## Modeling of slightly-compressible isentropic flows and compressibility effects on fluid-structure interactions.(English)Zbl 1411.76076

Summary: In this study, an aeroacoustic fluid model for slightly-compressible isentropic flows is developed and evaluated for its compressibility effects in the context of fluid-structure interactions. This model considers computational feasibility and accuracy by adding compressibility terms directly on the incompressible form of Navier-Stokes equation. Rather than solving for the full compressible form, our slightly-compressible form significantly reduces the complications in establishing stabilization and implementation of its finite element procedure, and yet still captures the fluctuating acoustic waves expected in the compressible form. Using this approach, we demonstrate that generations and propagations of acoustic waves can be accurately captured, without the inclusion of a fully compressible representation of the fluid. Upon the successful verification of its accuracy against analytical and known solutions, we then evaluate the fluid compressibility effect on fluid-structure interactions. Our results show that comparing to an incompressible fluid, a deformable solid generates sound waves while it is driven by the flow and vibrates in the fluid. A periodic volume change in the fluid is also observed, which can be considered as a sound source.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76N15 Gas dynamics (general theory)

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