Modeling, analysis and simulation of fluid-structure-contact interaction including seepage

Fluid-structure-contact interaction models describe situations where immersed structures may come into contact, as in cardiac valves. Yet modeling contact remains challenging due to the no-collision paradox and mechanical inconsistencies at contact and release. In this talk, we consider an approach based on modeling the fluid seepage through the microscopic surface asperities via a thin porous layer at the fluid-structure interface. First, we will show that, in the case of a rigid disk moving over a fixed horizontal plane, adding a surface Darcy model on the plane allows for contact, and hence removes the no-collision paradox of traditional FSI models, which rely on Dirichlet or Dirichlet/Navier boundary conditions. Numerical evidence supporting this result will also be provided. Finally, we will extend the porous seepage modeling to the case of moving elastic thin-walled structures and propose a stable discretization scheme with numerical illustrations.