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CutFEM for fully Eulerian fluid-structure interactions: Numerical Analysis
Stefan Frei1, Tobias Knoke2, Marc Steinbach2, Anne-Kathrin Wenske2, Thomas Wick2
1: Universität Konstanz, Germany; 2: Leibniz Universität Hannover, Germany
In a monolothic variational formulation of a fluid-structure interaction problem the Eulerian description of the fluid equations needs to be combined with the Lagrangian description of the solid. To this end, different methodologies have been proposed such as the well-known Arbitrary Lagrangian Eulerian method. Additional challenges arise, when the solid undergoes very large deformations or the topology changes. In these cases, a standard Arbitrary Lagrangian Eulerian formulation without any remeshing is likely to fail. A fully Eulerian description, which is achieved by rewriting the Lagrangian solids into the Eulerian framework instead, is able to handle these type of problems in a straight forward manner. Using geometrically unfitted techniques and capturing the interface between fluid and solid, the fluid-structutre interaction problem may now be solved without the cost of highly ansiotropic mesh cells that arise in fitted approaches. Previously, a CutFEM formulation using stabilization via jump based ghost penalization has been succesfully applied to nonlinear fluid-structure interaction problems including contact. In this talk, we will focus on the numerical analysis in terms of a linear FSI model problem with a fixed interface. Stability estimates including pressure stability are derived by means of inf-sup-stable finite elements for the fluid. Optimal convergence properties are shown and substantiated by a numerical experiment.
