Monolithic cut finite element–based approaches for fluid‐structure interaction

Summary Cut finite element method–based approaches toward 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 (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 regard 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, advanced fluid‐domain decomposition techniques are also considered, leading to 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 two‐ and three‐dimensional FSI cases of different complexity levels validate the methods and demonstrate their capabilities and limitations in different situations.