The particle finite element method. An overview

By Eugenio Oñate, Sergio R. Idelsohn, Facundo Del Pin, Romain Aubry. 2004

585 citations recorded by the source corpus.

We present a general formulation for the analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/0a6257254285aa7d792a1056a19c31f5f79d0576

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In Computational Mechanics

Citations in the corpus

Formulation of a dynamic material point method (MPM) for geomechanical problems (2013, methodology): “[98, 134] also classify the particle finite element method (PFEM) as a meshless method as it involves the meshless finite element interpolation.”
Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method (2018, methodology): “PFEM was first developed to solve fluid-structure interaction problems (Oñate et al. 2004) and then extended to other areas, like erosion, solid-solid interaction and thermo-plastic problems (Oñate et al.”
A coupled PFEM–Eulerian approach for the solution of porous FSI problems (2012, background): “This is useful to model the separation of solid particles from the bed surface and to follow their subsequent motion as individual particles with a known density, an initial acceleration and a velocity subjected to gravity forces [25].”
A monolithic Lagrangian approach for fluid–structure interaction problems (2010, methodology): “In treating problems involving free surface flows the boundary is determined at every time step using the so-called ‘alpha-shape’ technique [18,26].”
Possibilities of the particle finite element method for fluid–soil–structure interaction problems (2011, background): “Contact between the fluid particles and the fixed boundaries is accounted for by the incompressibility condition which naturally prevents the fluid nodes to penetrate into the solid boundaries [32, 36].”
Finite Particle Method for Progressive Failure Simulation of Truss Structures (2011, methodology): “An arbitrary Lagrangian-Eulerian formulation, such as the particle finite-element method (PFEM) (Onate et al. 2004) or the least squares finite-element method (LSFEM) (Oliver and Hermann 2005), could solve fluid-structure interaction problems.”
To mesh or not to mesh. That is the question (2006, methodology): “A complete description of several stabilizing methods as well as the stabilization used in the examples presented in this paper may be found in [13,24].”
Least squares moving particle semi-implicit method (2014, methodology): “The first class of meshfree/ particle methods is used with various weak formulations such as Galerkin methods, for example, diffuse element method (DEM) [73], element free Gelerkin (EFG) method [11,13– 15,67], reproducing Kernel particle method (RKPM) [21, 63–65], h-p cloud method [27,28,58,74], par”