Analysis of incompressible flows with free surfaces and slip walls using a position-based PFEM approach

Resumo

Moving-boundary incompressible flows with topological changes present major challenges for numerical simulation. The Particle Finite Element Method (PFEM) has proven to be a robust framework for such problems, especially due to its ability to handle large deformations and free surfaces. In the PFEM approach, a Delaunay triangulation is generated over the cloud of particles at each time step, and the alpha-shape method is employed to remove non-physical elements and define the domain boundaries. However, when wall particles are allowed to slide tangentially along slip boundaries, the resulting mesh may become distorted, leading to the removal of boundary elements by the alpha-shape procedure and ultimately causing artificial leakage and lost of physical boundary representation. This work proposes a position-based strategy to incorporate slip wall conditions into PFEM simulations while preserving mesh integrity. The method relies on a nodal repositioning technique that restores the original geometry of the slip boundary after particle motion, ensuring that wall elements are retained during remeshing. This approach enables the accurate and robust simulation of flows with free surfaces and sliding walls, without sacrificing the advantages of the position-based PFEM formulation. The proposed methodology also maintains compatibility with structural systems, allowing for straightforward monolithic coupling in fluid–structure interaction problems. Numerical examples demonstrate the accuracy and robustness of the formulation in preserving slip wall behavior and domain integrity, even in highly dynamic flow scenarios.