A particle finite element method based on Level–Set functions

Fernández, Eva; Février, Simon; Lacroix, Martin; Boman, Romain; Papeleux, Luc; Ponthot, Jean‐Philippe

doi:10.1016/j.jcp.2023.112187

Journal of Computational Physics

2023

DOI: 10.1016/j.jcp.2023.112187

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A particle finite element method based on Level–Set functions

Eva Fernández

Simon Février

Martin Lacroix

et al.

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2024

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Cited by 4 publications

References 30 publications

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Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Zorrilla,

Franci

2024

Engineering with Computers

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In this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve endemic limitations of the PFEM relative to boundary conditions treatment and mass conservation. In this new methodology, which we called Cut-PFEM, the fluid–wall interaction is not performed by adding interface elements, as is done in the standard PFEM boundaries. Instead, we use an implicit representation of (all or some of) the boundaries by introducing the use of a level set function. Such distance function detects the elements trespassing the (virtual) contours of the domain to equip them with opportunely boundary conditions, which are variationally enforced using Nitsche’s method. The proposed Cut-PFEM circumvents important issues associated with the standard PFEM contact detection algorithm, such as the artificial addition of mass to the computational domain and the anticipation of contact time. Furthermore, the Cut-PFEM represents a natural ground for the imposition of alternative wall boundary conditions (e.g., pure slip) which pose significant difficulties in a standard PFEM framework. Several numerical examples, featuring both no-slip and slip boundary conditions, are presented to prove the accuracy and robustness of the method in two-dimensional and three-dimensional scenarios.

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Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Zorrilla,

Franci

2024

Engineering with Computers

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Simulation of viscoelastic free-surface flows with the Particle Finite Element Method

Rizzieri,

Ferrara,

Cremonesi

2024

Comp. Part. Mech.

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Viscoelastic fluids are central in numerous applications from polymer manufacturing to the pharmaceutical industry and biological research. However, since analytical solutions are generally not available or too complex, it is common practice to study free-surface viscoelastic flows through numerical simulation techniques. This work proposes the use of the so-called particle finite element method (PFEM), a Lagrangian approach combining standard FEM techniques with a remeshing strategy. The PFEM is able to efficiently handle mesh distortion and to accurately track the free-surface evolution. Therefore, it is exploited in this work to deal with large displacements problems in the context of nonlinear viscoelasticity. An implementation of the Oldroyd-B constitutive model in the PFEM framework is here presented including details regarding how to deal with the transfer of the internal variables during remeshing events. Additionally, an innovative approach to impose unilateral Dirichlet boundary conditions ensuring optimal mass conservation is presented. The implementation is verified with two free-surface highly viscous benchmark flows: the impacting drop and the jet buckling problems. The results show perfect agreement with those obtained with other numerical techniques. The proposed framework opens the way for using PFEM in various applications, ranging from polymer extrusion to more sophisticated scenarios involving viscoelastic and viscoelasto-plastic constitutive laws.

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A particle-position-based finite element formulation for free-surface flows with topological changes

Avancini,

Franci,

Idelsohn

et al. 2024

Computer Methods in Applied Mechanics and Engineering

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A particle finite element method based on Level–Set functions

Cited by 4 publications

References 30 publications

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

Simulation of viscoelastic free-surface flows with the Particle Finite Element Method

A particle-position-based finite element formulation for free-surface flows with topological changes

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