Computational aeroacoustics with a high order discontinuous Galerkin scheme

The high order discontinuous Galerkin solver NoisSol for the linearized acoustic equations and its application to airfoil noise simulation are presented. Aiming at the fast simulation of the noise generation and propagation in domains with complex geometries, the discretization based on unstructured grids is seen as the favorable strategy. Further important requirements for an aeroacoustic solver are low dissipation and dispersion errors to enable the propagation of waves over a long distance to the far field. Discontinuous Galerkin schemes outrange finite volume schemes in these properties and are consequently the optimum choice for computational aeroacoustics (CAA) on unstructured grids. They furthermore convince with their low demands in grid quality, which avoids mesh postprocessing and optimization and eases the tool chain. For the simulation of aeroacoustics in flows with a low Mach number, the separation of flow and acoustic simulation is favorable, since both have to deal with different space and energy scales. For the acoustic calculation linearized equations can be used. They have transient source terms, which describe the excitation of the sound by flow phenomena. These sources as well as the linearization state of the equations depend on the local flow state. The linearization is done around the time averaged (’mean’) flow field. The transfer of source and mean flow data needs a coupling between both the flow solver grid and the acoustic grid. Therefor for each node or interpolation point in one grid the corresponding element in the other grid has to be known. Since a brute force approach for this search is infeasible for large scale applications, a new search algorithm has been developed. In the presented airfoil noise simulation it has been applied to the search of the corresponding CFD cells for the mean flow values, where it showed impressive results. It is applicable for any grid in 2D and 3D with elements of a standard type, such as triangles, quadrilaterals, tetrahedrons or hexahedrons. A hybrid grid coupling has been developed and implemented with the DLR code PIANO [13] to combine the advantages of the presented DG solver with