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Time-Harmonic Acoustic Scattering in a Complex Flow: a Full Coupling Between Acoustics and Hydrodynamics

Anne-Sophie Bonnet-Ben Dhia 1 Jean-François Mercier 1 Florence Millot 2 Sébastien Pernet 2 Emilie Peynaud 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
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 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 appropriate mathematical 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.
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Submitted on : Wednesday, April 2, 2014 - 3:58:11 PM
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Anne-Sophie Bonnet-Ben Dhia, Jean-François Mercier, Florence Millot, Sébastien Pernet, Emilie Peynaud. Time-Harmonic Acoustic Scattering in a Complex Flow: a Full Coupling Between Acoustics and Hydrodynamics. Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.555-572. ⟨10.4208/cicp.221209.030111s⟩. ⟨hal-00970817⟩



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