Coupled Discontinuous Galerkin/Finite Difference Solver on Hybrid Meshes for Computational Aeroacoustics

The study of a multidomain coupling algorithm of numerical methods applied to direct acoustic waves simulation is the focus of this paper. The idea is to be able to use meshing techniques and numerical methods of different natures, depending on the domain area, in order to meet the local requirements of the computation. Here, the linearized Euler equations are solved by carrying out a coupling between a discontinuous Galerkin method running on an unstructured mesh and a finite difference method running on a Cartesian grid. The aim is to take into account complex geometries by running a discontinuous Galerkin method and run a finite difference method away from the obstacles to reduce computational costs. In this paper, two different discontinuous Galerkin/finite difference coupling algorithms are presented, and some associated validation results in terms of precision and stability are discussed. An application of a hybrid solver in the framework of an acoustic benchmark dedicated to complex geometries is also presented.