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A. MALIDI, S. DUFOUR AND D. N’DRI(a) (b) (c)Figure A2. Mass computation for each uid: (a) rst level; (b) second level; and (c) third level.ACKNOWLEDGEMENTSThis work was sponsored in part by the Auto21 Network of Centres of Excellence of Canada, theNatural Sciences and Engineering Research Council of Canada and the Fonds quebecois de la recherchesur la nature et les technologies.REFERENCES1. Floryan JM, Rasmussen H. Numerical methods for viscous ows with moving boundaries. In Applied MechanicsReview, Metzner AWK (ed.). ASME: New York, 1989; 323–341.2. Hirt CW, Nichols BD. Volume of uid (VOF) method for the dynamics of free boundaries. Journal ofComputational Physics 1981; 39:201–225.3. Sethian JA. Level Set Methods. Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, andMaterials Science. Cambridge University Press: Cambridge, MA, 1999.4. Thompson E. Use of pseudo-concentration to follow creeping viscous ows during transient analysis.International Journal for Numerical Methods in Fluids 1986; 6:749–761.5. Dufour S, Malidi A. A free surface updating methodology for marker function-based Eulerian free surfacecapturing techniques on unstructured meshes. Communications in Numerical Methods in Engineering 2004;20:857–867.6. Dufour S, Pelletier D. Computations of multiphase ows with surface tension using an adaptive nite elementmethod. Numerical Heat Transfer, Part A 2001; 40:335–362.7. Johnson C. Numerical Solution of Partial Dierential Equations by the Finite Element Method. CambridgeUniversity Press: Cambridge, MA, 1987.8. Gao DM. A three-dimensional hybrid nite element-volume tracking model for mould lling in casting processes.International Journal for Numerical Methods in Fluids 1999; 29:877–895.9. Tezduyar ET, Aliabadi S. EDICT for 3D computation of two-uid interfaces. Computer Methods in AppliedMechanics and Engineering 2000; 190:403–410.10. Beliveau A, Fortin A, Demay Y. A two-dimensional numerical method for the deformation of drops with surfacetension. International Journal of Computational Fluid Dynamics 1998; 10:225–240.11. Fortin M, Fortin A. A generalization of Uzawa’s algorithm for the solution of the Navier–Stokes equations.Communications in Applied Numerical Methods 1985; 1:205–208.12. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. Journal ofComputational Physics 1992; 100:335–354.13. Rudman M. A volume-tracking method for incompressible multiuid ows with large density variations.International Journal for Numerical Methods in Fluids 1998; 28:357–378.14. Williams MW, Kothe DB, Puckett EG. Accuracy and convergence of continuum surface-tension models. InFluid Dynamics at Interfaces, Shyy W, Narayanan R (eds). Cambridge University Press: Cambridge, MA,1999; 294–305.15. Popinet S, Zaleski S. A front-tracking algorithm for accurate representation of surface tension. InternationalJournal for Numerical Methods in Fluids 1999; 30:775–793.16. Dufour S, Pelletier D. A study of drop dynamics using an adaptive nite element method. 14th AIAAComputational Fluid Dynamics Conference, Norfolk, VA, AIAA Paper 99-3318, 1999; 12.Copyright ? 2005 John Wiley & Sons, Ltd.Int. J. Numer. Meth. Fluids (in press)
A STUDY OF TIME INTEGRATION SCHEMES FOR MODELLING FREE SURFACE FLOWS17. Renardy Y, Renardy M. PROST: a parabolic reconstruction of surface tension for the volume-of-uid method.Journal of Computational Physics 2002; 183:400–421.18. Shin S, Abdel-Khalik SI, Daru V, Juric D. Accurate representation of surface tension using the level contourreconstruction method. Journal of Computational Physics 2005; 203:493–516.19. Hou TY, Lowengrub JS, Shelley MJ. Removing the stiness from interfacial ows with surface tension. Journalof Computational Physics 1994; 114:312–338.20. Dufour S, Malidi A. An Eulerian interface capturing methodology for the numerical modeling of free surfaceows with surface tension. Redaction, 2005.21. Gresho PM, Sani RL, Engelman MS. Incompressible Flow and the Finite Element Method: Advection–Diusionand Isothermal Laminar Flow. Wiley: New York, 1999.22. Cuvelier C, Segal A, van Steenhoven AA. Finite Element Methods and Navier–Stokes Equations. D. ReidelPublishing Company: Dordrecht, 1986.23. Engelman SE, Jamnia M-A. Transient ow past a circular cylinder: a benchmark solution. International Journalfor Numerical Methods in Fluids 1990; 11:985–1000.24. Taylor GI. The formation of emulsions in denable elds of ow. Proceedings of the Royal Society of London1934; 146(A):501–523.25. Bentley BJ, Leal LG. An experimental investigation of drop deformation and breakup in steady, two-dimensionallinear ows. Journal of Fluid Mechanics 1986; 167:241–283.26. Sussman M, Smereka P. Axisymmetric free boundary problems. Journal of Fluid Mechanics 1997; 341:269–294.27. Hnat JG, Buckmaster JD. Spherical cap bubbles and skirt formation. Physics of Fluids 1976; 19:182–194.28. de Sousa FS, Mangiavacchi N, Nonato LG, Castelo A, Tome MF, Ferreira VG, Cuminato JA, McKee S. Afront-tracking=front-capturing method for the simulation of 3D multi-uid ows with free surfaces. Journal ofComputational Physics 2004; 198:469–499.Copyright ? 2005 John Wiley & Sons, Ltd.Int. J. Numer. Meth. Fluids (in press)
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