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

Abstract

SUMMARYLarge 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 pseudospectral 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 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 2 /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.

Proper orthogonal decomposition analysis of flow characteristics of aerostatic bearings based on Large Eddy Simulation

“…According to [27], the spatial discretization process could be regarded as a physical space filter (denoted by -), which is imposed on each term of the N-S equations. The filtered N-S equations could be written into the following form:…”