A Nitsche-based formulation for fluid-structure interactions with contact

¹ Department of Mathematics, University College London, Gower Street, WC1E 6BT, London, UK
² Inria Paris, 75012 Paris, France
³ Sorbonne Université & CNRS, UMR 7598 LJLL, 75005 Paris, France

^* Corresponding author: s.frei@ucl.ac.uk

Received: 21 February 2019
Accepted: 14 October 2019

Abstract

We derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact. The approach is based on the work of Chouly and Hild (SIAM J. Numer. Anal. 51 (2013) 1295–1307) for contact problems in solid mechanics. We present two numerical approaches, both of them formulating the FSI interface and the contact conditions simultaneously in equation form on a joint interface-contact surface Γ(t). The first approach uses a relaxation of the contact conditions to allow for a small mesh-dependent gap between solid and wall. The second alternative introduces an artificial fluid below the contact surface. The resulting systems of equations can be included in a consistent fashion within a monolithic variational formulation, which prevents the so-called “chattering” phenomenon. To deal with the topology changes in the fluid domain at the time of impact, we use a fully Eulerian approach for the FSI problem. We compare the effect of slip and no-slip interface conditions and study the performance of the method by means of numerical examples.