An adaptive boundary element approach to transient free surface flow as applied to injection molding

An adaptive (Lagrangian) boundary element approach is proposed for the general two-dimensional simulation of confined moving-boundary flow of viscous incompressible fluids. Only the quasi-steady creeping (Stokes) flow of a Newtonian fluid is examined. The method is stable as it includes remeshing capabilities of the deforming moving boundary, and thus it can handle large deformations. An algorithm is developed for mesh refinement of the deforming moving-boundary mesh. Several flow problems are presented to illustrate the utility of the approach, with particular emphasis on cavity filling and viscous fingering, as applied to conventional and gas-assisted injection molding. The accuracy of the method is assessed through the problem of jet flow and the transient fountain flow between two flat plates. Copyright © 2000 John Wiley & Sons, Ltd.

[1]  R. Khayat Boundary element analysis of planar drop deformation in confined flow. Part II. Viscoelastic fluids , 1998 .

[2]  R. Khayat,et al.  Boundary element analysis of three‐dimensional mixing flow of Newtonian and viscoelastic fluids , 1998 .

[3]  R. Khayat,et al.  A COUPLED BOUNDARY/FINITE-ELEMENT APPROACH FOR THE THREE-DIMENSIONAL SIMULATION OF AIR VENTING IN BLOW MOLDING AND THERMOFORMING , 1998 .

[4]  R. Khayat,et al.  A boundary element analysis of planar drop deformation in the screw channel of a mixing extruder , 1998 .

[5]  R. Khayat,et al.  Boundary-element analysis of planar drop deformation in confined flow. Part 1. Newtonian fluids , 1997 .

[6]  D. Frayce,et al.  A DUAL RECIPROCITY BOUNDARY ELEMENT APPROACH TO THREE-DIMENSIONAL TRANSIENT HEAT CONDUCTION AS APPLIED TO MATERIALS PROCESSING , 1996 .

[7]  R. Khayat,et al.  Numerical simulation of transient planar flow of a viscoelastic material with two moving free surfaces , 1995 .

[8]  R. Khayat,et al.  A three-dimensional boundary-element approach to gas-assisted injection molding , 1995 .

[9]  Roger E. Khayat,et al.  PERTURBATION SOLUTION TO PLANAR FLOW OF A VISCOELASTIC FLUID WITH TWO MOVING FREE BOUNDARIES , 1994 .

[10]  R. Khayat,et al.  Uniaxial and biaxial unsteady inflations of a viscoelastic material , 1992 .

[11]  C. A. Brebbia,et al.  The multiple Reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary , 1991 .

[12]  Jerzy M. Floryan,et al.  Numerical Methods for Viscous Flows With Moving Boundaries , 1989 .

[13]  Andrew N. Hrymak,et al.  Transient free‐surface flows in injection mold filling , 1988 .

[14]  Carlos Alberto Brebbia,et al.  The dual reciprocity boundary element formulation for diffusion problems , 1987 .

[15]  M. Kawahara,et al.  LAGRANGIAN FINITE ELEMENT ANALYSIS APPLIED TO VISCOUS FREE SURFACE FLUID FLOW , 1987 .

[16]  A. B. Metzner,et al.  Transient free‐surface flows: Motion of a fluid advancing in a tube , 1987 .

[17]  Andrew N. Hrymak,et al.  Finite element simulation of fountain flow in injection molding , 1986 .

[18]  Tai-Shung Chung,et al.  The effect of melt compressibility on a high‐speed wire‐coating process , 1986 .

[19]  O. Hassager,et al.  An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow , 1985, Journal of Fluid Mechanics.

[20]  M. Kawahara,et al.  FINITE ELEMENT ANALYSIS OF WAVE MOTION , 1984 .

[21]  G. Homsy,et al.  Two-phase displacement in Hele Shaw cells: theory , 1984, Journal of Fluid Mechanics.

[22]  Kenneth J. Ruschak,et al.  A method for incorporating free boundaries with surface tension in finite element fluid‐flow simulators , 1980 .

[23]  L. Scriven,et al.  Separating how near a static contact line: Slip at a wall and shape of a free surface , 1980 .

[24]  Bruce Caswell,et al.  The solution of viscous incompressible jet and free-surface flows using finite-element methods , 1974, Journal of Fluid Mechanics.

[25]  P. Pedley,et al.  An Introduction to Fluid Dynamics , 1968 .

[26]  M. Wheeler,et al.  Numerical Simulation of Free-Boundary Problems , 1996 .

[27]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .