An efficient level set-based mesh adaptation for the particle finite element method

Alpha-shape; CFD; Edge splitting; Level set; PFEM; Ray-casting; Remeshing; Alpha-shapes; Discretizations; Edge-splitting; Free surfaces; Level Set; Mass conservation; Mesh adaptation; Particle-finite element method; Ray casting; Computational Mechanics; Mechanics of Materials; Mechanical Engineering; Physics and Astronomy (all); Computer Science Applications

Abstract :

[en] 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.

Research Center/Unit :

A&M - Aérospatiale et Mécanique - ULiège

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Lacroix, Martin ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Fernández, Eduardo ; Department of Aerospace and Mechanical Engineering, University of Liége, Liége, Belgium

Février, Simon ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Papeleux, Luc ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique

Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Language :

English

Title :

An efficient level set-based mesh adaptation for the particle finite element method

Publication date :

March 2026

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier B.V.

Volume :

450

Pages :

118644

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0045782525009168?httpAccept=text/xml

Name of the research project :

PFEM-FSI

Funders :

Walloon region
F.R.S.-FNRS - Fund for Scientific Research

Funding number :

T.0183.21

Available on ORBi :

since 24 June 2026

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