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Numerical Simulation of Acoustic Waveguides for Webster-Lokshin Model Using Diffusive Representations

Hélie, Thomas and Matignon, Denis Numerical Simulation of Acoustic Waveguides for Webster-Lokshin Model Using Diffusive Representations. (2003) In: Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 : Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003. Springer Berlin Heidelberg, 72-77. ISBN 978-3-642-62480-3

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Official URL: http://dx.doi.org/10.1007/978-3-642-55856-6_11


This paper deals with the numerical simulation of acoustic wave propagation in axisymmetric waveguides with varying cross-section using a Webster-Lokshin model. Splitting the pipe into pieces on which the model coefficients are nearly constant, analytical solutions are derived in the Laplace domain, enabling for the realization of the propagation by concatenating scattering matrices of transfer functions (§2). These functions involve standard differential and delay operators, as well as pseudo-differential operators of diffusive type, induced by both the viscothermal losses and the curvature. These operators are explicitly decomposed thanks to an asymptotic expansion, and the diffusive ones may be defined and classified (§3). Various equivalent diffusive realizations may be proposed, that are deeply linked to choices of cuts in the complex analysis of the transfer functions. Then, finite order approximations are given for their simulation (§4).

Item Type:Book Section
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole nationale supérieure des Télécommunications - ENST (FRANCE)
Other partners > Télécom Paris (FRANCE)
Other partners > Université Pierre et Marie Curie, Paris 6 - UPMC (FRANCE)
Other partners > Institut de Recherche et Coordination Acoustique/Musique - IRCAM (FRANCE)
Laboratory name:
Deposited On:30 Sep 2016 09:01

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