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Perfectly matched layers for the convected Helmholtz equation

Eliane Bécache 1 Anne-Sophie Bonnet-Ben Dhia 1 Guillaume Legendre 1
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 : In this paper, we propose and analyze perfectly matched absorbing layers for a problem of time harmonic acoustic waves propagating in a duct in presence of a uniform flow. The absorbing layers are designed for the pressure field, satisfying the convected scalar Helmholtz equation. A difficulty, compared to the Helmholtz equation, comes from the presence of so-called inverse upstream modes which become unstable, instead of evanescent, with the classical Bérenger's PMLs. We introduce here a new PML model which makes all outgoing waves evanescent. We then analyse the error due to the truncation of the domain and prove that the convergence is exponential with respect to the size of the layers, for both the classical and the new PML models. Numerical validations are finally presented.
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Submitted on : Tuesday, May 23, 2006 - 7:11:13 PM
Last modification on : Friday, December 3, 2021 - 11:34:05 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:43:21 PM


  • HAL Id : inria-00071896, version 1



Eliane Bécache, Anne-Sophie Bonnet-Ben Dhia, Guillaume Legendre. Perfectly matched layers for the convected Helmholtz equation. [Research Report] RR-4690, INRIA. 2003. ⟨inria-00071896⟩



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