Simulation of a Falling Elastic Ball using ALE-Fluid-Structure-Interaction with Finite Elements

Abstract

In this work, we show the viability of an Arbitrary Lagrangian Eulerian approach in a large deformation setting with contact by applying it to the example of a falling elastic ball. In the presented method the mesh motion is realized by solving an additional nonlinear harmonic equation, whereas discretization is achieved by finite differences in time and by a Galerkin finite element method in space. The resulting system of non-linear equations is solved by application of a Newton-like method. In a computational analysis with two parameter sets, we investigate the behavior of the elastic ball for different mesh refinements and time step sizes. Our results show the ALE method with proper choices of mesh refinement and time step size is indeed capable of simulating the falling elastic ball. Moreover, it provides results that are overall comparable to a fully Eulerian approach.