By Dr. Pierre Sagaut (auth.)
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Additional resources for Large Eddy Simulation for Incompressible Flows: An Introduction
10) 2. 11) This property is automatically satisfied, since the product of convolution verifies it independently of the characteristics of the kernel G. 3. > == i 0 . e. > =f. > =f. 19) In the linear case, the commutator satisfies all the properties of the Poissonbracket operator, as defined in classical mechanics. 14 2. Formal Introduction to Filtering which is equivalent to saying that G is not a projector (excluding the trivial case of the identity application). Let us recall that an application P is defined as being a projector if PoP = P.
J 1=1,00 l! J 1=1,00 a~) = 1-00+00 1+00 -00 (~- x)IG(X -~, t - a~l) = 00 1 +001+-00 (t' - and -00 l! 64) t)IG(x - ~,t - t')d~dt' . 65) Conditions for Convergence of the Taylor Series Expansions. A first analysis of the convergence properties of the Taylor series expansions discussed above was provided by Vasilyev et al. [488J, and is given below. 66) where time-dependence has been omitted for the sake of simplicity. 68) 26 2. 73) Pruett et al. 73). This proof is now presented. d 5 ezG(~)d~ , It is recalled that the filter is said to be non-negative if G(x) :2': 0, "Ix.
83) 3. Fast decay. e. Vn 2 0 . 4. Quasi-local in physical space. in the interval [-1/2,1/2]. 2 Spatial Filtering: Extension to the Inhomogeneous Case 29 Extension of the Top-Hat Filter to the Inhomogeneous Case: Properties. 85) There are a number of ways of extending this filter to the inhomogeneous case. The problem posed is strictly analogous to that of extending finite volume type schemes to the case of inhomogeneous structured grids: the control volumes can be defined directly on the computational grid or in a reference space carrying a uniform grid, after a change of variable.