Non‐reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow |
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Authors: | E Redon A‐S Bonnet‐Ben Dhia J‐F Mercier S Poernomo Sari |
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Affiliation: | 1. Université de Bourgogne, 9 Avenue Alain Savary, 21000 Dijon, France;2. LVA INSA de Lyon, 25 bis Avenue Jean Capelle, 69621 Villeurbanne, France;3. POEMS (UMR 7231 CNRS‐INRIA‐ENSTA), 32 Boulevard Victor, 75015 Paris, France;4. CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France |
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Abstract: | We consider a time‐harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non‐reflecting boundary condition on the artificial boundary by means of a Dirichlet‐to‐Neumann (DtN) map based on a modal decomposition. Compared with the hard‐walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft‐walled guide. However, an accurate approximation of the DtN map can be derived using some bi‐orthogonality relations, valid asymptotically for high‐order modes. Numerical validations show the efficiency of the method. The influence of the liner with or without mean flow is illustrated. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | Dirichlet‐to‐Neumann map non‐reflecting boundary condition finite elements acoustic waveguide mean flow impedance boundary condition liner |
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