Analysis of a large eddy simulation model based on anisotropic filtering (Q640955)

Anisotropic differential diffusion filters are introduced and applied to large eddy simulation of turbulent flows for domains with flat boundary. A justification of the approach is presented together with a mathematical validation based on the well-posedness of the partial differential equations. The properties of the anisotropic Helmholtz filter are studied and it is shown that the associated approximate large eddy simulation deconvolution models are well-posed in certain Sobolev spaces. This filtering approach is also known under the name Navier-Stokes \(\alpha\)-model. The present work is focused on flows with constant density and hence also suitable for the Boussinesq approximation. Furthermore some numerical results are recalled. Existence and uniqueness results of the initial value problem are presented using the Faedo-Galerkin method in appropriate anisotropic Sobolev spaces.