| Abstract: | This paper summarizes several results relative to discrete filters for subgrid‐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 unstructured meshes. Some equivalence classes for the discrete filters are defined, based either on a differential approximation or the associated transfer function. 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 filter is investigated. The selected models are: the dynamic Smagorinsky model, the mixed scale model (MSM), the selective MSM and the Liu–Meneveau–Katz (LMK) similarity model. Improved versions, which explicitly account for the 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 test filter, is done through a priori testing on a 1283 field issued from the large eddy simulation (LES) of freely decaying homogeneous isotropic turbulence. Copyright © 1999 John Wiley & Sons, Ltd. |
