Document Free access article
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 Mercier11 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