Abstract
AbstractA general methodology is presented in order to obtain a hierarchy of high‐order filter functions, starting from the standard top‐hat filter, naturally linked to control volumes flow simulations. The goal is to have a new filtered variable better represented in its high resolved wavenumber components by using a suitable deconvolution. The proposed formulation is applied to the integral momentum equation, that is the evolution equation for the top‐hat filtered variable, by performing a spatial reconstruction based on the approximate inversion of the averaging operator. A theoretical analysis for the Burgers' model equation is presented, demonstrating that the local de‐averaging is an effective tool to obtain a higher‐order accuracy. It is also shown that the subgrid‐scale term, to be modeled in the deconvolved balance equation, has a smaller absolute importance in the resolved wavenumber range for increasing deconvolution order. A numerical analysis of the procedure is presented, based on high‐order upwind and central fluxes reconstruction, leading to congruent control volume schemes. Finally, the features of the present high‐order conservative formulation are tested in the numerical simulation of a sample turbulent flow: the flow behind a backward‐facing step. Copyright © 2001 John Wiley & Sons, Ltd.
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