Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 44, Issue 3, Pages 1191-1217Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040617741
Keywords
aeroacoustics; Galbrun's equation; limiting absorption principle; perfectly matched layers; acoustic waveguide; modal decomposition
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This paper is devoted to the resolution of the time-harmonic linearized Galbrun equation, which models, via a mixed Lagrangian - Eulerian representation, the propagation of acoustic and hydrodynamic perturbations in a given flow of a compressible fluid. We consider here the case of a uniform subsonic flow in an infinite, two-dimensional duct. Using a limiting absorption process, we characterize the outgoing solution radiated by a compactly supported source. Then we propose a Fredholm formulation with perfectly matched absorbing layers for approximating this outgoing solution. The convergence of the approximated solution to the exact one is proved, and error estimates with respect to the parameters of the absorbing layers are derived. Several significant numerical examples are included.
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