Analysis of a Large Eddy Simulation model based on anisotropic filtering

We consider a new Large Eddy Simulation model, derived with the introduction of suitable horizontal (anisotropic) differential filters. One main advantage of this filtering is that, for channel flows, there is no need for artificial boundary conditions. Hence, we can deal with some realistic problems, equipped with Dirichlet boundary conditions, in special bounded domains (at least those bounded only in one direction). Recent numerical results for a similar model, based on a derivation with wave-number asymptotics, are also recalled. After a detailed analysis of the properties of the differential filter, we prove that the resulting initial–boundary value problem is well-posed in suitable anisotropic Sobolev spaces, giving a strong mathematical support to the model we propose. Some remarks on higher-accuracy Approximate Deconvolution Models are also given in the last section.