For the numerical simulation of time-harmonic acoustic scattering in a complex geom- etry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time-harmonic convection equation (for the vortices). In addition, the computational region is truncated by means of Perfectly Matched Layers at artificial boundaries. We implemented a hybrid numerical method which consists in coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally, numerical tests show the efficiency of the method.