A low Mach model for time harmonic acoustics in arbitrary flows

Anne-Sophie Bonnet-Ben Dhia 1, 2 Jean-François Mercier 1 Florence Millot 2 Sébastien Pernet 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 : This paper concerns the finite element simulation of the diffraction of a time-harmonic acoustic wave in the presence of an arbitrary mean flow. Considering the equation for the perturbation of displacement (due to Galbrun), we derive a low-Mach number formulation of the problem which is proved to be of Fredholm type and is therefore well suited for discretization by classical Lagrange finite elements. Numerical experiments are done in the case of a potential flow for which an exact approach is available, and a good agreement is observed.
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Journal articles
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Anne-Sophie Bonnet-Ben Dhia, Jean-François Mercier, Florence Millot, Sébastien Pernet. A low Mach model for time harmonic acoustics in arbitrary flows. Journal of Computational and Applied Mathematics, Elsevier, 2010, 234 (6), pp.1868-1875. ⟨10.1016/j.cam.2009.08.038⟩. ⟨hal-00975078⟩

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