On spatial filtering of flow variables in high-order finite volume methods

Abstract

A new method of spatial filtering in high-order finite volume methods is presented and assessed. The base of this method is to filter face-averaged variables (fluxes) and then the recovery of cell-averaged ones. Two kinds of filtering method are proposed. The first kind is highly dissipative and appropriate for the numerical regions that need high dissipation, e.g. sponge zones. The second kind, on the other hand, is a precise method and hence is suitable for applying the high-order finite difference filters to the finite volume methods. Applying high-order finite difference filters directly to the high-order finite volume methods without using the proposed method causes stability problems in the large eddy simulation of high Reynolds number flows. The test cases, namely, propagation of the one-dimensional wave packet, advection of a two-dimensional vortical wave and the large eddy simulation of turbulent round jet at Re=104 and 105 are used to examine the accuracy and performance of the proposed methods. The last test case shows the effectiveness of the proposed methods in the large eddy simulation of flows by high-order FVMs. The performance of filtering methods on a curvilinear wavy grid is also investigated.