Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-30T00:06:04.734Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Azerad, P., Analyse des Equations de Navier-Stokes en Bassin peu Profond et de l’Equation de Transport, PhD thesis, Neuchaˆtel, 1996.Google Scholar
[2]Bécache, E., Dhia, A.-S. Bonnet-Ben and Legendre, G., Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow, SIAM J. Numer. Anal., 44 (2006), 1191–1217.Google Scholar
[3]Bonnet-Ben Dhia, A. S., Mercier, J. F., Millot, F. and Pernet, S., A low mach model for time harmonic acoustics in arbitrary flows, J. Comput. Appl. Math., 234(6) (2010), 1868–1875.CrossRefGoogle Scholar
[4]Bonnet-Ben Dhia, A. S., Duclairoir, E. M., Legendre, G. and Mercier, J. F., Time-harmonic acoustic propagation in the presence of a shear flow, J. Comput. Appl. Math., 204(2) (2007), 428–439.Google Scholar
[5]Bonnet-Ben Dhia, A. S., Duclairoir, E. M. and Mercier, J. F., Acoustic propagation in a flow: numerical simulation of the time-harmonic regime, ESAIM Proc., 22 (2007), 1–14.CrossRefGoogle Scholar
[6]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, Series Studies in Mathematics and its Applications, North-Holland, Amsterdam, 1978.Google Scholar
[7]Ern, A. and Guermond, J.-L., Theory and Practice of Finite Elements, Applied Mathematical Sciences, Springer-Verlag, New York, 2004.Google Scholar
[8]Legendre, G., Rayonnement Acoustique dans un Fluide en Ecoulement: Analyse Mathématique et Numérique de l’Équation de Galbrun, PhD thesis, Paris VI University, 2003.Google Scholar
[9]Treyssede, F., Gabard, G. and Tahar, M. B., A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description, JASA, 113 (2003), 705–716.Google Scholar