Exact expansions for filtered-scales modelling with a wide class of LES filters

Carati, Daniele Winckelmans, Grégoire [UCL] Jeanmart, Hervé [UCL]

(eng) An exact expansion for the filtered-scale stress tensor in terms of the large-scale velocity and its derivatives is presented for large-eddy simulation (LES) that are based on filters with a C ∞ kernel (e.g., most filters defined in physical space, such as the Gaussian, the top hat, all discrete filters, etc.). This result constitutes a generalisation of the exact expansion proposed independently by Yeo and Leonard in the case of the Gaussian filter. An important consequence of this expansion is that the filtered-scale stress tensor does not introduce any irreversibility into the large-scale dynamics. An approximation of this expansion is also derived for filters with a compact support in Fourier space. In this case, the filtered-scale can be decomposed into two parts corresponding respectively to reversible and irreversible effects.