Commun. Comput. Phys., 11 (2012), pp. 508-524.


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

Lauris Joubert 1*, Patrick Joly 2

1 POEMS, CNRS-INRIA-ENSTA UMR 2706, 32 Boulevard Victor, 75015 Paris, France.
2 POEMS, CNRS-INRIA-ENSTA UMR 2706, INRIA Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France.

Received 18 December 2009; Accepted (in revised version) 4 January 2011
Available online 24 October 2011
doi:10.4208/cicp.181209.040111s

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.

AMS subject classifications: 35B35, 35Q35, 35C15

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Key words: Acoustics in flow, Galbrun's equations, asymptotic analysis, Laplace transform.

*Corresponding author.
Email: lauris.joubert@gmail.com (L. Joubert), Patrick.Joly@inria.fr (P. Joly)
 

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