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An ultra-weak method for acoustic fluid-solid interaction. (English) Zbl 1182.76949

This authors propose an ultra-weak variational formulation (UWVF) for a coupled system of Helmholtz and time-harmonic Navier equations which characterizes the scattering of sound in media consisting of fluid and elastic components. Due to the particular flux-type coupled conditions needed for UWVF, the standard fluid-solid transmission conditions must be rewritten in an unusual form to enforce the balance of normal displacement and force over the interface. Since spurious numerical resonances are known to hamper some computational techniques for fluid-solid problems, specific attention is given via numerical simulations to the resonances of the proposed method. Numerical tests show that this new scheme offers advantages compared to low-order finite element method schemes.

MSC:

76Q05 Hydro- and aero-acoustics
76M30 Variational methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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