On the use of high‐order finite‐difference discretization for LES with double decomposition of the subgrid‐scale stresses

Abstract

AbstractLarge eddy simulation (LES) with additional filtering of the non‐linear term, also coined LES with double decomposition of the subgrid‐scale stress, is considered. In the literature, this approach is mainly encountered in combination with pseudo‐spectral discretization methods. In this case, the additional filter is a sharp cut‐off filter, which appears in the eventual computational algorithm as the 2/3‐dealiasing procedure. In the present paper, the LES approach with additional filtering of the non‐linear term is evaluated in a spatial, finite‐difference discretization approach. The sharp cut‐off filter used in pseudo‐spectral methods is then replaced by a ‘spectral‐like’ filter, which is formulated and discretized in physical space. As suggested in the literature, the filter width Δ of this spectral‐like filter corresponds at least to 3/2 times the grid spacing h to avoid aliasing. Furthermore, spectral‐like discretization of the derivatives are constructed such that derivative‐discretization errors are low in the wavenumber range resolved by the filter, i.e. 0⩽kh⩽2π/3. The resulting method in combination with a Smagorinsky model is tested for decaying homogeneous isotropic turbulence and compared to standard lower‐order discretization methods. Further, an analysis is elaborated of the Galilean‐invariance problem, which arises when LES in double decomposition approach is combined with filters, which do not correspond to an orthogonal projection. The effects of a Galilean coordinate transformation on LES results, are identified in simulations, and we demonstrate that a Galilean transformation leads to wavenumber‐dependent shifts of the energy spectra. Copyright © 2007 John Wiley & Sons, Ltd.