Robust PFEM-FEM Partitioned Coupling Framework for the Simulation of Solids Under Complex Flow-Induced Loads

Simulating solids under complex, flow-induced loads presents a significant challenge in fields like aerospace, turbomachinery, and biological systems. These applications often involve intricate Fluid-Structure Interactions (FSI), which include free surfaces, large deformations, and strong coupling effects, that traditional simulation methods struggle to capture effectively. The finite element code Metafor, developed by the MN2L lab of the University of Liège, can handle large deformations, plasticity, damage and fracture, thermo-mechanical interactions and solid-solid contact, making it ideal for advanced mechanical analysis. However, it cannot simulate complex FSI problems on its own. In applications where strong interactions between a liquid and solid occur, using simplified boundary conditions to represent fluid behavior on the solid surface is insufficient. This thesis addresses that limitation by introducing a framework that couples a Particle Finite Element Method (PFEM) fluid solver with Metafor using a fully partitioned approach. This coupling enables dynamic simulation of both domains and provides more accurate flow-induced boundary conditions for the solid structure. The PFEM is a hybrid technique that combines the flexibility of particle-based methods with the precision of the Finite Element Method (FEM). The core idea of the PFEM is to apply the Lagrangian FEM framework for each time step, combined with a remeshing procedure between time steps that allows fluid parts to separate or merge. While PFEM has shown promising results in handling free-surface flows, splashing, and large deformations, challenges persist in mass conservation and mesh regularization, particularly in 3D configurations. Furthermore, the evolving and non-matching meshes between the fluid and solid solvers present a substantial difficulty in coupling the two domains. This work advances the state of the art in FSI through a coupled PFEM-FEM framework applicable to 2D and 3D problems. The first set of contributions enhances the PFEM by introducing a novel mesh refinement strategy that hinders element quality degradation during remeshing, specialized libraries to regularize mesh degeneracies, and a level set-based method to improve mass conservation. The second focus addresses numerical challenges related to the partitioned FSI coupling with evolving, non-matching meshes. These challenges are addressed by enforcing mechanical and thermal equilibrium between the solvers at each time step, supported by a flexible and efficient mesh interpolation technique. Particular attention has been given to the performance and scalability of the implementation. The proposed framework is validated against a wide range of experimental and numerical benchmarks from the literature. The variety of test cases and their agreement with published results confirm the robustness of the approach.