EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Free access article

Issue ESAIM: PROC
Volume 22, 2008
CANUM 2006 - Congrès National d'Analyse Numérique
Page(s) 1 - 14
DOI 10.1051/proc:072201
Published online 01 February 2008

ESAIM: Proc., 2008, Vol. 22, pp. 1-14
DOI: 10.1051/proc:072201

Acoustic propagation in a flow: numerical simulation of the time-harmonic regime

Anne-Sophie Bonnet-Ben Dhia1, 2, Eve-Marie Duclairoir1 and Jean-Francois Mercier1

1  Laboratoire POEMS, UMR 2706, CNRS-ENSTA-INRIA, 32 Boulevard Victor, 75015 Paris, FRANCE. E-mail: Anne-Sophie.Bonnet-Bendhia@ensta.fr; E-mail: Eve-Marie.Duclairoir@ensta.fr; E-mail: Jean-Francois.Mercier@ensta.fr
2  CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France


(Published online: 1 February 2008)

Abstract
We consider the time-harmonic acoustic radiation of a source in a moving fluid. The problem is set in a two-dimensional infinite duct and the mean flow is a subsonic parallel shear flow, with a regular profile. We deal with an equation (due to Galbrun) whose unknown is the displacement perturbation. We show how to solve the problem with a finite element method by writing a "regularized" or "augmented" formulation and using Perfectly Matched Layers to select the outgoing solution. Due to the presence of a non-local term coming from the regularization, an iterative process of resolution is preferred, which converges faster for weaker shear. Some mathematical results are established in the dissipative case. Numerical illustrations are finally presented.


Mathematics Subject Classification. 76Q05, 35J20, 65N30

Key words: aeroacoustics, Galbrun, finite elements, shear flow, regularization, PML


© EDP Sciences, ESAIM 2007


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.