High-order discontinuous Galerkin method on hexahedral elements for aeroacoustics

The propagation of acoustic waves in non-uniform flow in three-dimensional space is investigated by means of a numerical method based on the discontinuous Galerkin finite-element formulation. The propagation of acoustic waves in non-uniform flows can be described by the linearized Euler equations under the assumptions that there is no feedback from the acoustic field to the background flow field and the distance of propagation is not too large compared to the acoustic wave lengths. The discontinuous Galerkin method has some remarkable advantages with respect to flexibility in discretization of domains with complex geometries. The discontinuous Galerkin method is a highly compact finite-element projection method which provides a practical framework for the development of higher-order methods desired for computational aeroacoustics on non-smooth unstructured grids, as discussed in the literature. In the present study the higher-order discontinuous Galerkin method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid.