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

Published online by Cambridge University Press:  20 August 2015

A.S.Bonnet-Ben Dhia ,
J.F. Mercier ,
F. Millot ,
S. Pernet  and
E. Peynaud
A.S.Bonnet-Ben Dhia*
Affiliation:
POEMS, CNRS-INRIA-ENSTA UMR 7231, 32 Boulevard Victor, 75015 Paris, France CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France
J.F. Mercier*
Affiliation:
POEMS, CNRS-INRIA-ENSTA UMR 7231, 32 Boulevard Victor, 75015 Paris, France
F. Millot*
Affiliation:
CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France
S. Pernet*
Affiliation:
CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France
E. Peynaud*
Affiliation:
CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France
*
Corresponding author.Email:anne-sophie.bonnet-bendhia@ensta.fr
Corresponding author.Email address:jmercier@ensta.fr
Corresponding author.Email address:millot@cerfacs.fr
Corresponding author.Email address:pernet@cerfacs.fr
Corresponding author.Email address:peynaud@cerfacs.fr
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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.

Keywords

35Q3565N30Aeroacousticsscattering of sound in flowsGalbrun equationadvection equationfinite elementsdiscontinuous Galerkin method
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 555 - 572
Copyright
Copyright © Global Science Press Limited 2012

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References

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