Existence of a weak solution to a 3d nonlinear, moving boundary FSI problem

Abstract: We consider a nonlinear, moving boundary, fluid-structure interaction problem between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid flow is modeled by the time-dependent Navier-Stokes equations in a threedimensional cylindrical domain, while the cylindrical shell is described by the two-dimensional linearly elastic Koiter shell equations allowing displacements in all three spatial directions. The mesh-like structure is modeled as a onedimensional hyperbolic net made of linearly elastic curved rods. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time-discretization via Lie operator splitting method, Arbitrary Lagrangian-Eulerian mapping and non-trivial compactness result. This is a joint work with Suncica Canic and Boris Muha.

Mathematics

Audience: researchers in the topic

Necas PDE seminar