COMPUTATIONS OF MULTIPHASE FLOWS WITH SURFACE TENSION USING AN ADAPTIVE FINITE ELEMENT METHOD

References

• Liu , X. , Lienhard , J. H. and V . 1993 . The Hydraulic Jump in Circular Jet Impingement and in Other Thin Liquid Films . Experiments in Fluids , 15 : 108 – 116 .
   Google Scholar
• Aihara , T. , Kim , J. K. and Maruyama , S. 1990 . Effects of Temperature-Dependent Fluid Properties on Heat Transfer Due to an Axisymmetric Impinging Gas Jet Normal to a Flat Surface . Wärme-und Stoffübertragung , 25 : 145 – 153 .
   Web of Science ®Google Scholar
• Reddy , K. R. and Tanner , R. I. 1978 . Finite Element Solution of Viscous Jet Flows with Surface Tension . Computers and Fluids , 6 : 83 – 91 .
   Google Scholar
• Omodei , B. J. 1980 . On the Die-Swell of an Axisymmetric Newtonian Jet . Computers and Fluids , 8 : 275 – 289 .
   Web of Science ®Google Scholar
• Fortin , A. , Demay , Y. and Agassant , J.-F. 1992 . Computation of Stationary Interface Between Generalized Newtonian Fluids . Rev. Ew. Éléments Finis , 1 : 181 – 196 .
   Google Scholar
• Thompson , E. 1986 . Use of Pseudo-Concentration to Follow Creeping Viscous Flows During Transient Analysis . Int. J. Numer. Methods Fluids , 6 : 749 – 761 .
   Web of Science ®Google Scholar
• Nickell , R. E. , Tanner , R. I. and Caswell , B. 1974 . The Solution of Viscous Incompressible Jet and Free-Surface Flows Using Finite-Element Methods . J. Fluid Mech. , 65 : 189 – 206 .
   Web of Science ®Google Scholar
• Floryan , J. M. and Rasmussen , H. 1989 . “ Numerical Methods for Viscous Flows with Moving Boundaries ” . In Applied Mechanics Review , Edited by: Metzner , A. K. Vol. 42 , 323 – 341 . New York : ASME .
   Google Scholar
• Hirt , C. W. and Nichols , B. D. 1981 . Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries . J. Comput. Phys. , 39 : 201 – 225 .
   Web of Science ®Google Scholar
• Popinet , S. and Zaleski , S. 1999 . A Front-Tracking Algorithm for Accurate Representation of Surface Tension . Int. J. Numer. Methods fluids , 30 : 775 – 793 .
   Web of Science ®Google Scholar
• Li , J. , Renardy , Y. and Renardy , M. 2000 . Numerical Simulation of Breakup of a Viscous Drop in Simple Shear Flow Through a Volume-of-Fluid Method . Phys. Fluids , 12 : 269 – 282 .
   Web of Science ®Google Scholar
• J.-F. Hétu, Y. Lauzé, and G. Salloum, Finite Element Simulation of Mould Filling Processes, in Proceedings of the CFD 94 Conference, pp. 443-450, Toronto, 1995.
   Google Scholar
• S. Dufour and D. Pelletier, An Adaptive Finite Element Method for Incompressible Flows with Interfaces, in Proceedings of the 29th AIAA Fluid Dynamics Conference, AIAA Paper 98-2969, American Institute of Aeronautics and Astronautics (AIAA), Albuquerque, NM, 1998.
   Google Scholar
• S. Dufour and D. Pelletier, A Study of Drop Dynamics Using an Adaptive Finite Element Method, in Proceedings of the 14th AIAA Computational Fluid Dynamics Conference, AIAA Paper 99-3318, American Institute of Aeronautics and Astronautics (AIAA), Norfolk, VA, 1999.
   Google Scholar
• S. Dufour, D. Pelletier, J.-F. Hétu, and A. Garcia-Rejón, A Numerical Study of Multilayer Flow Behavior inside Blow Molding Dies, in S. Kim (ed.), Proceedings of the 1996 First Joint Topical Conference on Processing, Structure and Properties of Polymeric Materials, pp. 166-168, American Institute of Chemical Engineers (AIChE) and Polymer Processing Society (PPS), American Institute of Chemical Engineers, New York, 1996.
   Google Scholar
• Fortin , A. , Carrier , P. and Demay , Y. 1995 . Numerical Simulation of Coextrusion and Film Casting . Int. J. Numer. Methods Fluids , 20 : 31 – 57 .
   Web of Science ®Google Scholar
• Franca , L. P. , Frey , S. L. and Hughes , T. J. R. 1992 . Stabilized Finite Element Methods I. Application to the Advective-Diffusive Model . Comput. Methods Appl. Mech. Engrg. , 95 : 253 – 276 .
   Web of Science ®Google Scholar
• Brackbill , J. U. , Kothe , D. B. and Zemach , C. 1992 . A Continuum Method for Modeling Surface Tension . J. Comput. Phys. , 100 : 335 – 354 .
   Web of Science ®Google Scholar
• étu , J.-F. H and Pelletier , D. 1992 . Fast Adaptive Finite Element Scheme for Viscous Incompressible Flows . AIAA J. , 30 : 2677 – 2682 .
   Google Scholar
• Pelletier , D. , Ilinca , F. and étu , J.-F. H . 1994 . Adaptive Remeshing for Convective Heat Transfer with Variable Fluid Properties . J. Thermophys. Heat Transfer , 8 : 687 – 694 .
   Web of Science ®Google Scholar
• L. Ignat, D. Pelletier, and F. Ilinca, An Adaptive Finite Element Method for Turbulent Heat Transfer, in Proceedings of the 34th Aerospace Sciences Meeting & Exhibit, AIAA Paper 97-0607, American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, 1996.
   Google Scholar
• F. Ilinca and D. Pelletier, A Unified Approach for Adaptive Solutions of Compressible and Incompressible Flows, in Proceedings of the 35th Aerospace Sciences Meeting & Exhibit, AIAA Paper 97-0330, American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, 1997.
   Google Scholar
• É. Turgeon, D. Pelletier, and F. Ilinca, Compressible Heat Transfer Computations by an Adaptive Finite Element Method, in Proceedings of the 37th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 99-0875, American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, 1999.
   Google Scholar
• U+0C9. Turgeon and D. Pelletier, Computation of Jet Impingement Heat Transfer by an Adaptive Finite Element Algorithm, in Proceedings of the 7th AIAAjASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 98-2585, American Institute of Aeronautics and Astronautics (AIAA), Albuquerque, NM, 1998.
   Google Scholar
• Zienkiewicz , O. C. and Zhu , J. Z. 1992 . The Superconvergent Patch Recovery and A Posteriori Error Estimates . Part 1: The Recovery Technique, Int. J. Numer. Methods Eng. , 33 : 1331 – 1364 .
   Web of Science ®Google Scholar
• Zienkiewicz , O. C. and Zhu , J. Z. 1992 . The Superconvergent Patch Recovery and A Posteriori Error Estimates. Part 2 Error Estimates and Adaptivity . Int. J. Numer. Methods Eng. , 33 : 1365 – 1382 .
   Web of Science ®Google Scholar
• Barth , J. T. and Sethian , J. A. 1998 . Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains . J. Comput. Phys. , 145 : 1 – 40 .
   Web of Science ®Google Scholar
• Tezduyar , T. , Aliabadi , S. and Behr , M. 1998 . Enhanced-Discretization Interface-Capturing Technique (EDICT) for Computation of Unsteady Flows with Interfaces . Comput. Methods Appl. Mech. Engrg. , 155 : 235 – 248 .
   Web of Science ®Google Scholar
• Lafaurie , B. , Nardone , C. , Scardovelli , R. , Zaleski , S. and Zanetti , G. 1994 . Modelling Merging and Fragmentation in Multiphase Flows with SURFER . J. Comput. Phys. , 113 : 134 – 147 .
   Web of Science ®Google Scholar
• D. Jacqmin, An Energy Approach to the Continuum Surface Tension Method, in Proceedings of the 34th Aerospace Sciences Meeting & Exhibit, AIAA Paper 96-0858, American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, 1996.
   Google Scholar
• M. J. Williams, D. B. Kothe, and E. G. Puckett, Convergence and Accuracy of KernelBased Continuum Surface Tension Models, Tech. Rep. LA-UR-98-2268, Los Alamos National Laboratory, Los Alamos, NM, 1998.
   Google Scholar
• Weatherburn , C. E. 1927 . On Differential Invariants in Geometry of Surfaces . with Some Applications to Mathematical Physics, The Quarterly Journal of Pure and Applied Mathematics , 50 : 230 – 269 .
   Google Scholar
• Johnson , C. 1987 . Numerical Solution of Partial Differential Equations by the Finite Element Method , Cambridge : Cambridge University Press .
   Google Scholar
• Franca , L. P. and Frey , S. L. 1992 . Stabilized Finite Element Methods: II. The Incompressible Navier-Stokes Equations . Comput. Methods Appl. Mech. Engrg. , 99 : 209 – 233 .
   Web of Science ®Google Scholar
• Hughes , T. J. R. , Mallet , M. and Mizukami , A. 1986 . A New Finite Element Formulation for Computational Fluid Dynamics: II. Beyond SUPG . Comput. Methods Appl. Mech. Engrg. , 54 : 341 – 355 .
   Web of Science ®Google Scholar
• Galeão , A. C. and do Carmo , E. G. D. 1988 . A Consistent Approximate Upwind Petrov-Galerkin Method for Convection-Dominated Problems . Comput. Methods Appl. Mech. Engrg. , 68 : 83 – 95 .
   Web of Science ®Google Scholar
• Codina , R. 1993 . A Discontinuity-Capturing Crosswind-Dissipation for the Finite Element Solution of the Convection-Diffusion Equation . Comput. Methods Appl. Mech. Engrg. , 110 : 325 – 342 .
   Web of Science ®Google Scholar
• éliveau , A. B , Fortin , A. and Demay , Y. 1998 . A Two-Dimensional Numerical Method for the Deformation of Drops with Surface Tension . Int. J. of Computational Fluid Dynamics , 10 : 225 – 240 .
   Google Scholar
• Layton , W. and Polman , B. 1996 . Oscillation Absorption Finite Element Methods for Convection-Diffusion Problems . SIAM J. Sci. Comput. , 17 : 1328 – 1346 .
   Google Scholar
• Peraire , J. , Vahdati , M. , Morgan , K. and Zienkiewicz , O. C. 1987 . Adaptive Remeshing for Compressible Flow Computations . J. Comput. Phys. , 72 : 449 – 466 .
   Web of Science ®Google Scholar
• Fortin , M. and Fortin , A. 1985 . A Generalization of Uzawa's Algorithm for the Solution of the Navier-Stokes Equations . Communications in Applied Numerical Methods , 1 : 205 – 208 .
   Google Scholar
• Navti , S. E. , Ravindran , K. , Taylor , C. and Lewis , R. W. 1997 . Finite Element Modelling of Surface Tension Effects Using a Lagrangian-Eulerian Kinematic Description . Comput. Methods Appl. Mech. Engrg. , 147 : 41 – 60 .
   Google Scholar
• S. Dufour and D. Pelletier, An Adaptive Finite Element Method for Multiphase Flows with Surface Tension, in S. R. Idelsohn, E. Oñate, and E. N. Dvorkin (eds.), Computational Mechanics: New Trends and Applications, International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, 1998.
   Google Scholar
• Goren , S. L. and Wronaki , S. 1966 . The Shape of Low-Speed Capillary Jets of Newtonian Liquids . J. Fluid Mech. , 25 : 185 – 198 .
   Web of Science ®Google Scholar