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Rayonnement acoustique dans un écoulement cisaille : une méthode d'éléments finis pour la simulation du régime harmonique.

Eve-Marie Duclairoir 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : In this work, the time-harmonic acoustic radiation of a source in an infinite duct, filled with a parallel shear flow, is considered. The phenomenon is modelled by the Galbrun equation whose unknown is the displacement perturbation u. The aim of this study is to compute a finite element method which could be extended to more complex geometries and flows. A previous PhD work achieved by Guillaume Legendre dealt with this problem in the case of a uniform flow, by writing a ”regularized” formulation of the Galbrun equation in order to overcome a lack of ellipticity. This work aims to extend this method to non uniform flows. The additional difficulty comes from the fact that the vorticity ψ = rot u (which is involved in regularization) can not be calculated a priori anymore because the shear effect produces an interaction between acoustics and hydrodynamics. In a dissipative regime, we get the relation between ψ and u thanks to a convolution (along the streamlines). For the slow flows, this relation (which corresponds to a very oscillating integral) can be approximated by a simpler deferential term. The use of the approximation leads to a new model called”low Mach”. A similar approach is applied in order to solve the non dissipative problem by the means of PML (Perfectly Matched Layers). The two approaches (exact and "low Mach") have been validated by 2D and 3D numerical simulations.
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https://pastel.archives-ouvertes.fr/pastel-00002409
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Submitted on : Wednesday, July 28, 2010 - 3:03:22 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM
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Eve-Marie Duclairoir. Rayonnement acoustique dans un écoulement cisaille : une méthode d'éléments finis pour la simulation du régime harmonique.. Mathématiques [math]. Ecole Polytechnique X, 2007. Français. ⟨pastel-00002409⟩

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