Discrete filters for large eddy simulation

This paper summarizes several results relative to discrete filters for subg rid-scale (SGS) models based on a multi-level filtering procedure. First, a theoretical study of discrete filters in physical space is performed. The analysis is done in the uniform one-dimensional case, and is then extended to the general multi-dimensional case for arbitrary structured and unstruct ured meshes. Some equivalence classes for the discrete filters are defined, based either on a differential approximation or the associated transfer fu nction. Methods for the definition of discrete filters are proposed in the general case, including the approximation of continuous convolution filters . Second, the sensitivity of several SGS models with respect to the test fi lter is investigated. The selected models are: the dynamic Smagorinsky mode l, the mixed scale model (MSM), the selective MSM and the Liu-Meneveau-Katz (LMK) similarity model. Improved versions, which explicitly account for th e spectral width of the test filter of the MSM and the LMK similarity model are proposed. The analysis, which reveals a significant influence of the t est filter, is done through a priori testing on a 128(3) field issued from the large eddy simulation (LES) of freely decaying homogeneous isotropic tu rbulence. Copyright (C) 1999 John Whey & Sons, Ltd.