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Efficient solution of a wave equation with fractional-order dissipative terms

Haddar, Houssem and Li, Jing Rebeca and Matignon, Denis Efficient solution of a wave equation with fractional-order dissipative terms. (2010) Journal of Computational and Applied Mathematics, vol. 2 (n° 6). pp. 2003-2010. ISSN 0377-0427

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Official URL: http://dx.doi.org/10.1016/j.cam.2009.08.051

Abstract

We consider a wave equation with fractional-order dissipative terms modeling viscothermal losses on the lateral walls of a duct, namely the Webster-Lokshin model. Diffusive representations of fractional derivatives are used, first to prove existence and uniqueness results, then to design a numerical scheme which avoids the storage of the entire history of past data. Two schemes are proposed depending on the choice of a quadrature rule in the Laplace domain. The first one mimics the continuous energy balance but suffers from a loss of accuracy in long time simulation. The second one provides uniform control of the accuracy. However, even though the latter is more efficient and numerically stable under the standard CFL condition, no discrete energy balance has been yet found for it. Numerical results of comparisons with a closed-form solution are provided.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA
Other partners > Ecole Nationale Supérieure de Techniques Avancées - ENSTA (FRANCE)
Other partners > Ecole Polytechnique (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS
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Deposited By:Denis Matignon

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