Numerical Analysis and Scientific Computing Preprint Seria An extended ALE method for fluid-structure interaction problems with large structural displacements

Standard Arbitrary Lagrangian-Eulerian (ALE) methods for the simulation of fluid-structure interaction (FSI) problems fail when the structural displacement is large. We propose an extended ALE method that successfully deals with this problem without remeshing. The extended ALE approach relies on a variational mesh optimization technique, combined with an additional constraint which is imposed to enforce the alignment of the structure with certain edges of the fluid triangulation without changing connectivity. This method is applied to a 2D FSI benchmark problem modeling valves: a thin elastic 1D leaflet, modeled by an inextensible beam equation, is immersed in a 2D incompressible, viscous fluid driven by the time-dependent inlet and outlet data. The fluid and structure are fully coupled via the kinematic and dynamic coupling conditions. The problem is solved using a Dirichlet-Neumann algorithm, which is enhanced by an adaptive relaxation procedure based on Aitken’s acceleration. The proposed method is assessed through several numerical tests, including a comparison with a standard ALE method when the structural displacement is small. It is shown that that proposed method deals well with both small and large displacements, and that thanks to the interface alignment, the hydrodynamic force at the interface can be computed accurately.