The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves

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

578 citations recorded by the source corpus.

Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology. Copyright © 2004 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ef28a61f12057c25dc7d4f13d0d2688420a1578e

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

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”
The particle finite element method. An overview (2004, unknown): “Details of the treatment of the contact conditions at the solid-fluid interface are given in Section 8 [Idelsohn et al. (2004)].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “Similarly, the meshless finite element method [51] and the particle finite element method (PFEM) [52,53] reconstruct Delaunay tessellations [149] which give bounded O n   time for efficiency, and use non-Sibsonian interpolation”
To mesh or not to mesh. That is the question (2006, methodology): “This paper starts with a discussion about the problems to generate a mesh, the problems to use a meshless method and finishes by solving some fluid mechanics problems using the particle finite element method [11].”
On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM) (2015, methodology): “In contrast to classical PFEM ap9 proximations [2], in which the free boundary is obtained by a geometrical technique (α-shape 10 method), in this work the boundary is treated as a material surface, and the boundary nodes are 11 removed or inserted by means of an error function.”
Immersed particle method for fluid–structure interaction (2009, background): “The related work of O˜nate and Idelsohn should also be mentioned [ 6 , 7], where structures are linked to nearly incompressible fluids modeled by particle finite elements.”
Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments (2010, methodology): “Idelsohn and his co-workers applied the particle finite element method to solve incompressible flows with free-surfaces and breaking waves [381].”
A monolithic Lagrangian approach for fluid–structure interaction problems (2010, methodology): “This class of Lagrangian methods was proposed in the late 90s [18,19] and developed further in recent works [20,21].”
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.”
Possibilities of the particle finite element method for fluid–soil–structure interaction problems (2011, methodology): “In our work we use an innovative mesh generation scheme based on the extended Delaunay tesselation [17,19,20].”