Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 86, Issue 11, Pages 1360-1378Publisher
WILEY-BLACKWELL
DOI: 10.1002/nme.3108
Keywords
Dirichlet-to-Neumann map; non-reflecting boundary condition; finite elements; acoustic waveguide; mean flow; impedance boundary condition; liner
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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 (C) 2011 John Wiley & Sons, Ltd.
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