Assessment of aeroacoustic resolution properties of DG schemes and comparison with DRP schemes

Abstract

We discuss the aeroacoustic resolution properties of the discontinuous Galerkin (DG) schemes in detail and compare their performance with the state of the art finite difference (FD) schemes, including the classical dispersion-relation-preserving (DRP) schemes. Analysis shows that, even though the DG schemes are slightly dissipative, their overall dispersion and dissipation properties are comparable with the corresponding DRP schemes on the same stencil. For the convenience of a direct comparison with FD schemes, we write the DG schemes in the form of block finite difference schemes. Ample numerical tests, including the tests on nozzle flow problems, are performed and we observe that the DG schemes and DRP schemes with the same stencil produce comparable numerical results. Since the DG schemes are flexible on non-uniform meshes and general unstructured meshes, they should be good candidates for computational aeroacoustics, especially those on complex geometry.