High-order filtering for control volume flow simulation
A general methodology is presented in order to obtain a hierarchy of high-order filter functions, starting front 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 (C) 2001 John Wiley & Sons, Ltd.
high-order filtering approximate deconvolution control volume approach large-eddy simulation