Discontinuous Galerkin methods for the acoustic conservation equations with application to aeroacoustic

The acoustic conservation equations are a subset of the compressible flow equations and describe the generation and propagation of acoustic waves by the two acoustic primary variables: acoustic pressure and acoustic particle velocity. Therefore, the equations (an exact reformulation of the APE-2) can be natively used in the context of hybrid aeroacoustic. In order to achieve a stable finite element (FE) approximation by the continuous Galerkin method, these two physical quantities have to be defined in different Sobolev spaces to fulfill the Ladyzhenskaya–Babuška–Brezzi condition. Another approach is to apply the Discontinuous Galerkin (DG) method, which enforces coupling between elements via numerical fluxes in surface integrals only and thus has advantages regarding computational efficiency. We present a high-order DG formulation that yields optimal spatial and temporal convergence rates and provide implementational details in the context of hybrid aeroacoustics. Furthermore, the application to an aeroacoustic test case demonstrates the developed DG approach’s suitability for aeroacoustic computations.