Three-dimensional mesh adaptation in PFEM

Abstract: Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a natural choice. One such method is the Particle Finite Element Method (PFEM). As a hybrid particle-based and mesh-based method, PFEM leverages advantages from both approaches. The equations of motion are solved on a mesh using the finite element method and the obtained velocity field is used to displace the nodes of this mesh, considered as particles carrying all the relevant information across time steps. To avoid element distortion, the mesh is frequently re-generated. This introduces some challenges: How can the new shape of the domain be detected? How can the quality of the elements be kept acceptable? Can adaptive mesh refinement increase the accuracy and efficiency of the solver? Can PFEM simulations be performed in the presence of complex boundary geometries? In this work, three contributions to the geometry and mesh component of PFEM are introduced for three-dimensional free surface flow simulations. First, we propose a different domain reconstruction approach than the classically used alpha-shape procedure, namely through the use of the advected boundary from the previous time step as a predicate to represent the new shape of the domain. Second, an adaptive refinement procedure is proposed in two steps: refinement of the boundary surface followed by quality-based node insertion in the bulk. Third, an approach for managing boundaries in complex geometries is presented. A series of applications is shown to demonstrate the interest of the approach.