Past Event: Oden Institute Seminar

Fluid-Structure Interaction in ALE, Fully Eulerian, and EALE Coordinates

Thomas Wick, Institute of Applied Mathematics, University of Heidelberg, Germany

Abstract

In this talk, we compare novel formulations for fluid-structure interac- tion problems to the arbitrary Lagrangian-Eulerian (ALE) framework. The well-established ALE approach provides a simple procedure to couple fluid equations with structural deformations. In such a setting, the fluid equations are transformed to a fixed reference domain. However, the mesh moving becomes the critical part for large structural deformations or contact with walls or other structures. To overcome the deficiency, we present the novel fully Eulerian approach (which has only been tested for preliminary problems so far) to formulate fluid-structure interaction problems. The idea is the opposite way to the ALE method. The fluid equations are kept in their natural coordinates and the structure is transformed into the Eulerian framework. However, the interface is allowed to intersect mesh cells, which is the major drawback of this method. We present a methodology how to cope with this deficiency. Finally, in our third technique, the fully Eulerian approach is coupled with the ALE method and formulated in one common framework. This technique allows to set up elastic structure deformations in different coordinate systems. Each problem is formulated in a monolithic fashion that allows to compute sensitivities for a posteriori error estimation and gradient-based optimization. The nonlinear problem is solved with Newton’s method. Time discretization is based on finite difference schemes whereas the spatial discretization is done with a Galerkin finite element scheme. The performance of all three techniques is demonstrated with the help of numerical examples.