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

Abstract

In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction with contact 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. To handle contact, 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 formulation, discretization and implementation are substantiated with an elastic falling ball that comes into contact with the bottom boundary, constituting a challenging state-of-the-art benchmark.