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An improved multimodal approach for non-uniform acoustic waveguides

Christophe Hazard 1 Éric Lunéville 1 
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 explores from the point of view of numerical analysis a method for solving the acoustic time-harmonic wave equation in a locally non-uniform 2D waveguide. The multimodal method is based on a spectral description of the acoustic field in each transverse section of the guide, using Fourier-like series. In the case of sound-hard boundaries, the weak point of the method lies in the poor convergence of such series due to a poor approximation of the field near the boundaries. A remedy was proposed by Athanassoulis & Belibassakis (1999, J. Fluid Mech., 389, 275-301), where the convergence is improved thanks to the use of enhanced series. The present paper proposes a theoretical analysis of their idea and studies further improvements. For a general model which includes different kinds of non-uniformity (varying cross section, bend and inhomogeneous medium), a hybrid spectral/variational formulation is introduced. Error estimates are provided for a semi-discretized problem which concerns the effect of spectral truncation. These estimates are confirmed by numerical results. © The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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Submitted on : Thursday, October 17, 2013 - 2:12:10 PM
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Christophe Hazard, Éric Lunéville. An improved multimodal approach for non-uniform acoustic waveguides. IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2008, 73 (4), pp.668-690. ⟨10.1093/imamat/hxn006⟩. ⟨hal-00873082⟩



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