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

TL;DR

This paper introduces a Nitsche-based method for fluid-structure interaction problems involving contact, using a monolithic variational formulation and Eulerian approach to handle contact and topology changes effectively.

Contribution

It develops a novel Nitsche-based formulation for FSI with contact, incorporating contact conditions directly into the variational framework and addressing topology changes during impact.

Findings

The method effectively models contact in FSI problems.

Numerical examples demonstrate the approach's robustness.

Comparison of slip and no-slip conditions shows impact on results.

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 Journal on Numerical Analysis. 2013;51(2):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 $\Gamma(t)$. 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.