Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., and Jan, Y.-J., 2001, “A Front-Tracking Method for the Computations of Multiphase Flow,” J. Comput. Phys.

[CrossRef]169 , pp. 708–759.

Hou, T. Y., Lowengrub, J. S., and Shelley, M. J., 2001, “Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials,” J. Comput. Phys.

[CrossRef]169 , pp. 302–323.

Jacqmin, D., 1999, “Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling,” J. Comput. Phys.

[CrossRef]155 , pp. 96–127.

Jamet, D., Lebaigue, O., Coutris, N., and Delhaye, J. M., 2001, “The Second Gradient Method for the Direct Numerical Simulation of Liquid-Vapor Flows With Phase Change,” J. Comput. Phys.

[CrossRef]169 , pp. 624–651.

Hirt, C. W., and Nichols, B. D., 1981, “Volume of Fluid Method (VOF) for the Dynamics of Free Boundaries,” J. Comput. Phys.

[CrossRef]39 , pp. 201–225.

Brackbill, J. U., Kothe, D. B., and Zemach, C., 1992, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys.

[CrossRef]100 , pp. 335–354.

Sethian, J. A., 1999, "*Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science*", Cambridge University Press, Cambridge, England.

Osher, S., and Fedkiw, R. P., 2001, “Level Set Methods: an Overview and Some Recent Results,” J. Comput. Phys.

[CrossRef]169 , pp. 463–502.

CFX-4, 2000, AEA Technology, Harwell, Oxfordshire, OX11 0RA, UK.

FIDAP 8.60, 2001, Fluid Dynamics Analysis Package, Fluent Inc., 10 Cavendish Court, Lebanon, NH, 03766, USA.

Rider, W. J., and Kothe, D. B., 1998, “Reconstructing Volume Tracking,” J. Comput. Phys.

[CrossRef]141 , pp. 112–152.

Barth, T. J., and Sethian, J. A., 1998, “Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains,” J. Comput. Phys.

[CrossRef]145 , pp. 1–40.

Sussman, M., Smereka, P., Osher, S., 1994, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,” J. Comput. Phys.

[CrossRef]114 , pp. 146–159.

Sussman, M., and Smereka, P., 1997, “Axisymmetric Free Boundary Problems,” J. Fluid Mech.

[CrossRef]341 , pp. 269–294.

Sussman, M., and Fatemi, E., 1999, “An Efficient Interface-Preserving Level Set Redistancing Algorithm and its Application to Interfacial Incompressible Fluid Flow,” SIAM J. Sci. Comput. (USA)

[CrossRef]20 , pp. 1165–1191.

Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H., and Welcome, M. L., 1999, “An Adaptive Level Set Approach for Incompressible Two-Phase Flow,” J. Comput. Phys.

[CrossRef]148 , pp. 81–124.

Yu, J.-D., Sakai, S., and Sethian, J. A., 2003, “A Coupled Level Set Projection Method Applied to Ink Jet Simulation,” Interfaces Free Boundaries

[CrossRef]5 , pp. 459–482.

Chang, Y. C., Hou, T. Y., Merriman, B., and Osher, S., 1996, “A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows,” J. Comput. Phys.

[CrossRef]124 , pp. 449–464.

Tornberg, A.-K., and Engquist, B., 2000, “A Finite Element Based Level-Set Method for Multiphase Flow Applications,” Comput. Visual Sci.3 , pp. 93–101.

Sussman, M., and Puckett, E. G., 2000, “A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows,” J. Comput. Phys.

[CrossRef]162 , pp. 301–337.

Mulder, W., Osher, S., and Sethian, J. A., 1992, “Computing Interface Motion in Compressible Gas Dynamics,” J. Comput. Phys.

[CrossRef]100 , pp. 209–228.

Shepel, S. V., 2002, “Numerical Simulation of Filling and Solidification of Permanent Mold Castings,” Ph.D. thesis, University of Notre Dame, Notre Dame, IN.

Hetu, J.-F., and Ilinca, F., 1999, “A Finite Element Method for Casting Simulations,” Numer. Heat Transfer, Part A

[CrossRef]36 , pp. 657–679.

Pillapakkam, S. B., and Singh, P., 2001, “A Level-Set Method for Computing Solutions to Viscoelastic Two-Phase Flow,” J. Comput. Phys.

[CrossRef]174 , pp. 552–578.

Chessa, J., and Belytschko, T., 2003, “An Enriched Finite Element Method and Level Sets for Axisymmetric Two-Phase Flow with Surface Tension,” Int. J. Numer. Methods Eng.

[CrossRef]58 , pp. 2041–2064.

Dussan, V. E., 1979, “On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines,” Annu. Rev. Fluid Mech.

[CrossRef]11 , pp. 371–400.

Rhie, C. M., and Chow, W. L., 1983, “Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation,” AIAA J.21 , pp. 1527–1532.

Van Doormaal, J. P., and Raithby, G. D., 1984, “Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows,” Numer. Heat Transfer, 7 , pp. 147–163.

Adalsteinsson, D., and Sethian, J. A., 1999, “The Fast Construction of Extension Velocities in Level Set Methods,” J. Comput. Phys.

[CrossRef]148 , pp. 2–22.

Sussman, M., 2003, “A Second Order Coupled Level Set and Volume-of-Fluid Method for Computing Growth and Collapse of Vapor Bubbles,” J. Comput. Phys.

[CrossRef]187 , pp. 110–136.

Hughes, T. J., Franca, L. P., and Balestra, M., 1986, “A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Flow Problem Accomodating Equal-Order Interpolations,” Comput. Methods Appl. Mech. Eng.

[CrossRef]59 , pp. 85–99.

Martin, J. C., and Moyce, W. J., 1952, “An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane,” Philos. Trans. R. Soc. London244 , pp. 312–324.

Munz, C.-D., and Maschek, W., 1992, “Comparison of Results of Two-Phase Fluid Dynamics Codes and Sloshing Experiments,” Technical Report No. KfK 5091, Kernforschungszentrum Karlsruhe Gmbh, Karlsruhe, Germany.

Meier, M., 1999, “Numerical and Experimental Study of Large Steam-Air Bubbles Injected in a Water Pool,” Ph.D. thesis No. 13091, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland.

Bhaga, D., and Weber, M. E., 1981, “Bubbles in Viscous Liquids: Shapes, Wakes, and Velocities,” J. Fluid Mech.105 , pp. 61–85.

Ginzburg, I., and Wittum, G., 2001, “Two-Phase Flows on Interface Refined Grids Modeled With VOF, Staggered Finite Volumes, and Spline Interpolants,” J. Comput. Phys.

[CrossRef]166 , pp. 302–335.

Koh, C. J., and Leal, L. G., 1990, “An Experimental Investigation on the Stability of Viscous Drops Translating Through a Quiescent Fluid,” Phys. Fluids A

[CrossRef]2 (12), pp. 2103–2109.

Tomiyama, A., Sou, A., Zun, I., Sakaguchi, T., 1994, “Three-Dimensional Detailed Numerical Simulation of Bubbly Upflow in a Vertical Square Duct,” "*Proc. German-Japanese Symp. on Multi-Phase Flow*", Karlsruhe, Germany, U.Müller, T.Saito, and K.Rsut, eds., Kernforschungszentrum, pp. 487–497.