Arbitrary Lagrangian-Eulerian (ALE)-Based Finite Element Methods for Rigid Solids Immersed in Fluids

Abstract

Arbitrary Lagrangian-Eulerian approaches are widely used in CFD, especially in multiphysics problems. They involve two tasks, namely the computation of the physical variables (velocity, stress, force, torque, etc.) and the determination of a suitable mesh deformation. We consider here a decoupled treatment of these two tasks, with high-order temporal schemes obtained by extrapolation, as discussed in F. Montefuscolo et.al. (J Comp Phys, 278:133-147, 2014) for capillary problems. Extensions of these schemes to fluid/rigid-body interaction are presented, adopting a variational formulation made popular by R. Glowinski et.al. in their work on Fictitious Domain Methods (J Comp Phys, 169:363426, 2001). The Arbitrary Lagrangian-Eulerian discretization turns the variational fluid-solid problem into a Differential-Algebraic Equation system for which several schemes, with different orders of accuracy, are implemented and evaluated. Special attention is dedicated to issues of stability, which is a fundamental obstacle towards the effective simulation of microfluidic fluid-solid interaction problems.