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
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
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.