Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

Abstract

A set of explicit finite difference schemes with large stencil was optimized to obtain maximum resolution characteristics for various spatial truncation orders. The effect of integral interval range of the objective function on the optimized schemes’ performance is discussed. An algorithm is developed for the automatic determination of this integral interval. Three types of objective functions in the optimization procedure are compared in detail, which show that Tam’s objective function gets the best resolution in explicit centered finite difference scheme. Actual performances of the proposed optimized schemes are demonstrated by numerical simulation of three CAA benchmark problems. The effective accuracy, strengths, and weakness of these proposed schemes are then discussed. At the end, general conclusion on how to choose optimization objective function and optimization ranges is drawn. The results provide clear understanding of the relative effective accuracy of the various truncation orders, especially the trade-off when using large stencil with a relatively high truncation order.