Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-prt4h Total loading time: 0.165 Render date: 2021-10-16T01:10:31.313Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

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*
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.

Type
Research Article
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), 11911217.CrossRefGoogle 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), 18681875.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.CrossRefGoogle 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), 114.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.CrossRefGoogle 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), 705716.CrossRefGoogle ScholarPubMed
6
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *