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Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts

Publikace na Matematicko-fyzikální fakulta |
2024

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

In this paper, we study an interaction problem between a 3D compressible viscous fluid and a 3D nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have self-contact or contact with the rigid boundary of the fluid container.

For this problem, a global weak solution with defect measure is constructed by using a multi-layered approximation scheme which decouples the body and the fluid by penalizing the fluid velocity and allowing the fluid to pass through the body, while the body is supplemented with a contact-penalization term. The resulting defect measure is a consequence of pressure concentrations that can appear where the fluid meets the (generally irregular) points of self-contact of the solid.

Moreover, we study some geometrical properties of the fluid-structure interface and the contact surface. In particular, we prove a lower bound on area of the interface.