Validation of the particle finite element method (PFEM) for simulation of free surface flows

Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows.Design/methodology/approach – A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature.Findings – Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution.Originality/value – Details of the input data for all the examples studied are given...

[1]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[2]  Wing Kam Liu,et al.  Meshfree and particle methods and their applications , 2002 .

[3]  G. Dilts MOVING-LEAST-SQUARES-PARTICLE HYDRODYNAMICS-I. CONSISTENCY AND STABILITY , 1999 .

[4]  Eugenio Oñate,et al.  ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems , 2008 .

[5]  Arthur Veldman,et al.  A Volume-of-Fluid based simulation method for wave impact problems , 2005 .

[6]  K. N. Seetharamu,et al.  The Finite Element Method , 2005 .

[7]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[8]  Eugenio Oñate,et al.  A mesh-free finite point method for advective-diffusive transport and fluid flow problems , 1998 .

[9]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1994, ACM Trans. Graph..

[10]  S. Koshizuka A particle method for incompressible viscous flow with fluid fragmentation , 1995 .

[11]  Eugenio Oñate,et al.  Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches , 2006 .

[12]  Eugenio Oñate,et al.  The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves , 2004 .

[13]  Rene Kahawita,et al.  The SPH technique applied to free surface flows , 2006 .

[14]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[15]  Eugenio Oñate,et al.  Fluid-structure interaction using the particle finite element method , 2006 .

[16]  E. Oñate,et al.  The particle finite element method. An overview , 2004 .

[17]  J. Mason,et al.  Algorithms for approximation , 1987 .

[18]  W. Hager,et al.  Ski Jump Hydraulics , 2005 .

[19]  Eugenio Oñate,et al.  Multi-fluid flows with the Particle Finite Element Method , 2009 .

[20]  Eugenio Oñate,et al.  A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation , 2000 .

[21]  Sivakumar Kulasegaram,et al.  Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems , 2004 .

[22]  Willi H. Hager,et al.  Flip Bucket without and with Deflectors , 2000 .

[23]  Eugenio Oñate,et al.  A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation , 2001 .

[24]  J. Z. Zhu,et al.  The finite element method , 1977 .

[25]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[26]  Eugenio Oñate,et al.  Particle finite element method in fluid-mechanics including thermal convection-diffusion , 2005 .