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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 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : This paper is devoted to the resolution of the time-harmonic linearized Galbrun's 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 amplitude 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.
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Submitted on : Friday, May 19, 2006 - 8:45:12 PM
Last modification on : Thursday, October 27, 2022 - 4:03:06 AM
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  • HAL Id : inria-00070521, version 1


Eliane Bécache, Anne-Sophie Bonnet-Ben Dhia, Guillaume Legendre. Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow. [Research Report] RR-5486, INRIA. 2005, pp.35. ⟨inria-00070521⟩



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