By Dr. Pierre Sagaut (auth.)
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Additional resources for Large Eddy Simulation for Incompressible Flows: An Introduction
Van der Ven's analysis has been generalized by Vasilyev et al.  so as to contain previous works (SOCF and Van der Ven's filters) as special cases. As for SOCF, the filtering process is defined thanks to the use of a reference space. We now consider that the physical domain [a, b] is mapped into the domain [a, ß]. Ghosal and Moin used a = -00 and ß = +00. 1. 1. Correspondances for Vasilyev's high-order commuting filters. 2 Extension to the Inhomogeneous Case (jJ(~) = ls-; ~-'" G (() cjJ(~ - ,1()d( .
Sharp cutoff filter. Associated transfer function. 2 Extension to the Inhomogeneous Case 19 It is trivially verified that the first two filters are positive while the sharp eutoff filter is not. The top-hat filter is loeal in the physieal spaee (its support is eompact) and non-loeal in the Fourier spaee, inversely from the sharp eutoff filter, whieh is loeal in the spectral spaee and non-loeal in the physical spaee. As for the Gaussian filter, it is non-loeal both in the spectral and physieal spaees.
3 Decomposition of the Non-linear Term. 19) The new L term, called Leonard tensor, represents interactions among the large scales. 21) This decomposition will be designated hereafter the Leonard or tripie decomposition. 21) can be obtained directly from the Navier-Stokes equations without using the Leonard decomposition for this. It should be noted that the term UiUj is a quadratic term and that it contains frequencies that are in theory higher than each of the terms composing. So in order to represent it completely, more degrees of freedom are needed than for·each of the terms Ui and u/.
Large Eddy Simulation for Incompressible Flows: An Introduction by Dr. Pierre Sagaut (auth.)