|Title:||Homogenization of the fluid–structure interaction in acoustics of porous media perfused by viscous fluid|
|Citation:||ROHAN, E., NAILI, S. Homogenization of the fluid–structure interaction in acoustics of porous media perfused by viscous fluid. Zeitschrift für angewandte Mathematik und Physik, 2020, roč. 71, č. 4, s. 1-28. ISSN 0044-2275.|
|Keywords:||Homogenization;porous media;acoustic waves;Navier Stokes equations;fluid structure interaction;dynamic permeability;advection;modelování a optimalizace|
|Abstract in different language:||This paper aims to clarify the homogenization results of the fluid–structure interaction in porous structures under the quasi-static and dynamic loading regimes. In the latter case, the acoustic fluctuations yield naturally a linear model which can be introduced in the configuration deformed as the consequence of the steady permanent flow. We consider a Newtonian slightly compressible fluid under the barotropic acoustic approximation. In contrast with usual simplifications, the advection phenomenon of the Navier–Stokes equations is accounted for. The homogenization results are based on the periodic unfolding method combined with the asymptotic expansion technique which provide a straight procedure leading the local problems for corrector functions yielding the effective model parameters and the macroscopic model. We show that the local problems for the solid and fluid parts are decoupled even in the dynamic interactions including the wall shear stress on the periodic interfaces. The dynamic permeability depends on the fluid flow properties including the advection effects associated with an assumed stationary perfusion of the porous structure.|
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