An efficient level set-based mesh adaptation for the particle finite element method
Martin Lacroix, Eduardo Fernández, Simon Février, Luc Papeleux, Romain Boman, Jean-Philippe Ponthot
Abstract
The Particle Finite Element Method (PFEM) is a discretization technique that combines the flexibility of particle-based methods with the precision of finite elements, using a Lagrangian approach to naturally track evolving interfaces and automatic remeshing to prevent mesh distortion. Historically, the PFEM has relied on the extraction of an α -shape from a Delaunay triangulation of the cloud of nodes forming fluid domain during the remeshing process. This approach helps to maintain good quality elements throughout the simulation, but introduces shortcomings that demand geometrical treatments tailored to each problem. In order to improve the remeshing process in PFEM, Falla et al. (2023) proposed a 2D mesh adaptation technique based on the edge splitting, showing promising results in terms of mass conservation and mesh quality. In parallel, Fernández et al. (2023) proposed the use of a level set (LS) function instead of the α -shape criterion, demonstrating improved mass conservation and free surface smoothness compared to standard approaches. While both innovative and foundational, these approaches have been limited to 2D applications, and the computation of the LS adds significant execution time to the PFEM. In this work, we propose a new remeshing algorithm, building upon the advances achieved by Falla and Fernández, designed to deliver good performance while extending the capability to handle 3D scenarios effectively. The interest of the LS lies in its ability to consider the overall fluid volume rather than focusing on the shape of individual elements as in the classical α -shape. Consequently, the LS allows for a better control over the connecting elements that are created during the fluid/fluid or fluid/solid contact, which helps to reduce spurious mass creation when merging free surfaces. The methodology is presented and validated using free surface flow problems in 2D and 3D. Finally, an overview of computation times is provided.