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A Low Frequency Model for Acoustic Propagation in a 2D Flow Duct: Numerical Computation

Published online by Cambridge University Press:  20 August 2015

Lauris Joubert  and
Patrick Joly
Lauris Joubert*
Affiliation:
POEMS, CNRS-INRIA-ENSTA UMR 2706, 32 Boulevard Victor, 75015 Paris, France
Patrick Joly*
Affiliation:
POEMS, CNRS-INRIA-ENSTA UMR 2706, INRIA Rocquencourt, BP105, 78153 Le Chesnay Cedex, France
*
Corresponding author.Email:lauris.joubert@gmail.com
Email address:Patrick.Joly@inria.fr
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Abstract

In this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.

Keywords

35B3535Q3535C15Acoustics in flowGalbrun’s equationsasymptotic analysisLaplace transform
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 508 - 524
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Bonnet-BenDhia, A.S., Duruflé, M., and Joly, P.. Construction et analyse mathématique d’un modele approché pour la propagation d’ondes acoustiques dans un tuyau mince parcouru par un fluide en écoulement. Technical report, INRIA Research Report, 2007.Google Scholar
[2]Bonnet-BenDhia, A.S., Duruflé, M., Joly, P., and Joubert, L.. Stability of acoustic propagation in a 2d flow duct: A low frequency approach. submitted.Google Scholar
[3]Brambley, E.J.. Fundamental problems with the model of uniform flow over acoustic linings. Journal of Sound and Vibration, 322(4-5):1026–1037, 2009.Google Scholar
[4]Castel, N., Cohen, G., and Duruflé, M.. Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic. Journal of Computational Acoustics, 17(2):175–196, 2009.Google Scholar
[5]Galbrun, H.. Propagation d’une onde sonore dans l’atmosphere terrestre et théorie des zones de silence. Gauthier-Villars, Paris, 1931.Google Scholar
[6]Joly, P. and Weder, R.. A quasi 1D model for aeroacoustics in thin ducts. Submitted.Google Scholar
[7]Legendre, G.. Rayonnement acoustique dans un fluide en écoulement: Analyse mathématique et numérique de l’équation de Galbrun. PhD thesis, 2003.Google Scholar
[8]Schwartz, L.. Theorie des Distributions. Hermann, Paris, 1950.Google Scholar
[9]Stroud, A.H. and Secrest, D.. Gaussian Quadrature Formulas. Prentice-Hall Englewood Cliffs, NJ, 1966.Google Scholar