A Meshless Method for 21/2D Mold Filling Simulations Using Point Set Surfaces

K.C. Estácio, L.G. Nonato, N. Mangiavacchi


In this work a novel meshless technique for mold filling simulation is presented. The governing equation for this kind of problem is named Hele-Shaw and it is derivated applying some simplifications on the 3D conservation equations. This approach is also commonly called 21/2D, referring to limitations of the mold geometry to narrow and weakly curved channels. Since products manufactured by injection molding in real life, as for example buckets, automobiles bumpers and cell phone casings, are not expected to be planar, in this work the mold cavity is modeled by point set surfaces. Thus, no computational effort referring to either mesh generation or mesh maintenance is required for the numerical solution of the governing equations. The developed technique for simulating the free surface position, velocity and pressure distribution in the injection molding process using this 21/2D approach is presented and discussed. The details of our framework, which is based on Smoothed Particle Hydrodynamics Method and a Meshless Volume of Fluid Method is also presented.


[1] T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P Krysl. Meshless methods: An overview and recent developments, Comput. Methods Appl. Mech. Engrg., 139 (1996), 3–47.

A.J. Cuadros-Vargas, L.G. Nonato, Imesh: Quality mesh generation from images in “ECCOMAS - European Congress On Computational Methods in Applied Sciences and Engineering”, 2006, Egmond aan Zee, Netherlands.

Easymesh: a free 2D quality mesh generator based on Delaunay triangulation. http://www.dinma.univ.trieste.it/nirftc/research/easymesh/ [05 July 2007].

M. Ellero, R.I. Tanner, SPH Simulations of Transient Viscoelastic Flows at Low Reynolds Number, Journal of Non-Newtonian Fluid Mechanics, 132, No.1-3 (2005), 61–72.

K.C. Estacio, L.G. Nonato, N. Mangiavacchi, Solution of Hele-Shaw Equation in Surfaces Defined by Non Organized Points, in “XXVII CILAMCE - Iberian Latin American Congress on Computational Methods in Engineering”, 2006, Bel´em, Brazil.

K.C. Estacio, N. Mangiavacchi, Simplified model for mold filling simulations using CVFEM and unstructured meshes, Communications in Numerical Methods in Engineering, 23, No. 5 (2007), 345–361.

R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Roy. Astron. Soc., 181 (1977), 375–389.

C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39 (1981), 201–225.

E. Holm, H. Langtangen, A unified finite element model for the injection molding process, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 413–429.

P. Kennedy, “Flow Analysis of Injection Molds”, Hanser Publishers, New York, 1995.

G.R. Liu, “Meshfree Methods – Moving Beyond the Finite Element Method”, CRC Press, 2003.

N.B. Lucy, A numerical approach to the testing of frission, Astronomical Journal, 82 (1977), 1013–1024.

C.L. Tucker III, editor, “Computer Modeling for Polymer Processing - Fundamentals”, Computed Aided Engineering for Polymer Processing. Hanser Publishers, Munich, 1989.

DOI: https://doi.org/10.5540/tema.2007.08.02.0239

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

Indexed in:



Desenvolvido por:

Logomarca da Lepidus Tecnologia