SC Colloquium: "A fully Eulerian approach for fluid-structure interactions with contact"
Numerical Analysis Group
Institute of Applied Mathematics
This talk is concerned with the simulation of fluid-structure interaction problems with large solid displacements up to contact of different solids or a solid with a wall. To be able to deal with the topology changes arising in the fluid domain, we use a monolithic fully Eulerian approach.
A monolithic Eulerian approach poses several challenges for a finite element discretization, as the solid and the interface move over mesh lines and the solution is not smooth across the interface. If the position of the interface is not considered in the discretization, severe stability and accuracy issues might arise.
In this talk, we present accurate discretization schemes in space and time as well as a robust numerical framework to circumvent these issues. The basic idea of the discretization in both space and time is to resolve the interface locally within the discretization. The spatial discretization uses a fixed patch mesh independent of the interface location and a local refinement that takes the interface into account. In this way, moving interfaces can be resolved without re-meshing. For time discretization, we develop a time-stepping scheme based on a Galerkin ansatz in time on space-time trajectories that follow the movement of the interface. For both space and time discretization, we show second-order convergence estimates.
Finally, we present simple contact algorithms based on a penalty force and using an active set strategy for the case that no fluid layer remains between the solids. We apply the numerical framework to simulate plaque growth in arteries and to the problem of a bouncing ball including contact with the ground and bouncing down some stairs.