Deconvolution methods for Large-Eddy Simulation

In this paper we review the development and the recent progress of deconvolution modeling for Large-Eddy Simulation. Eddy-viscosity models do not optimally exploit information contained in the resolved scales. This is indicated by low correlations of modeled and exact subgrid-scale stresses. An attempt to extract more information from the large scales led to the formulation of dynamic eddy-viscosity models. The first deconvolution models are the expansion-deconvolution model of Leonard (1974) and the scalesimilarity model of Bardina (1983). Since the filter operation is singular, deconvolution can only be performed approximately, and the inverse operation requires regularization. Discrete-kernel regularizations were proposed by Geurts (1997), a regularized subgrid-scale estimation by Domaradzki & Saiki (1998). Stolz & Adams (1999) propose a deconvolution method which is based on a truncated series expansion of the kernel in terms of multiple filter operations. At higher Reynolds numbers, deconvolution models usually do not provide a sufficient amount of subgrid-scale dissipation, and therefore in general require a secondary regularization. For this purpose deconvolution models are mostly combined with eddy-viscosity regularizations. A non-eddy-viscosity regularization can be constructed by employing a secondary filter level. By applying the secondary filter to the filtered solution a relaxation term can be defined, which provides subgrid-scale dissipation. This approach is used by Stolz & Adams (1999) in the combination with their approximate deconvolution model, and by Adams & Leonard (1999) in employing regularized deconvolution for the computation of discontinuous solutions of conservation laws.