Commun. Comput. Phys., 11 (2012), pp. 555-572.


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

A. S. Bonnet-Ben Dhia 1*, J. F. Mercier 2, F. Millot 3, S. Pernet 3, E. Peynaud 3

1 POEMS, CNRS-INRIA-ENSTA UMR 7231, 32 Boulevard Victor, 75015 Paris, France; and CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France.
2 POEMS, CNRS-INRIA-ENSTA UMR 7231, 32 Boulevard Victor, 75015 Paris, France.
3 CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France.

Received 22 December 2009; Accepted (in revised version) 3 January 2011
Available online 24 October 2011
doi:10.4208/cicp.221209.030111s

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.

AMS subject classifications: 35Q35, 65N30

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Key words: Aeroacoustics, scattering of sound in flows, Galbrun equation, advection equation, finite elements, discontinuous Galerkin method.

*Corresponding author.
Email: anne-sophie.bonnet-bendhia@ensta.fr (A. S. Bonnet-Ben Dhia), jmercier@ensta.fr (J. Mercier), millot@cerfacs.fr (F. Millot), pernet@cerfacs.fr (S. Pernet), peynaud@cerfacs.fr (E. Peynaud)
 

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