On the relation between subgrid-scale modeling and numerical discretization in large-eddy simulation

Subgrid-scale models in LES operate on a range of scales which is marginally resolved by the discrete approximation. Accordingly, the discrete approximation method and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or vice versa. Approaches where SGS models and numerical discretizations are fully linked are called implicit SGS models. Different approaches to SGS modeling can be taken. Mostly, given nonlinearly stable discretizations schemes for the convective fluxes are used as main element of implicit SGS models. Recently we have proposed to design nonlinear discretization schemes in such a way that their truncation error functions as SGS model in regions where the flow is turbulent and as a second-order accurate discretization in regions where the flow is laminar. In this paper we review the current status on this so-called adaptive local deconvolution method (ALDM) and provide some application results. © Springer-Verlag Berlin Heidelberg 2007.