Final work :Approaches to improve mass conservation in PFEM for the simulation of free-surface flows

Abstract

Solving complex simulations while ensuring high accuracy is a challenge, as seen in simulations that involve free-surfaces and large displacements. One way to better solve them is via the Particle Finite Element Method (PFEM). The Particle Finite Element Method (PFEM) is a numerical method that discretizes the body into a set of points. This set of points is used to create a Finite Element mesh that moves in time following the cloud of points. PFEM then combines a Lagrangian description with the classical Finite Element Method. The strength of PFEM is that it solves problems that involve large displacements and severe topological changes. However, current PFEM implementations do not guarantee mass conservation. Therefore, it is necessary to find an approach that improves it. This work focuses on implementing numerical techniques related to the mesh to improve the conservation of mass in PFEM.

In this study, the aforementioned techniques to improve mass conservation are implemented for the in-house PFEM Matlab code of the LTAS-MN2L group at the University of Liege. A study of the proposed methodologies is also presented, including: (1) a sloshing problem, (2) three different dam breaks. It is concluded that the Adjustment of the fluid’s height method that addresses both terms of mass variation yields the greatest improvement in mass conservation. Cruchaga’s approach is physically more coherent, as it corrects the free surface nodes’ positions based on the velocity of each node.