Investigation using statistical closure theory of the influence of the filter shape on scale separation in large-eddy simulation

Abstract

The influence of the filter shape on scale separation in large-eddy simulation (LES) is investigated using the eddy-damped quasi-normal Markovian (EDQNM) modelling approach, for discrete filters of order 2–12. The LES subgrid-scale (SGS) stress tensor is split into a represented SGS tensor based on the scales resolved by the mesh, and a non-represented SGS tensor involving the unresolved scales. The investigation of the kinetic energy spectra associated with these quantities shows that the features of the SGS tensor strongly depend on the filter shape. In particular, for the second-order filter, the SGS stress tensor dynamics is dominated by the interactions between the resolved scales. The effective LES cut-off wavenumber is finally evaluated and recast in term of efficiency rates in order to estimate the computational cost required to achieve a given spectral resolution. Sharp cut-off filters appear to be well appropriate to perform an efficient scale separation in LES.