Functional Modeling: Extension to Anisotropic Cases

Abstract

The developments of the previous chapters are all conducted in the isotropic framework, which implies that both the filter used and the flow are isotropic. They can be extended to anisotropic or inhomogeneous cases only by localizing the statistical relations in space and time and introducing heuristic procedures for adjusting the models. But when large-eddy simulation is applied to inhomogeneous flows, we very often have to use anisotropic grids, which correspond to using a anisotropic filter. So there are two factors contributing to the violation of the hypotheses underlying the models presented so far: filter anisotropy (respectively inhomogeneity) and flow anisotropy (respectively inhomogeneity).