We study the existence of a weak solution to a regularized, moving boundary, fluid-structure interaction problem with multi-layered poroelastic media consisting of a reticular plate located at the interface between the free flow of an incompressible, viscous fluid modeled by the 2D Navier–Stokes equations, and a poroelastic medium modeled by the 2D Biot equations. The existence result holds for both the elastic and viscoelastic Biot model. The free fluid flow and the poroelastic medium are coupled via the moving interface (the reticular plate) through the kinematic and dynamic coupling conditions. The reticular plate is “transparent” to fluid flow. The nonlinear coupling over the moving interface presents a major difficulty since both the fluid domain and the poroelastic medium domain are functions of time, and the finite energy spaces do not provide sufficient regularity for the corresponding weak formulation to be well-defined. This is why in this manuscript we consider a regularized problem by employing convolution with a smooth kernel only where needed. The resulting problem is still very challenging due to the nonlinear coupling and the motion of the fluid and Biot domains. We provide a constructive existence proof for this regularized fluid-poroelastic structure interaction problem. This regularized problem is consistent with the original, nonregularized problem in the sense that the weak solutions constructed here, converge, as the regularization parameter tends to zero, to a classical solution of the original, nonregularized problem when such a classical solution exists, assuming viscoelasticity in the Biot poroelastic matrix [1]. Furthermore, the existence result presented in this manuscript, is a crucial stepping stone for the singular limit problem in which the thickness of the reticular plate tends to zero. Namely, in [1] we will show that, in the case of a Biot poroviscoelastic matrix, the moving boundary problem obtained in the singular limit as the thickness of the plate tends to zero, has a weak solution.
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Jeffrey Kuan 1; Sunčica Čanić 1; Boris Muha 2

@article{CRMECA_2023__351_S1_505_0, author = {Jeffrey Kuan and Sun\v{c}ica \v{C}ani\'c and Boris Muha}, title = {Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media}, journal = {Comptes Rendus. M\'ecanique}, pages = {505--534}, publisher = {Acad\'emie des sciences, Paris}, volume = {351}, number = {S1}, year = {2023}, doi = {10.5802/crmeca.190}, language = {en}, }
TY - JOUR AU - Jeffrey Kuan AU - Sunčica Čanić AU - Boris Muha TI - Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media JO - Comptes Rendus. Mécanique PY - 2023 SP - 505 EP - 534 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.190 LA - en ID - CRMECA_2023__351_S1_505_0 ER -
%0 Journal Article %A Jeffrey Kuan %A Sunčica Čanić %A Boris Muha %T Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media %J Comptes Rendus. Mécanique %D 2023 %P 505-534 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.190 %G en %F CRMECA_2023__351_S1_505_0
Jeffrey Kuan; Sunčica Čanić; Boris Muha. Existence of a weak solution to a regularized moving boundary fluid-structure interaction problem with poroelastic media. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 505-534. doi : 10.5802/crmeca.190. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.190/
[1] Fluid-poroelastic structure interaction with moving boundary (2023) (In draft form. To be submitted)
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