| Abstract: | For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagationand convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonicconvection equation (for the vortices). We first establish the well-posedness of thistime harmonic convection equation in the appropriate mathematical framework. Thenthe complete problem, with Perfectly Matched Layers at the artificial boundaries, isproved to be coercive + compact, and a hybrid numerical method for the solutionis proposed, coupling finite elements for the Galbrun equation and a DiscontinuousGalerkin scheme for the convection equation. Finally a 2D numerical result shows theefficiency of the method. |
