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Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow

Eliane Bécache 1 Anne-Sophie Bonnet-Ben Dhia 1 Guillaume Legendre 1, 2 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper is devoted to the resolution of the time-harmonic linearized Galbrun equation, which models, via a mixed Lagrangian-Eulerian representation, the propagation of acoustic and hydrodynamic perturbations in a given flow of a compressible fluid. We consider here the case of a uniform subsonic flow in an infinite, two-dimensional duct. Using a limiting absorption process, we characterize the outgoing solution radiated by a compactly supported source. Then we propose a Fredholm formulation with perfectly matched absorbing layers for approximating this outgoing solution. The convergence of the approximated solution to the exact one is proved, and error estimates with respect to the parameters of the absorbing layers are derived. Several significant numerical examples are included. © 2006 Society for Industrial and Applied Mathematics.
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Submitted on : Thursday, October 31, 2013 - 3:50:51 PM
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Eliane Bécache, Anne-Sophie Bonnet-Ben Dhia, Guillaume Legendre. Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2006, 44 (3), pp.1191-1217. ⟨10.1137/040617741⟩. ⟨hal-00876236⟩



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