Numerical Modeling and Simulations of Fully Eulerian Fluid-Structure Interaction using a Ghost-Penalty Cut Finite Element Approach

  • Frei, Stefan (University of Konstanz)
  • Knoke, Tobias (Leibniz University Hannover)
  • Steinbach, Marc Christian (Leibniz University Hannover)
  • Wenske, Anne-Kathrin (Leibniz University Hannover)
  • Wick, Thomas (Leibniz University Hannover)

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In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction in Eulerian coordinates. In the Eulerian description fluid flow modeled by the incompressible Navier-Stokes equations remains in Eulerian coordinates, while elastic solids are transformed from Lagrangian coordinates into the Eulerian system. A monolithic description is adopted. For the spatial discretization, we employ an unfitted finite element method with ghost penalties based on inf-sup stable finite elements. Our model does also include contact. To handle that, we use a relaxation of the contact condition in combination with a unified Nitsche approach that takes care implicitly of the switch between fluid-structure interaction and contact conditions. The temporal discretization is based on a backward Euler scheme with implicit extensions of solutions at the previous time step. The nonlinear system is solved with a semi-smooth Newton's method with line search. Our developments are substantiated with different numerical tests.