A fully partitioned Lagrangian framework for FSI problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects

Abstract

In this work a fully partitioned Lagrangian framework for the solution of fluid–structure interaction (FSI) problems involving free surfaces, large solid displacements and deformations, and strong added mass effects is presented. The fluid is simulated using the Particle Finite Element Method (PFEM), while Metafor, a large deformations nonlinear Finite Element code, is employed to simulate the solid part. The fully partitioned coupling is ensured through an Interface Quasi-Newton Inverse Least Squares (IQN-ILS) (Degroote et al., 2009) strategy to avoid added mass effects. The Lagrangian particle nature of the PFEM allows the simulation of problems involving free surfaces and very large solid displacements, usually difficult to achieve with traditional body-fitted CFD techniques. We show that owing to the generality of its formulation the PFEM can be used as is in the framework of fully partitioned FSI coupling schemes, where minimal information (i.e. loads and displacements at the FSI interface) is exchanged between the fluid and the solid solvers. More importantly, we demonstrate that a fully partitioned PFEM–FEM coupling based on the IQN-ILS strategy allows the simulation of a very large spectrum of FSI problems without incurring added-mass instabilities. The performance of the IQN-ILS coupling strategy in a fully Lagrangian framework is also assessed and compared to more traditional approaches such as Block-Gauss–Seidel (BGS) iterations with Aitken relaxation. An extensive work of verification and benchmarking is proposed, aiming to encompass all the combinations of physical and numerical parameters possibly leading to added-mass instabilities, and testing the IQN-ILS strategy on different benchmarks beyond those already proposed in the literature. The coupling is performed through CUPyDO (Thomas et al., 2019), a general Python framework for partitioned FSI coupling.