement, and allow for a 30% reduction in the number of required ltering operations. 2. Accomplishments 2.1 A new family of dynamic eddy viscosity models The LES equations are obtained from the Navier-Stokes equations by applying a lter, denoted by an overline, which is assumed to damp scales smaller than. In the context of eddy viscosity models, the unknown subgrid-scale stress generated (1) The eddy viscosity, e , has dimensions L 2 =T, where L is length and T is time. The characteristic length in the problem is obviously L c =. Following the Kolmogorov (1941) dimensional analysis, the characteristic time may be expressed as a function of the rate of energy transfer within the inertial range E: T c = ((2 =E) 1=3. The \Kolmogorov expression" for the eddy viscosity is thus: