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Mathematical analysis of the acoustic diffraction by a muffler containing perforated ducts

Anne-Sophie Bonnet-Ben Dhia 1 Dora Drissi 2 Nabil Gmati 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : We consider the three-dimensional scalar problem of acoustic propagation in a muffler. We develop and analyze a Fredholm-type formulation for a stationary fluid in the timeharmonic setting. We prove a homogenization result for a muffler containing periodically perforated ducts. Essentially, the perforated boundaries become completely transparent when the period of perforations, which is assumed to be of the same order as the size of perforations, tends to zero. We also derive a homogenized impedance condition when the perforated duct is coated by an absorbing material. We present numerical examples in two dimensions, obtained from coupling finite elements in the muffler with modal decompositions in the inlet and outlet ducts, which demonstrate the limiting validity of the theoretical results. © World Scientific Publishing Company.
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Anne-Sophie Bonnet-Ben Dhia, Dora Drissi, Nabil Gmati. Mathematical analysis of the acoustic diffraction by a muffler containing perforated ducts. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2005, 15 (7), pp.1059-1090. ⟨10.1142/s0218202505000649⟩. ⟨hal-00876243⟩



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