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:aco...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 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).We first establish the well-posedness of this time harmonic convection equation in the appropriatemathematical framework.Then the complete problem,with Perfectly Matched Layers at the artificial boundaries,is proved to be coercive+compact,and a hybrid numerical method for the solution is proposed,coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation.Finally a 2D numerical result shows the efficiency of the method.展开更多
文摘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 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).We first establish the well-posedness of this time harmonic convection equation in the appropriatemathematical framework.Then the complete problem,with Perfectly Matched Layers at the artificial boundaries,is proved to be coercive+compact,and a hybrid numerical method for the solution is proposed,coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation.Finally a 2D numerical result shows the efficiency of the method.
