A locally enriched space-time finite element method for fluid-structure interaction of thin flexible bodies

The concept of a numerical method for investigating interaction phenomena of viscous fluid flow and flexible structures of negligible thickness like membranes and plates on a topologically fixed fluid discretization is presented. The linear elastic and geometrically nonlinear structure is embedded into the flow field described by the incompressible Navier-Stokes equations using locally enriched space-time finite elements. Since the formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns and the integration of governing equations is perfomed on the enriched space-time discretization, the realization of a strong coupling of the physical domains becomes very comfortable and results in a monolithic system. Forthcoming numerical examples of fluid-stucture interaction will show the ability of the developed methodology in order to describe the behavior of coupled systems where available mesh moving strategies are not longer applicable and would need the introduction of time-consuming remeshing algorithms.