Low-Dispersion Finite Volume Scheme for Aeroacoustic Applications

The development ofa low-dispersion numerical scheme is described in the context of a finite volume discretization of the governing fluid dynamic equations. Although low-dispersion finite difference schemes have been developed recently for uniform Cartesian meshes, current finite volume methods do not possess low-dispersion characteristics. A low-dispersion finite volume scheme is presented and applied to some common acoustics problems. The two-dimensional unsteady Euler equations linearized about a mean flow are solved using a finite volume formulation. The surface integrals are computed using flow properties at cell faces, interpolated from cell nodes. The interpolation process is chosen such that it accurately represents sinusoidal waves of short wavelengths at the cell faces. A number of classical acoustics problems are solved, and where possible, comparisons with other numerical and exact solutions are given. This scheme has low dispersion and may be retrofitted easily into existing finite volume codes. The resulting numerical method combines the flexibility and versatility of the finite volume method while minimizing numerical dispersion errors in a manner similar to that of the classical dispersion-relation-preserving scheme.