A Fully Eulerian Formulation for Fluid-Structure Interaction problems

The mutual interaction between fluids and solids plays an important role for the overall dynamics of systems in a variety of applications in physics, biology or engineering. Important applications include for example hemodynamical problems and aerodynmics.

This project deals with the development of efficient and robust discretizations for the solution of fluid-structure interaction problems. We are especially interested in problems, where the solid undergoes large deformations or movements up to contact with the boundary.
The well-studied Arbitrary Lagrangian Eulerian (ALE) method tends to fail for applications of this kind due to degeneration of the underlying finite element grid. In a Fully Eulerian Method, in contrast, solid and interface move over a fixed background mesh. This ansatz is thus capable of dealing with arbitrary movements up to contact.
A standard finite element method for spatial discretization leads to a reduced order of convergence in the interface cells, however, and may cause numerical instabilities when the interface moves over grid cells. One key ingredient of this project is the design of a locally modified finite element scheme which is well-suited and robust for moving interface problems.