A State of the Art Review of the Particle Finite Element Method (PFEM)
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ORIGINAL PAPER
A State of the Art Review of the Particle Finite Element Method (PFEM) Massimiliano Cremonesi1 · Alessandro Franci2 · Sergio Idelsohn3 · Eugenio Oñate2 Received: 1 July 2020 / Accepted: 22 July 2020 © The Author(s) 2020
Abstract The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.
1 Introduction The last decades have seen a growing interest in the development of computational methods for the simulation of engineering problems. A robust and efficient numerical simulation is particularly complex in the presence of multiphysics phenomena and/or large deformations of the physical domains. Typical examples can be found in unsteady free-surface fluid dynamics problems, fluid–structure interaction applications with large motions of fluid–solid interfaces, non-linear solid mechanics with large changes of the topology and contact of solid bodies, and thermalmechanical coupled analysis in the presence of phase-change phenomena. To tackle these complex problems, the Finite Element Method (FEM) has been generally privileged. In order to solve a problem in mechanics with the FEM, the reference * Massimiliano Cremonesi [email protected] 1
Politecnico di Milano, Milan, Italy
2
International Center for Numerical Methods in Engineering (CIMNE), Universitat Politècnica de Catalunya (UPC), Barcelona, Spain
3
International Center for Numerical Methods in Engineering (CIMNE), Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
configuration1 should be provided with a mesh. Depending on the framework considered, different FEM approaches arise. For continuum mechanics problems, in a Eulerian approach, the finite element mesh is fixed and the material moves across the grid, being the mesh nodes dissociated from physical particles. Due to the relative motion between the material and the grid, convective terms appear
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