A Symmetry and Dispersion-Relation Preserving High-Order Scheme for Aeroacoustics and Aerodynamics

Abstract

A new high-order, finite-volume scheme is presented that preserves the symmetry property and the dispersion relation of the convective operator. The scheme is applied to large-eddy simulation of compressible, turbulent flow and to the solution of the linearized Euler equations for aeroacoustic applications. For large-eddy simulation, the discretization is based on the skew-symmetric form, which ensures that the kinetic energy is conserved by the convective operator. This property minimizes the interference of numerical errors with the subgrid-scale model and also enhances numerical stability. Low numerical dispersion is obtained by extending the dispersion-relation preserving scheme of Tam & Webb to finite-volume schemes. The proposed finite-volume scheme is unique in that it is truly fourth-order accurate, conservative, symmetry preserving and dispersion-relation preserving on non-uniform, curvilinear structured grids.