Monolithic cut finite element based approaches for fluid-structure interaction

TL;DR

This paper introduces innovative cut finite element methods for fluid-structure interaction that combine fixed-grid and moving mesh approaches, enabling efficient handling of complex, moving, and topologically changing fluid domains.

Contribution

It presents new monolithic cut finite element approaches for FSI that simplify mesh generation and effectively manage large structural motions and topological changes.

Findings

Validated methods with various 2D and 3D FSI cases.

Demonstrated high potential for simplified mesh handling.

Showcased ability to deal with large motions and topological changes.

Abstract

Cut finite element method (CutFEM) based approaches towards challenging fluid-structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed-grid) and established Arbitrary-Lagrangian-Eulerian (ALE) (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving domain problems and to demonstrate their high potential with regards to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed-grid FSI method, also advanced fluid domain decomposition techniques are considered rendering in highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche-based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various 2D and 3D FSI-cases of different complexity validate the methods and demonstrate their capabilities and limitations in different situations.