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Perfectly matched layers for the convected Helmholtz equation

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 : In this paper, we propose and analyze perfectly matched absorbing layers for a problem of time-harmonic acoustic waves propagating in a duct in the 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 perfectly matched layers (PMLs). We investigate here a PML model, recently introduced for time-dependent problems, which makes all outgoing waves evanescent. We then analyze 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. © 2004 Society for Industrial and Applied Mathematics.
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Submitted on : Monday, November 4, 2013 - 10:40:02 AM
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Eliane Bécache, Anne-Sophie Bonnet-Ben Dhia, Guillaume Legendre. Perfectly matched layers for the convected Helmholtz equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2004, 42 (1), pp.409-433. ⟨10.1137/s0036142903420984⟩. ⟨hal-00876246⟩



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