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A low-Mach number model for time-harmonic acoustics in arbitrary flows. (English) Zbl 1407.76139
Summary: 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.

MSC:
76Q05 Hydro- and aero-acoustics
76M10 Finite element methods applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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