Direct numerical simulations of Gas-Liquid multiphase flows

Direct Numerical Simulations of Gas-liquid Multiphase Flows

Volumn 9780521782401, Issue , 2011, Pages 1-324

  Tryggvason, Gretar ^a   Scardovelli, Ruben ^b   Zaleski, Stephane ^c  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b UNIVERSITY OF BOLOGNA   (Italy)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

MASS TRANSFER; MULTIPHASE FLOW; NUMERICAL MODELS; STUDENTS;

GAS LIQUIDS; GOVERNING EQUATIONS; GRADUATE STUDENTS;

DIRECT NUMERICAL SIMULATION;

EID: 84926117312     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511975264     Document Type: Book

References (450)

1. Abramowitz, M. and Stegun, I. (eds.) (1964). Handbook of Mathematical Func-tions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55. US Government Printing Office, Washington, DC.
2. Afkhami, S., Zaleski, S., and Bussmann, M. (2009). A mesh-dependent model for applying dynamic contact angles to VOF simulations. J. Comput. Phys., 228: 5370-5389.
3. Agarwal, D., Welch, S.W.J., Biswas, G., and Durst, F. (2004). Planar simulation of bubble growth in film boiling in near-critical water using a variant of the VOF method. ASME J. Heat Transfer, 126: 329-338.
4. Agresar, G., Linderman, J.J., Tryggvason, G., and Powell. K.G. (1998). An adap-tive, Cartesian, front-tracking method for the motion, deformation and adhesion of circulating cells. J. Comput. Phys., 43: 346-380.
5. Al-Rawahi, N. and Tryggvason, G. (2002). Numerical simulation of dendritic so-lidification with convection: two-dimensional geometry. J. Comput. Phys., 180: 471-496.
6. Al-Rawahi, N. and Tryggvason, G. (2004). Numerical simulation of dendritic so-lidification with convection: Three-dimensional flow. J. Comput. Phys., 194: 677-696.
7. Alexiades, V. and Solomon, A.D. (1993). Mathematical Modeling of Melting and Freezing Processes. Hemisphere.
8. Amsden, A.A. (1993). KIVA-3: a KIVA program with block-structured mesh for complex geometries. Technical report, LA-12503-MS, Los Alamos National Lab., NM.
9. Antal, S.P., Lahey, R.T., and Flaherty, J.E. (1991). Analysis of phase distribution in fully developed laminar bubbly two-phase flows. Int. J. Multiphase Flow, 15: 635-652.
10. Aris, R. (1962). Vectors, Tensors and Basic Equations of Fluid Mechanics. Dover.
11. Arp, P.A., Foister, R.T., and Mason, S.G. (1980). Some electrohydrodynamic ef-fects in fluid dispersions. Adv. Colloid Interface Sci., 12: 295-356.
12. Ashgriz, N. and Poo, J.Y. (1991). FLAIR: flux line-segment model for advection and interface reconstruction. J. Comput. Phys., 93: 449-468.
13. Ashgriz, N., Shirani, E., and Mostaghini, J. (2005). Interface pressure calculation based on conservation of momentum for front capturing methods. J. Comput. Phys., 203: 154-175.
14. Aubert, F., Aulisa, E., Manservisi, S., and Scardovelli, R. (2006). Interface track-ing with dynamically-redistributed surface markers in unstructured quadrangular grids. Comput. Fluids, 35: 1332-1343.
15. Aulisa, E., Manservisi, S., and Scardovelli, R. (2003a). A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows. J. Comput. Phys., 188: 611-639.
16. Aulisa, E., Manservisi, S., Scardovelli, R., and Zaleski, S. (2003b). A geometrical area-preserving volume of fluid advection method. J. Comput. Phys., 192: 355- 364.
17. Aulisa, E., Manservisi, S., and Scardovelli, R. (2004). A surface marker algo-rithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking. J. Comput. Phys., 197: 555-584.
18. Aulisa, E., Manservisi, S., Scardovelli, R., and Zaleski, S. (2007). Interface recon-struction with least-squares fit and split advection in three-dimensional Cartesian geometry. J. Comput. Phys., 225: 2301-2319.
19. Azpitarte, O.E. and Buscaglia, G.C. (2003). Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows. Chem. Eng. Sci., 58: 3765-3776.
20. Baker, G.R., Meiron, D.I., and Orszag, S.A. (1980). Vortex simulation of the Rayleigh-Taylor instability. Phys. Fluids, 23: 1485-1490.
21. Baker, G.R., Meiron, D.I., and Orszag, S.A. (1982). Generalized vortex methods for free surface flows problems. J. Fluid Mech., 123: 477.
22. Bargteil, A.W., Goktekin, T.G., O’Brien, J.F., and Strain, J.A. (2006). A semi-Lagrangian contouring method for fluid simulation. ACM Trans. Graphics (TOG), 25(1): 19-38.
23. Bassano, E. and Castagnolo, D. (2003). Marangoni migration of a methanol drop in cyclohexane matrix in a closed cavity. Microgravity Sci. Technol., XIV(1): 20-33.
24. Batchelor, G.K. (1970). An Introduction to Fluid Dynamics. Cambridge University Press.
25. Bayvel, L. and Orzechowski, Z. (1993). Liquid Atomization. Taylor and Francis.
26. Beckermann, C., Diepers, H.-J., Steinbach, I., Karma, A., and Tong, X. (1999). Modeling melt convection in phase-field simulations of solidification. J. Com-put. Phys., 154: 468-496.
27. Bell, J.B., Colella, P., and Glaz, H.M. (1989). A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys., 85: 257-283.
28. Ben Rayana, F., Cartellier, A., and Hopfinger, E. (2006). Assisted atomization of a liquid layer: investigation of the parameters affecting the mean drop size prediction. In Proc. ICLASS 2006, Aug. 27-Sept.1, Kyoto Japan. Academic Publication and Printings. (ISBN 4-9902774-1-4).
29. Berenson, P.J. (1961). Film boiling heat transfer from a horizontal surface. J. Heat Transfer, 83: 351-358.
30. Bierbrauer, F. (1995). Water drop impact on galvanised steel surfaces. In Proc. The Splash and Free Surface Workshop (ed. J.-L. Liow and P. Schwarz), The University of Melbourne, Melbourne, Australia.
31. Birdsall, C.K. and Langdon, A.B. (1985). Plasma Physics via Computer Simula-tion. McGraw-Hill.
32. Birkhoff, G. (1954). Taylor instability and laminar mixing. Rep. LA-1862; appen-dices in Rep. LA-1927, Los Alamos Scientific Laboratory (unpublished).
33. Blake, J.R. and Gibson, D.C. (1981). Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech., 111: 123-140.
34. Blake, T.D. and Shikmurzaev, Y. (2002). Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci., 253: 196-202.
35. Boeck, T. and Zaleski, S. (2005). Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile. Phys. Fluids, 17: 032106.
36. Boeck, T., Li, J., Lopez-Pages, E., Yecko, P., and Zaleski, S. (2007). Ligament formation in sheared liquid-gas layers. Theor. Comput. Fluid Dyn., 21: 59-76.
37. Boettinger, W.J., Warren, J.A., Beckermann, C., and Karma, A. (2002). Phase field simulations of solidification. Annu. Rev. Mater. Res., 32: 163-194.
38. Bonn, D., Eggers, J., Indekeu, J., Meunier, J., and Rolley, E. (2009). Wetting and spreading. Rev. Mod. Phys., 81: 739-805.
39. Boris, J.P. and Book, D.L. (1973). Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys., 11: 38-69.
40. Bothe, D., Koebe, M., Wielage, K., and Warnecke, H.J. (2003). FEDSM2003- 45155: VOF-simulations of mass transfer from single bubbles and bubble chains rising in aqueous solutions. In Proc. 2003 ASME Joint U.S.-European Fluids Eng. Conf., Honolulu, USA.
41. Bothe, D., Schmidtke, M., and Warnecke, H.-J. (2006). VOF-simulation of the lift force for single bubbles in a simple shear flow. Chem. Eng. Technol., 29: 1048-1053.
42. Boulton-Stone, J.M. and Blake, J.R. (1993). Gas-bubbles bursting at a free-surface. J. Fluid Mech., 254: 437-466.
43. Brackbill, J.U. and Ruppel, H.M. (1986). FLIP: a method for adaptively zoned, particle-in-cell calculations in two dimensions. J. Comput. Phys., 65: 314-343.
44. Brackbill, J.U., Kothe, D.B., and Zemach, C. (1992). A continuum method for modeling surface tension. J. Comput. Phys., 100: 335-354.
45. Bradley, S.G. and Stow, C.D. (1978). Collision between liquid drops. Phil. Trans. R. Soc. Lond. A, 287: 635.
46. Brady, J.F. and Bossis, G. (1988). Stokesian dynamics. Annu. Rev. Fluid Mech., 20: 111-157.
47. Brenner, M. and Gueyffier, D. (1999). On the bursting of viscous films. Phys. Fluids, 11: 737-739.
48. Briggs, W.L. (1987). A Multigrid Tutorial. SIAM Books, Philadelphia.
49. Broder, D. and Sommerfeld, M. (2007). Planar shadow image velocimetry for the analysis of the hydrodynamics in bubbly flows. Meas. Sci. Technol., 18: 2513- 2528.
50. Bunner, B. and Tryggvason, G. (2002a). Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech., 466: 17-52.
51. Bunner, B. and Tryggvason, G. (2002b). Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech., 466: 53-84.
52. Bunner, B. and Tryggvason, G. (2003). Effect of bubble deformation on the stabil-ity and properties of bubbly flows. J. Fluid Mech., 495: 77-118.
53. Carey, V.P. (2007). Liquid Vapor Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Trans-fer Equipment, 2nd edition, Taylor & Francis.
54. Cartellier, A. and Riviere, N. (2001). Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particle. Phys. Fluids, 13: 2165- 2181.
55. Ceniceros, H.D. and Roma, A.M. (2005). A multi-phase flow method with a fast, geometry-based fluid indicator. J. Comput. Phys., 205: 391-400.
56. Cha, P.-H., Yeon, D.-H., and Yoon, J.-K. (2005). Phase-field model for multicom-ponent alloy solidification. J. Cryst. Growth, 274: 281-293.
57. Chahine, G.L. and Duraiswami, R. (1992). Dynamic interactions in a multibubble cloud. ASME J. Fluids Eng., 114(4): 680-686.
58. Chan, R.K.-C. and Street, R.L. (1970). A computer study of finite-amplitude water waves. J. Comput. Phys., 6: 68-94.
59. Chandra, S. and Avedisian, C.T. (1991). On the collision of a droplet with a solid surface. Proc. R. Soc. London, Ser. A: Math. Phys. Sci., 432(1884): 13-41.
60. Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
61. Chang, Y.C., Hou, T.Y., Merriman, B., and Osher, S. (1996). Temporal evolution of periodic disturbances in two-layer Couette flow. J. Comput. Phys., 124: 449- 464.
62. Chapman, R.B. and Plesset, M.S. (1972). Nonlinear effects in the collapse of a nearly spherical cavity in a liquid. Trans. ASME, J. Basic Eng., 94: 142.
63. Che, J., Ceccio, S.L., and Tryggvason, G. (2004). Computations of structures formed by the solidification of impinging molten metal drops. J. Appl. Math. Model., 28: 127-144.
64. Chen, S., Johnson, D.B., Raad, P.E., and Fadda, D. (1997a). The surface marker and micro cell method. Int. J. Numer. Meth. Fluids, 25: 749-778.
65. Chen, S., Merriman, B., Osher, S., and Smereka, P. (1997b). A simple level set method for solving Stefan problems. J. Comput. Phys., 135: 8-29.
66. Chern, I.-L., Glimm, J., McBryan, O., Plohr, B., and Yaniv, S. (1986). Front track-ing for gas dynamics. J. Comput. Phys., 62: 83-110.
67. Choi, H.G. and Joseph, D.D. (2001). Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation. J. Fluid Mech., 438: 101-128.
68. Chorin, A.J. (1968). Numerical solutions of the Navier-Stokes equations. Math. Comput., 22: 745-762.
69. Chorin, A.J. (1967). A numerical method for solving incompressible viscous flow problems. J. Comput. Phys., 2: 12.
70. Christiansen, J.P. (1973). Numerical simulation of hydrodynamics by the method of point vortices. J. Comput. Phys., 13: 363-379.
71. Clift, R., Grace, J.R., and Weber, M.E. (1978). Bubbles, Drops, and Particles. Academic Press.
72. Coriell, S.R. and McFadden, G.B. (1993). Morphological stability. In Handbook of Crystal Growth, vol. 1B (ed. D.T.J. Hurle), Elsevier, pp. 785-857.
73. Cortelezzi, L. and Prosperetti, A. (1981). Small amplitude waves on the surface of a layer of a viscous liquid. Q. Appl. Math., 38: 375-388.
74. Cortez, R. and Minion, M. (2000). The blob projection method for immersed boundary problems. J. Comput. Phys., 161: 428-453.
75. Coward, A.V., Renardy, Y.Y., Renardy, M., and Richards, J.R. (1997). Temporal evolution of periodic disturbances in two-layer Couette flow. J. Comput. Phys., 132: 346-361.
76. Crapper, G.D., Dombrowski, N., Jepson, W.P., and Pyott, G.A.D. (1973). A note on the growth of Kelvin-Helmholtz waves on thin liquid sheets. J. Fluid. Mech., 57: 671-672.
77. Cristini, V., B?awzdziewicz, J., and Loewenberg, M. (1998). Drop breakup in three-dimensional viscous flows. Phys. Fluids., 10: 1781-1784.
78. Cummins, S.J., Francois, M.M., and Kothe, D.B. (2005). Estimating curvature from volume fractions. Comput. Struct., 83: 425-434.
79. Daly, B.J. (1969a). A technique for including surface tension effects in hydrody-namic calculations. J. Comput. Phys., 4: 97-117.
80. Daly, B.J. (1969b). Numerical study of the effect of surface tension on interface instability. Phys. Fluids, 12: 1340-1354.
81. Daly, B.J. and Pracht, W.E. (1968). Numerical study of density-current surges. Phys. Fluids, 11: 15-30.
82. Dandy, D.S. and Leal, G.L. (1989). Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers. J. Fluid Mech., 208: 161-192.
83. Davidson, M.R. and Rudman, M. (2002). Volume-of-fluid calculation of heat or mass transfer across deforming interfaces in two-fluid flow. Numer. Heat Trans-fer Part B Fund., 41: 291-308.
84. Davies, J.T. and Rideal, E.K. (1966). Interfacial Phenomena. Academic Press.
85. Davis, R.H., Schonberg, J.A., and Rallison, J.M. (1989). The lubrication force between two viscous drops. Phys. Fluids A: Fluid Dyn., 1: 77-81.
86. de Gennes, P.G. (1985). Wetting: statics and dynamics. Rev. Mod. Phys., 57: 827-863.
87. de Gennes, P.G., Quere, D., and Brochard, F. (2003). Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer Verlag.
88. de Josselin de Jong, G. (1960). Singularity distribution for the analysis of multiple-fluid flow through porous media. J. Geophys. Res., 65: 3739-3758.
89. DeBar, R. (1974). Fundamentals of the KRAKEN code. Technical Report UCIR- 760, LLNL.
90. Deckwer, W.-D. (1992). Bubble Column Reactors. Wiley.
91. Deen, N.G., van Sint Annaland, M., and Kuipers, J.A.M. (2004). Multi-scale mod-eling of dispersed gas-liquid two-phase flow. Chem. Eng. Sci., 59: 1853-1861.
92. DeGregoria, A.J. and Schwartz, L.W. (1985). Finger breakup in Hele-Shaw cells. Phys. Fluids, 28: 2313.
93. Delale, C.F., Nas, S., and Tryggvason, G. (2005). Direct numerical simulations of shock propagation in bubbly liquids. Phys. Fluids, 17: 121705.
94. Dhir, V.K. (1998). Boiling heat transfer. Annu. Rev. Fluid Mech., 30: 365-401.
95. Ding, H., Spelt, P.D.M., and Shu, C. (2007). Diffuse interface model for incom-pressible two-phase flows with large density ratios. J. Comput. Phys., 226: 2078-2095.
96. Dombrowski, N. and Johns, W.R. (1963). The aerodynamic instability and disin-tegration of viscous liquid sheets. Chem. Eng. Sci., 18: 203-214.
97. Drew, D.A. (1983). Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech., 15: 261-291.
98. Drew, D.A. and Passman, S.L. (1999). Theory of Multicomponent Fluids. Springer.
99. Drumright-Clarke, M.A. and Renardy, Y. (2004). The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia. Phys. Fluids, 16: 14-21.
100. Druzhinin, O.A. and Elghobashi, S.E. (2001). Direct numerical simulation of a three-dimensional spatially-developing bubble-laden mixing layer with two-way coupling. J. Fluid Mech., 429: 23-61.
101. Du, J., Fix, B., Glimm, J., Jia, X., Li, X., Li, Y., and Wu, L. (2006). A simple package for front tracking. J. Comput. Phys., 213: 613-628.
102. Duchemin, L., Popinet, S., Josserand, C., and Zaleski, S. (2002). Jet formation in bubbles bursting at a free surface. Phys. Fluids, 14(9): 3000-3008.
103. Dussan, V.E.B. (1979). On the spreading of liquid on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech., 11: 371-400.
104. E, W. and Engquist, B. (2003). The heterogeneous multiscale methods. Commun. Math. Sci., 1: 87-133.
105. Edgerton, H. (1987). Stopping Time. Harry N. Abrams, New York.
106. Edwards, D.A., Brenner, H., and Wasan, D.T. (1961). Interfacial Transport Pro-cesses and Rheology. Butterworth.
107. Eggers, J. (1993). Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett., 71: 3458-3461.
108. Eggers, J. and Dupont, T.D. (1994). Drop formation in a one-dimensional approx-imation of the Navier-Stokes equation. J. Fluid Mech., 262: 205-221.
109. Eggers, J. and Villermaux, E. (2008). Physics of liquid jets. Rep. Prog. Phys., 71: 036601.
110. Ellingsen, K. and Risso, F. (2001). On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity. J. Fluid Mech., 440: 235-268.
111. Ervin, E.A. and Tryggvason, G. (1997). The rise of bubbles in a vertical shear flow. ASME J. Fluid Eng., 119: 443-449.
112. Esmaeeli, A. and Tryggvason, G. (1996). An inverse energy cascade in two-dimensional, low Reynolds number bubbly flows. J. Fluid Mech., 314: 315-330.
113. Esmaeeli, A. and Tryggvason, G. (1998). Direct numerical simulations of bubbly flows. Part I. Low Reynolds number arrays. J. Fluid Mech., 377: 313-345.
114. Esmaeeli, A. and Tryggvason, G. (1999). Direct numerical simulations of bubbly flows. Part II. Moderate Reynolds number arrays. J. Fluid Mech., 385: 325-358.
115. Esmaeeli, A. and Tryggvason, G. (2004a). A front tracking method for computa-tions of boiling in complex geometries. Int. J. Multiphase Flow, 30: 1037-1050.
116. Esmaeeli, A. and Tryggvason, G. (2004b). Computations of film boiling. Part I: numerical method. Int. J. Heat Mass Transfer, 47: 5451-5461.
117. Esmaeeli, A. and Tryggvason, G. (2004c). Computations of film boiling. Part II: multi-mode film boiling. Int. J. Heat Mass Transfer, 47: 5463-5476.
118. Esmaeeli, A. and Tryggvason, G. (2005). A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number. Phys. Fluids, 17: 093303.
119. Fadlun, E.A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J. (2000). Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys., 161: 35-60.
120. Farmer, E.E. (1973). Relative detachability of soil particles by simulated rainfall. Soil Sci. Soc. Am. J., 37: 629-633.
121. Fauci, L.J. and Dillon, R. (2006). Biofluidmechanics of reproduction. Annu. Rev. Fluid Mech., 38: 371-394.
122. Fedkiw, R., Aslam, T., Merriman, B., and Osher, S. (1999). A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys., 152: 457-492.
123. Feng, J., Hu, H.H., and Joseph, D.D. (1994). Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1. Sedimation. J. Fluid Mech., 261: 95-134.
124. Feng, J., Hu, H.H., and Joseph, D.D. (1995). Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech., 277: 271-301.
125. Fernandez, A. (2008a). Response of an emulsion of leaky dielectric drops im-mersed in a simple shear flow: drops more conductive than the suspending fluid. Phys. Fluids, 20: 043303.
126. Fernandez, A. (2008b). Response of an emulsion of leaky dielectric drops im-mersed in a simple shear flow: drops less conductive than the suspending fluid. Phys. Fluids, 20: 043304.
127. Fernandez, A., Che, J., Ceccio, S.L., and Tryggvason, G. (2005). The effects of electrostatic forces on the distribution of drops in a channel flow - two-dimensional oblate drops. Phys. Fluids, 17: 093302.
128. Foote, G.B. (1973). A numerical method for studying liquid drop behavior: simple oscillations. J. Comput. Phys., 11: 507-530.
129. Foote, G.B. (1975). The water drop rebound problem: dynamics of collision. J. Atmos. Sci., 32: 390-402.
130. Fortes, A., Joseph, D.D., and Lundgren, T. (1987). Nonlinear mechanics of flu-idization of beds of spherical particles. J. Fluid Mech., 177: 467-483.
131. Foster, N. and Fedkiw, R. (2001). Practical animation of liquids. In Proc. 28th Annual Conf. on Computer Graphics and Interactive Techniques. ACM Press, New York, NY, pp. 23-30.
132. Francois, M.M., Cummins, S.J., Dendy, E.D., Kothe, D.B., Sicilian, J.M., and Williams, M.W. (2006). A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Com-put. Phys., 213(1): 141-173.
133. Frumkin, A. and Levich, V.G. (1947). O vliyanii poverkhnostno-aktivnikh veshestv na dvizhenie na granitse zhidkikh sred. Zh. Fiz. Khim., 21: 1183-1204.
134. Fukai, J., Shiiba, Y., Yamamoto, T., Miyatake, O., Poulikakos, D., Megaridis, C.M., and Zhao, Z. (1995). Wetting effects on the spreading of a liquid droplet collid-ing with a flat surface: experiment and modeling. Phys. Fluids, 7: 236-247.
135. Furusaki, S., Fan, L.-S., and Garside, J. (2001). The Expanding World of Chemical Engineering (2nd edition). Taylor and Francis.
136. Fuster, D., Agbaglah, G., Josserand, C., Popinet, S., and Zaleski, S. (2009a). Nu-merical simulation of droplets, bubbles and waves: state of the art. Fluid Dyn. Res. 41: 065001.
137. Fuster, D., Bague, A., Boeck, T., Le Moyne, L., Leboissetier, A., Popinet, S., Ray, P., Scardovelli, R., and Zaleski, S. (2009b). Simulation of primary at-omization with an octree adaptive mesh refinement and VOF method. Int. J. Multiphase Flow, 35: 550-565.
138. Gao, P., Yin, Z., and Hu, W. (2008). Thermocapillary motion of droplets at large Marangoni numbers. Adv. Space Res., 41(12): 2101-2106.
139. Ge, Y. and Fan, L.-S. (2006). Three-dimensional direct numerical simulation for film-boiling contact of moving particle and liquid droplet. Phys. Fluids, 18: 117104.
140. Gerlach, D., Tomar, G., Biswas, G., and Durst, F. (2006). Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows. Int. J. Heat Mass Transfer, 49: 740-754.
141. Gibou, F., Chen, L., Nguyen, D., and Banerjee, S. (2007). A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change. J. Comput. Phys., 222: 536-555.
142. Gilmanov, A., Sotiropoulos, F., and Balaras, E. (2003). A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Carte-sian grids. J. Comput. Phys., 191: 660-669.
143. Glicksman, M.E., Coriell, S.R., and McFadden, G.B. (1986). Interaction of flows with the crystal-melt interface. Annu. Rev. Fluid Mech., 18: 307-335.
144. Glimm, J. and McBryan, O. (1985). A computational model for interfaces. Adv. Appl. Math., 6: 422-435.
145. Glimm, J., Marchesin, D., and McBryan, O. (1981). A numerical method for two phase flow with an unstable interface. J. Comput. Phys, 39: 179-200.
146. Glimm, J., Grove, J.W., Li, X.L., Oh, W., and Sharp, D.H. (2001). A critical analysis of Rayleigh-Taylor growth rates. J. Comput. Phys., 169: 652-677.
147. Glowinski, R., Pan, T.W., Helsa, T.I., Joseph, D.D., and Periaux, J. (2001). A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys., 169: 363-426.
148. Goldstein, D., Handler, R., and Sirovich, L. (1993). Modeling a no-slip flow bound-ary with an external force field. J. Comput. Phys., 105: 354-366.
149. Gordillo, J.M. and Perez-Saborid, M. (2005). On the first wind atomization regime. J. Fluid. Mech, 541: 1-20.
150. Guet, S., Ooms, G., Oliemans, R.V.A., and Mudde, R.F. (2004). Bubble size effect on low liquid input drift-flux parameters. Chem. Eng. Sci., 59: 3315-3329.
151. Guet, S., Ooms, G., and Oliemans, R.V.A. (2005). Simplified two-fluid model for gas-lift efficiency predictions. AIChe J., 51: 1885-1896.
152. Gueyffier, D. and Zaleski, S. (1998). Formation de digitations lors de L'impact D'une goutte sur un film liquide. C. R. Acad. Sci. Paris ser. II b, 326: 839-844.
153. Gueyffier, D., Nadim, A., Li, J., Scardovelli, R., and Zaleski, S. (1999). Vol-ume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys., 152: 423-456.
154. Hadamard, J. (1911). Mouvement permanent lent D'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris, 152: 1735-1738.
155. Hammerlin, G. and Hoffmann, K.-H. (1991). Numerical Mathematics. Springer.
156. Harlow, F.H. (1964). The particle-in-cell computing method for fluid dynamics. Methods Comput. Phys., 3: 319-343.
157. Harlow, F.H. and Fromm, J.E. (1965). Computer experiments in fluid dynamics. Sci. Am., 212: 104.
158. Harlow, F.H. and Shannon, J.P. (1967). The splash of a liquid drop. J. Appl. Phys., 38: 3855-3866.
159. Harlow, F.H. and Welch, J.E. (1965). Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids, 8: 2182- 2189.
160. Harlow, F.H. and Welch, J.E. (1966). Numerical study of large-amplitude free-surface motions. Phys. Fluids, 9: 842-851.
161. Harvie, D.J.E. and Fletcher, D.F. (2000). A new volume of fluid advection algo-rithm: the Stream scheme. J. Comput. Phys., 162: 1.
162. Hervet, H. and de Gennes, P.G. (1984). Dynamique du mouillage: films precurseurs sur solide ‘sec’. C. R. Acad. Sci. Paris, Ser. II, 299: 499-503.
163. Hinch, E.J. (1984). A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech., 144: 463-465.
164. Hirt, C.W. and Nichols, B.D. (1981). Volume of fluid (VOF) method for the dy-namics of free boundaries. J. Comput. Phys., 39: 201-226.
165. Hirt, C.W., Cook, J.L., and Butler, T.D. (1970). A Lagrangian method for calcu-lating the dynamics of an incompressible fluid with a free surface. J. Comput. Phys., 5: 103-124.
166. Hockney, R.W. and Eastwood, J.W. (1981). Computer Simulation Using Particles. McGraw-Hill.
167. Hooper, A.P. and Boyd, W.G.C. (1983). Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech., 128: 507-528.
168. Hou, T.Y., Lowengrub, J.S., and Shelley, M.J. (2001). Boundary integral methods for multicomponent fluids and multiphase materials. J. Comput. Phys., 169: 302-362.
169. Hu, H.H. (1996). Direct simulation of flows of solid-liquid mixtures. Int. J. Mul-tiphase Flow, 22: 335-352.
170. Hu, H.H., Patankar, N.A., and Zhu, M.Y. (2001). Direct numerical simulations of fluid-solid systems using arbitrary-Lagrangian-Eularian techniques. J. Comput. Phys., 169: 427-462.
171. Hua, J. and Lou, J. (2007). Numerical simulation of bubble rising in viscous liquid. J. Comput. Phys., 222: 769-795.
172. Hua, J., Lim, L.K., and Wang, C.-H. (2008). Numerical simulation of deforma-tion/motion of a drop suspended in viscous liquids under influence of steady electric fields. Phys. Fluids, 20: 113302.
173. Huh, C. and Scriven, L. (1971). Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Coll. Interf. Sci, 35: 85.
174. Ishii, M. (1987). Interfacial Area Modeling, Vol. 3, McGraw-Hill, Chapter 3, pp. 31-62.
175. Ishii, M. and Zuber, N. (1979). Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J., 25: 843-855.
176. Issa, R.I. (1985). Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys., 62: 40-65.
177. Jacqmin, D. (1999). Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys., 155: 96-127.
178. Jacqmin, D. (2000). Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech., 402: 57-88.
179. James, A.J. and Lowengrub, J. (2004). A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J. Comput. Phys., 201: 685-722.
180. Jamet, D., Lebaigue, O., Coutris, N., and Delhaye, J.M. (2001). Feasibility of using the second gradient theory for the direct numerical simulations of liquid-vapor flows with phase-change. J. Comput. Phys., 169: 624-651.
181. Jan, Y.-J. (1994). Computational studies of bubble dynamics. PhD thesis, The University of Michigan.
182. Jeong, J.-H., Goldenfield, N., and Dantzig, J.A. (2001). Phase field model for three-dimensional dendritic growth with fluid flow. Phys. Rev. E, 64: 041602.
183. Johansson, B.C.V. (1993). Boundary conditions for open boundaries for the in-compressible Navier-Stokes equation. J. Comput. Phys., 105: 233-251.
184. Johnson, A. A. and Tezduyar, T.E. (1997). 3D simulation of fluid-particle interac-tions with the number of particles reaching 100. Comput. Methods Appl. Mech. Eng., 145: 301-321.
185. Josserand, C. and Zaleski, S. (2003). Droplet splashing on a thin liquid film. Phys. Fluids, 15: 1650-1657.
186. Juric, D. and Tryggvason, G. (1998). Computations of boiling flows. Int. J. Multi-phase Flow, 24: 387-410.
187. Kadioglu, S.Y. and Sussman, M. (2008). Adaptive solution techniques for simulat-ing underwater explosions and implosions. J. Comput. Phys., 227: 2083-2104.
188. Kajishima, T. and Takiguchi, S. (2002). Interaction between particle clusters and fluid turbulence. Int. J. Heat Fluid Flow, 23: 639-646.
189. Kanai, A. and Miyata, H. (2001). Direct numerical simulation of wall turbulent flows with microbubbles. Int. J. Numer. Methods Fluids, 35: 593-615.
190. Kang, I.S. and Leal, L.G. (1987). Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. I. Finite-difference scheme and its applications to the deformation of a bubble in a uniaxial straining flow. Phys. Fluids, 30: 1929-1940.
191. Karma, A. and Rappel, W.J. (1997). Phase-field simulation of three-dimensional dendrites: is microscopic solvability theory correct? J. Cryst. Growth, 174: 54-64.
192. Karma, A. and Rappel, W.-J. (1998). Quantitative phase-field modeling of den-dritic growth in two and three dimensions. Phys. Rev. E, 57: 4323-4349.
193. Kashinsky, O.N. and Randin, V.V. (1999). Downward bubbly gas-liquid flow in a vertical pipe. Int. J. Multiphase Flow, 25: 109-138.
194. Kawamura, T. and Kodama, Y. (2002). Numerical simulation method to resolve interactions between bubbles and turbulence. Int. J. Heat Fluid Flow, 23: 627- 638.
195. Keller, J.B. and Miksis, M.J. (1983). Surface tension driven flows. SIAM J. Appl. Math., 43(2): 268-277.
196. Kermeen, R.W. (1956). Water tunnel tests of NACA 4412 and Walchner profile 7 hydrofoils in non-cavitating and cavitating flows. Technical report, California Institute of Technology Hydro. Lab. Rep. 47-5.
197. Khinast, J.G., Koynov, A.A., and Leib, T.M. (2003). Reactive mass transfer at gas-liquid interfaces: impact of micro-scale fluid dynamics on yield and selectivity of liquid-phase cyclohexane oxidation. Chem. Eng. Sci., 58: 3961-3971.
198. Kim, J. and Moin, P. (1985). Application of a fractional step method to incom-pressible Navier-Stokes equations. J. Comput. Phys., 59: 308-323.
199. Kim, J., Kim, D., and Choi, H. (2001). An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys., 171: 132-150.
200. Kitagawa, A., Sugiyama, K., and Murai, Y. (2004). Experimental detection of bubble-bubble interactions in a wall-sliding bubble swarm. Int. J. Multiphase Flow, 30: 1213-1234.
201. Klimenko, V.V. (1981). Film boiling on a horizontal plate - new correlation. Int. J. Heat Mass Transfer, 24: 69-79.
202. Kobayashi, R. (1992). Simulations of three-dimensional dendrites. In Pattern For-mation in Complex Dissipative Systems (ed. S. Kai). World Scientific, Singapore, pp. 121-128.
203. Kobayashi, R. (1993). Modeling and numerical simulations of dendritic crystal-growth. Phys. D, 63: 410-423.
204. Koplik, J., Banavar, J.R., and Willemsen, J.F. (1988). Molecular dynamics of Poiseuille flow and moving contact lines. Phys. Rev. Lett., 60: 1282-1285.
205. Koynov, A., Khinast, J.G., and Tryggvason, G. (2005). Mass transfer and chemical reactions in bubble swarms with dynamic interfaces. AIChE. J., 51: 2786-2800.
206. Kuo, T.C., Pan, C., and Chieng, C.C. (1997). Eulerian-Lagrangian computations on phase distribution of two-phase bubbly flows. Int. J. Numer. Methods Fluids, 24: 579-593.
207. Ladd, A.J.C. (1993). Dynamical simulations of sedimenting spheres. Phys. Fluids A, 5: 299-310.
208. Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., and Zanetti, G. (1994). Mod-elling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys., 113: 134-147.
209. Lai, M.-C. and Peskin, C.S. (2000). An immersed boundary method with formal second order accuracy and reduced numerical viscosity. J. Comput. Phys., 160: 705-719.
210. Lance, M. and Bataille, J. (1991). Turbulence in the liquid phase of a uniform bubbly air-water flow. J. Fluid Mech., 222: 95-118.
211. Lasheras, J.C. and Hopfinger, E.J. (2000). Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech., 32: 275-308.
212. Leboissetier, A. (2002). Simulation numerique directe de L'atomisation primaire D'un jet liquide a haute vitesse. Technical report, Universite de Paris 6. These de doctorat.
213. Lee, J. and Pozrikidis, C. (2006). Effect of surfactants on the deformation of drops and bubbles in Navier-Stokes flow. Comput. Fluids, 35: 43-60.
214. Lee, L. and LeVeque, R.J. (2003). An immersed interface method for incompress-ible Navier-Stokes equations. SIAM J. Sci. Comput., 25: 832-856.
215. Lee, R.C. and Nydahl, J.E. (1989). Numerical calculations of bubble growth in nucleate boiling from inception through departure. J. Heat Transfer, 111: 474- 479.
216. Lee, Y.-W., Ananth, R., and Gill, W.N. (1993). Selection of length scale in uncon-strained dendritic growth with convection in the melt. J. Cryst. Growth, 132: 226-230.
217. Lefebvre, A.H. (1989). Atomization and Sprays. Taylor and Francis.
218. Lenard, P. (1892). u ber die Electricitat der Wasserfalle. Ann. Phys., 46: 584-636.
219. Leonard, B.P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng., 19: 59-98.
220. Li, J. (1995). Calcul D'interface affine par morceaux (Piecewise linear interface calculation). C. R. Acad. Sci. Paris, Ser. IIb (Paris), 320: 391-396.
221. Li, J. (1996). Resolution numerique de L'equation de Navier-Stokes avec recon-nection D'interfaces. Methode de suivi de volume et application a L'atomisation. Technical report, Universite de Paris 6. These de doctorat.
222. Liow, J.L., Morton, D.E., Guerra, E., and Gray, N.B. (1996). Dynamics of splash formation in gas injected systems. In The Howard Worner Int. Symp. on Injection in Pyrometallurgy, Melbourne, pp. 175-190.
223. Lister, J. and Zhang, W.W. (1999). Similarity solutions for van der Waals rupture of a thin film on a solid substrate. Phys. Fluids, 11: 2454-2462.
224. Liu, H., Krishnan, S., Marella, S., and Udaykumar, H.S. (2005). Sharp interface Cartesian grid method II: a technique for simulating droplet interactions with surfaces of arbitrary shape. J. Comput. Phys., 210: 32-54.
225. Liu, T.J. (1997). Investigation of the wall shear stress in vertical bubbly flow under different bubble size conditions. Int. J. Multiphase Flow, 23: 1085-1109.
226. Liu, T.J. and Bankoff, S.G. (1993). Structure of air-water bubbly flow in a vertical pipe - I. Liquid mean velocity and turbulence measurements. Int. J. Heat Mass Transfer, 36: 1049-1060.
227. Loewenberg, M. and Hinch, E.J. (1996). Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech., 321: 395-419.
228. Longuet-Higgins, M.S. and Cokelet, E.D. (1976). The deformation of steep surface waves on water. Proc. R. Soc. London Ser. A, 358: 1.
229. Lopez, J., Hernandez, J., Gomez, P., and Faura, F. (2004). A volume of fluid method based on multidimensional advection and spline interface reconstruc-tion. J. Comput. Phys., 195: 718-742.
230. Lopez De Bertodano, M., Lahey, R.T., Jr., and Jones, O.C. (1987). Development of a k-model for bubbly two-phase flow. J. Fluids Eng., 13: 327-343.
231. Lopez De Bertodano, M., Lahey, R.T., Jr., and Jones, O.C. (1994). Phase distri-bution in bubbly two-phase flow in vertical ducts. Int. J. Multiphase Flow, 20: 805-818.
232. Louge, M.Y. (1994). Computer simulations of rapid granular flows of spheres interacting with a flat, frictional boundary. Phys. Fluids, 6: 2253-2269.
233. Lu, J. and Tryggvason, G. (2006). Numerical study of turbulent bubbly downflows in a vertical channel. Phys. Fluids, 18: 103302.
234. Lu, J. and Tryggvason, G. (2007). Effect of bubble size in turbulent bubbly down-flow in a vertical channel. Chem. Eng. Sci., 62: 3008-3018.
235. Lu, J. and Tryggvason, G. (2008). Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys. Fluids, 20: 040701.
236. Lu, J., Fernandez, A., and Tryggvason, G. (2005a). The effect of bubbles on the wall shear in a turbulent channel flow. Phys. Fluids, 17: 095102.
237. Lu, J., Biswas, S., and Tryggvason, G. (2006). A DNS study of laminar bubbly flows in a vertical channel. Int. J. Multiphase Flow, 32: 643-660.
238. Lu, Y., Beckermann, C., and Ramirez, J.C. (2005b). Three-dimensional phase field simulations of the effect of convection on free dendritic growth. J. Cryst. Growth, 280: 320-334.
239. Luo, R., Pan, X.H., and Yang, X.Y. (2003). Laminar light particle and liquid two-phase flows in a vertical pipe. Int. J. Multiphase Flow, 29: 603-620.
240. MacIntyre, F. (1972). Flow patterns in breaking bubbles. J. Geophys. Res., 77(27): 5211-5228.
241. MacNeice, P., Olson, K.M., Mobarry, C., de Fainchtein, R., and Packer, C. (2000). PARAMESH: a parallel adaptive mesh refinement community toolkit. Comput. Phys. Commun., 126: 330-354.
242. Marella, S., Krishnan, S., Liu, H., and Udaykumar, H.S. (2005). Sharp interface Cartesian grid method I: an easily implemented technique for 3D moving bound-ary computations. J. Comput. Phys., 214: 1-31.
243. Marmottant, P. and Villermaux, E. (2001). Ligament mediated drop formation. Phys. Fluids, 13: S7.
244. Marmottant, P. and Villermaux, E. (2002). Atomisation primaire dans les jets coax-iaux. Combustion (Rev. des Sci. Tech. Combustion), 2: 89-126.
245. Martin, D.F. (1998). An adaptive cell-centered projection method for the incompressible Euler equations. PhD thesis, University of California, Berkeley.
246. Meiburg, E. and Homsy, G.M. (1988). Nonlinear unstable viscous fingers in Hele-Shaw flows. II. Numerical simulation. Phys. Fluids, 31: 429.
247. Melcher, J.R. and Taylor, G.I. (1969). Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech., 1: 111-146.
248. Menchaca-Rocha, A., Huidobro, F., Martinez-Davalos, A., Michaelian, K., Perez, A., Rodriguez, V., and Carjan, N. (2000). Coalescence and fragmenta-tion of colliding mercury drops. J. Fluid Mech., 346: 291-318.
249. Miller, G.H. and Colella, P. (2002). A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing. J. Comput. Phys., 183: 26-82.
250. Mitchell, T.M. and Hammitt, F.H. (1973). Asymmetric cavitation bubble collapse. Trans. ASME, J. Fluids Eng., 95: 29.
251. Mittal, R. and Iaccarino, G. (2005). Immersed boundary methods. Annu. Rev. Fluid Mech., 37: 239-261.
252. Morton, D., Rudman, M., and Jong-Leng, L. (2000). An investigation of the flow regimes resulting from splashing drops. Phys. Fluids, 12(4): 747-763.
253. Mukherjee, A. and Dhir, V.K. (2004). Study of lateral merger of vapor bubbles during nucleate pool boiling. J. Heat Transfer, 126: 1023-1039.
254. Mukherjee, A. and Kandlikar, S.G. (2007). Numerical study of single bubbles with dynamic contact angle during nucleate pool boiling. Int. J. Heat Mass Transfer, 50: 127-138.
255. Muradoglu, M. and Kayaalp, A.D. (2006). An auxiliary grid method for com-putations of multiphase flows in complex geometries. J. Comput. Phys., 214: 858-877.
256. Muradoglu, M. and Tryggvason, G. (2008). A front-tracking method for com-putation of interfacial flows with soluble surfactants. J. Comput. Phys., 227: 2238-2262.
257. Nakamura, T. and Yabe, T. (1999). Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space. Com-put. Phys. Commun., 120: 122.
258. Nas, S. and Tryggvason, G. (2003). Thermocapillary interaction of two bubbles or drops. Int. J. Multiphase Flow, 29: 1117-1135.
259. Nas, S., Muradoglu, M., and Tryggvason, G. (2006). Pattern formation of drops in thermocapillary migration. Int. J. Heat Mass Transfer, 49: 2265-2276.
260. Navier, C.L. (1823). Sur les lois du mouvement des fluides. Mem. Acado. Sci. France, 6: 389-440 (appeared in 1827).
261. Nestler, B. (2005). A 3D parallel simulator for crystal growth and solidification in complex alloy systems. J. Cryst. Growth, 275: 273-278.
262. Nie, X.B., Chen, S.Y., E, W.N., and Robbins, M.O. (2004). A continuum and molecular dynamics hybrid method for micro-and nano-fluid flow. J. Fluid Mech., 500: 55-64.
263. Nikolopoulos, N., Theodorakakos, A., and Bergeles, G. (2007). Three-dimensional numerical investigation of a droplet impinging normally onto a wall film. J. Comput. Phys., 227: 1428-1469.
264. Nobari, M.R. and Tryggvason, G. (1996). Numerical simulations of three-dimensional drop collisions. AIAA J., 34: 750-755.
265. Nobari, M.R., Jan, Y.-J., and Tryggvason, G. (1996). Head-on collision of drops - a numerical investigation. Phys. Fluids, 8: 29-42.
266. Noh, W.F. and Woodward, P. (1976). SLIC (simple line interface calculation). In Proceedings, Fifth International Conference on Fluid Dynamics (eds. A.I. van de Vooren and P.J. Zandbergen), Lecture Notes in Physics, volume 59. Berlin, Springer, Berlin, pp. 330-340.
267. Nordmark, H.O. (1991). High-order vortex methods with regridding. J. Comput. Phys., 97: 366.
268. Oguz, H. and Prosperetti, A. (1990). Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech., 219: 143-179.
269. Oguz, H. and Prosperetti, A. (1993). Dynamics of bubble growth and detachment from a needle. J. Fluid Mech., 257: 111-145.
270. O’Keefe, J.D. and Ahrens, T.J. (1986). Oblique impact: a process for obtaining meteorite samples from other planets. Science, 234(4774): 346.
271. Oran, E.S. and Boris, J.P. (1987). Numerical Simulation of Reactive Flow. Elsevier.
272. Oron, A., Davis, S.H., and Bankoff, S.G. (1997). Long-scale evolution of thin films. Rev. Mod. Phys., 69: 931-980.
273. Osher, S. and Fedkiw, R. (2002). Level Set Methods and Dynamic Implicit Sur-faces. Springer.
274. Osher, S. and Fedkiw, R.P. (2001). Level set methods: an overview and some recent results. J. Comput. Phys., 169: 463-502.
275. Osher, S. and Sethian, J. (1988). Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys., 79: 12-49.
276. Osher, S. and Shu, C.-W. (1991). High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal., 28: 907-922.
277. Pan, T.W., Joseph, D.D., Bai, R., Glowinski, R., and Sarin, V. (2002). Fluidization of 1204 spheres: simulation and experiment. J. Fluid Mech., 451: 169-191.
278. Pasandideh-Fard, M., Chandra, S., and Mostaghimi, J. (2002). A three-dimensional model of droplet impact and solidification. Int. J. Heat Mass Transfer, 45: 2229- 2242.
279. Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow. Taylor and Francis.
280. Peng, D., Merriman, B., Zhao, H., Osher, S., and Kang, M. (1999). A PDE based fast local level set method. J. Comput. Phys., 155: 410-438.
281. Peregrine, D.H., Shoker, G., and Symon, A. (1990). The bifurcation of liquid bridges. J. Fluid. Mech., 212: 25-39.
282. Peskin, C.S. (1977). Numerical analysis of blood flow in the heart. J. Comput. Phys., 25: 220.
283. Peskin, C.S. (2002). The immersed boundary method. Acta Numer., 11: 479-517.
284. Peskin, C.S. and McQueen, D.M. (1989). A three-dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous in-compressible fluid. J. Comput. Phys., 81: 372-405.
285. Peskin, C.S. and Printz, B.F. (1993). Improved volume conservation in the compu-tation of flows with immersed boundaries. J. Comput. Phys., 105: 33-46.
286. Pilliod, J.E., Jr. and Puckett, E.G. (2004). Second-order accurate volume-of-fluid algorithms for tracking material interfaces. J. Comput. Phys., 199: 465-502.
287. Plapp, M. (2007). Three-dimensional phase-field simulations of directional solidi-fication. J. Cryst. Growth, 303: 49-57.
288. Plateau, J. (1873). Statique Experimentale et Theorique des Liquide. Gauthier-Villars.
289. Pomeau, Y. (2002). Recent progress in contact line dynamics: a review. C. R. Acad. Sci. Paris, Ser. IIb, (Paris). Mec., 330: 207-222.
290. Popinet, S. (2003). Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys., 190: 572-600.
291. Popinet, S. (2008). The Gerris flow solver. http://gfs.sf.net.
292. Popinet, S. (2009). An accurate adaptive solver for surface-tension-driven interfa-cial flows. J. Comput. Phys., 228: 5838-5866.
293. Popinet, S. and Zaleski, S. (1999). A front-tracking algorithm for accurate repre-sentation of surface tension. Int. J. Numer. Methods Fluids, 30: 775-793.
294. Popinet, S. and Zaleski, S. (2002). Bubble collapse near a solid boundary: a nu-merical study of the influence of viscosity. J. Fluid Mech., 464: 137-163.
295. Poschel, T. and Schwage, T. (2005). Computational Granular Dynamics: Models and Algorithms. Springer.
296. Powell, K. (1998). Solution of the Euler equations on solution-adaptive Carte-sian grids. In Computational Fluid Dynamics Reviews, (eds. M. Hafez, and K. Oshima), volume 1. World Scientific, pp. 65-92.
297. Pozrikidis, C. (1992). Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
298. Pozrikidis, C. (2001). Interfacial dynamics for Stokes flow. J. Comput. Phys., 169: 250-301.
299. Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1993). Numeri-cal Recipes in C: The Art of Scientific Computing. Cambridge University Press.
300. Prosperetti, A. (1981). Motion of two superposed viscous fluids. Phys. Fluids, 24: 1217-1223.
301. Prosperetti, A. (2007). Averaged Equations for Multiphase Flow. Cambridge Uni-versity Press, pp. 237-281.
302. Prosperetti, A. and Oguz, H.N. (1993). The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech., 25: 577-602.
303. Prosperetti, A. and Tryggvason, G. (2007). Computational Methods for Multiphase Flow. Cambridge University Press.
304. Puckett, E.G. (1991). A volume-of-fluid interface tracking algorithm with applica-tions to computing shock wave refraction. In Proceedings of the 4th Int. Symp. on Computational Fluid Dynamics, Davis, CA (ed. H. Dwyer) pp. 933-938.
305. Puckett, E.G., Almgren, A.S., Bell, J.B., Marcus, D.L., and Rider, W.J. (1997). A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys., 130: 269-282.
306. Pumphrey, H.C. and Elmore, P.A. (1990). The entrainment of bubbles by drop impacts. J. Fluid Mech., 220: 539-567.
307. Purvis, R. and Smith, F.T. (2005). Droplet impact on water layers: post-impact analysis and computations. Phil. Trans. R. Soc. A, 363: 1209-1221.
308. Quirk, J.J. (1994). An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies. Comput. Fluids, 23: 125-142.
309. Radl, S., Koynov, A., Tryggvason, G., and Khinast, J.G. (2008). DNS-based prediction of the selectivity of fast multiphase reactions: hydrogenation of ni-troarenes. Chem. Eng. Sci., 63: 3279-3291.
310. Rallison, J.M. and Acrivos, A. (1978). A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech., 89: 191-200.
311. Ranade, V. (2001). Computational Flow Modeling for Chemical Reactor Engi-neering. Academic Press.
312. Rayleigh, J.W. Strutt, Baron. (1879). On the capillary phenomena of jets. Proc. R. Soc. London, 29: 71-97.
313. Rayleigh, J.W. Strutt, Baron. (1900). Scientific Papers. Cambridge University Press.
314. Raynal, L. (1997). PhD thesis, Universite Joseph Fourier, Grenoble.
315. Rein, M. (1993). Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res., 12(2): 61-93.
316. Renardy, Y. and Renardy, M. (2002). PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys., 183: 400-421.
317. Rhie, C.M. and Chow, W.L. (1983). Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J., 21(11): 1525-1532.
318. Richtmyer, R.D. and Morton, K.W. (1967). Difference Methods for Initial Value Problems. Interscience, New York.
319. Richtmyer, R.D. (1960). Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math., 13: 297-319.
320. Rider, W.J. and Kothe, D.B. (1998). Reconstructing volume tracking. J. Comput. Phys., 141: 112-152.
321. Rieber, M. and Frohn, A. (1999). A numerical study on the mechanism of splash-ing. Int. J. Heat Fluid Flow, 20(5): 455-461.
322. Rioboo, R., Bauthier, C., Conti, J., Voue, M., and De Coninck, J. (2003). Exper-imental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp. Fluids, 35(6): 648-652.
323. Robinson, P.B., Blake, J.R., Kodama, T., Shima, A., and Tomita, Y. (2001). Interac-tion of cavitation bubbles with a free surface. J. Appl. Phys., 89(12): 8225-8237.
324. Roisman, I.V., Rioboo, R., and Tropea, C. (2002). Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc. R. Soc. Lond. Ser. A, 458(2022): 1411-1430.
325. Roisman, I.V., Horvat, K., and Tropea, C. (2006). Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys. Fluids, 18(10): 102104-102104.
326. Rothman, D.H. and Zaleski, S. (1997). Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics. Cambridge University Press.
327. Rudman, M. (1997). Volume-tracking methods for interfacial flow calculations. Int. J. Numer. Methods Fluids, 24: 671-691.
328. Rybczynski, W. (1911). u ber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium. Bull. Acad. Sci. Crac., A: 40-46.
329. Ryskin, G. and Leal, L.G. (1984). Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech., 148: 19-35.
330. Saiki, E.M. and Biringen, S. (1996). Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method. J. Comput. Phys., 123: 450-465.
331. Sainsbury, G.L. and Cheeseman, I.C. (1950). Effect of rain in calming the sea. Nature, 166(4210): 79.
332. Sangani, A.S. and Didwania, A.K. (1993). Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech., 250: 307-337.
333. Sankaranarayanan, K., Shan, X., Kevrekidis, I.G., and Sundaresan, S. (2002). Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J. Fluid Mech., 452: 61-96.
334. Sankaranarayanan, K., Kevrekidis, I.G., Sundaresan, S., Lu, J., and Tryggvason, G. (2003). A comparative study of lattice Boltzmann and front-tracking finite-difference methods for bubble simulations. Int. J. Multiphase Flow, 29: 109- 116.
335. Saville, D.A. (1997). Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech., 29: 27-64.
336. Scardovelli, R. and Zaleski, S. (2000). Analytical relations connection linear inter-faces and volume fractions in rectangular grids. J. Comput. Phys., 164: 228-237.
337. Scardovelli, R. and Zaleski, S. (2003). Interface reconstruction with least-square fit and split Lagrangian-Eulerian advection. Int J. Numer. Methods Fluids, 41: 251-274.
338. Schlick, T. (2002). Molecular Modeling and Simulation. Springer.
339. Schmidt, A. (1996). Computations of three dimensional dendrites with finite ele-ments. J. Comput. Phys., 126: 293-312.
340. Schultz, W.W., Huh, J., and Griffin, O.M. (1994). Potential-energy in steep and breaking waves. J. Fluid Mech, 278: 201-228.
341. Scriven, L.E. (1960). The Marangoni effects. Chem. Eng. Sci., 12: 98-108.
342. Serizawa, A., Kataoka, I., and Michiyoshi, I. (1975a). Turbulence structure of air-water bubbly flow - II. Local properties. Int. J. Multiphase Flow, 2: 235-246.
343. Serizawa, A., Kataoka, I., and Michiyoshi, I. (1975b). Turbulence structure of air-water bubbly flow - III. Transport properties. Int. J. Multiphase Flow, 2: 247-259.
344. Sethian, J.A. (2001). Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J. Comput. Phys., 169: 503-555.
345. Sethian, J.A. and Strain, J. (1992). Crystal growth and dendritic solidification. J. Comput. Phys., 98: 231-253.
346. Shan, X.W. and Chen, H.D. (1993). Lattice Boltzmann model for simulationg flows with multiple phases and components. Phys. Rev. E, 47: 1815-1819.
347. Shikmurzaev, Y.D. (1997). Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech., 334: 211-249.
348. Shin, S. and Juric, D. (2002). Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys, 180: 427-470.
349. Shin, S., Abdel-Khalik, S.I., Daru, V., and Juric, D. (2005a). Accurate representa-tion of surface tension using the level contour reconstruction method. J. Comput. Phys., 203: 493-516.
350. Shin, S., Abdel-Khalik, S.I., and Juric, D. (2005b). Direct three-dimensional nu-merical simulation of nucleate boiling using the level contour reconstruction method. Int. J. Multiphase Flow, 31: 1231-1242.
351. Shin, S.W. and Juric, D. (2000). Computation of microstructure in solidification with fluid convection. J. Mech. Behav. Mater., 11: 313.
352. Shopov, P.J., Minev, P.D., Bazhekov, I.B., and Zapryanov, Z.D. (1990). Interaction of a deformable bubble with a rigid wall at moderate Reynolds numbers. J. Fluid Mech., 219: 241-271.
353. Shu, C.W. and Osher, S. (1989). Efficient implementation of essentially non-oscillatory shock capturing schemes, II. J. Comput. Phys., 83: 32-78.
354. Shyy, W. and Rao, M.M. (1994). Enthalpy based formulations for phase-change problems with application to g-jitter. Microgravity Sci. Technol., 7: 41-49.
355. Shyy, W., Udaykumar, H.S., Rao, M., and Smith, R. (1996). Computational Fluid Dynamics with Moving Boundaries. Taylor and Francis.
356. Smereka, P. (1993). On the motion of bubbles in a periodic box. J. Fluid Mech., 254: 79-112.
357. So, S., Morikita, H., Takagi, S., and Matsumoto, Y. (2002). Laser doppler ve-locimetry measurement of turbulent bubbly channel flow. Exp. Fluids, 33: 135- 142.
358. Son, G. and Dhir, V.K. (1997). Numerical simulation of saturated film boiling on a horizontal surface. J. Heat Transfer, 119: 525-533.
359. Son, G. and Dhir, V.K. (1998). Numerical simulation of film boiling near critical pressures with a level set method. J. Heat Transfer, 120: 183-192.
360. Son, G., Dhir, V.K., and Ramanujapu, N. (1999). Dynamics and heat transfer associated with a single bubble during nucleate boiling on a horizontal surface. J. Heat Transfer, 121: 623-631.
361. Son, G., Ramanujapu, N., and Dhir, V.K. (2002). Numerical simulation of bubble merger process on a single nucleation site during pool nucleate boiling. ASME J. Heat Transfer, 124: 51-62.
362. Song, M. and Tryggvason, G. (1999). The formation of a thick border on an ini-tially stationary fluid sheet. Phys. Fluids, 11: 2487-2493.
363. Song, Q., Luo, R., Yang, X.Y., and Wang, Z. (2001). Phase distributions for upward laminar dilute bubbly flows with non-uniform bubble sizes in a vertical pipe. Int. J. Multiphase Flow, 27: 379-390.
364. Stow, C.D. and Hadfield, M.G. (1981). An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proc. R. Soc. Lond. Ser. A, 373(1755): 419-441.
365. Subramanian, R.S. and Balasubramaniam, R. (2001). The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.
366. 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., 187: 110-136.
367. Sussman, M. and Fatemi, E. (1999). An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput., 20(4): 1165-1191.
368. 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., 162: 301-337.
369. Sussman, M. and Smereka, P. (1997). Axisymmetric free boundary problems. J. Fluid Mech., 341: 269-294.
370. Sussman, M., Smereka, P., and Osher, S. (1994). A level set approach for com-puting solutions to incompressible two-phase flows. J. Comput. Phys., 114: 146-159.
371. Sussman, M., Fatemi, E., Smereka, P., and Osher, S. (1998). An improved level set method for incompressible two-phase flows. Comput. Fluids, 27: 663-680.
372. 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 flows. J. Comput. Phys., 148: 81-124.
373. Swaminathan, C.R. and Voller, V.R. (1993). On the enthalpy method. Int. J. Numer. Methods Heat Fluid Flow, 3: 233-244.
374. Swarztrauber, P.N. and Sweet, R.A. (1979). Algorithm 541: efficient Fortran sub-programs for the solution of separable elliptic partial differential equations [D3]. ACM Trans. Math. Software, 5(3): 352-364.
375. Sweby, P.K. (1984). High-resolution schemes using flux limiters for hyperbolic conservation-laws. SIAM J. Numer. Anal., 21: 995-1011.
376. Takada, N., Misawa, M., Tomiyama, A., and Hosokawai, S. (2001). Simulation of bubble motion under gravity by lattice Boltzmann method. J. Nucl. Sci. Technol., 38: 330-341.
377. Takagi, S., Matsumoto, Y., and Huang, H. (1997). Numerical analysis of a single rising bubble using boundary-fitted coordinate system. JSME Int. J., Ser. B, 40: 42-50.
378. Takahira, H., Horiuchi, T., and Banerjee, S. (2004). An improved three-dimensional level set method for gas-liquid two-phase flows. J. Fluids Eng., 126: 578.
379. Takewaki, H. and Yabe, T. (1987). The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations. J. Comput. Phys., 70: 355-372.
380. Takewaki, H., Nishiguchi, A., and Yabe, T. (1985). Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations. J. Comput. Phys., 61: 261-268.
381. Tan, L. and Zabaras, N. (2007). A level set simulation of dendritic solidification of multi-component alloys. J. Comput. Phys., 221: 9-40.
382. Tasoglu, S., Demirci, U., and Muradoglu, M. (2008). The effect of soluble sur-factant on the transient motion of a buoyancy-driven bubble. Phys. Fluids, 20: 040805.
383. Taylor, G.I. (1963). Generation of Ripples by Wind Blowing over a Viscous Liquid. Cambridge University Press, Cambridge, UK, pp. 244-254.
384. Taylor, G.I. (1966). Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. R. Soc. Lond. Ser. A, 291: 159-166.
385. Thompson, J.F., Soni, B.K., and Weatherill, N.P. (1998). Handbook of Grid Gen-eration. CRC Press.
386. Thomson, J.J. and Newall, H.F. (1885). On the formation of vortex rings by drops falling into liquids, and some allied phenomena. Proc. R. Soc. Lond., 39: 417- 436.
387. Thoroddsen, S.T. (2002). The ejecta sheet generated by the impact of a drop. J. Fluid Mech., 451: 373-381.
388. Tomar, G., Biswas, G., Sharma, A., and Agrawal, A. (2005). Numerical simulation of bubble growth in film boiling using a coupled level-set and volume-of-fluid method. Phys. Fluids, 17: 112103.
389. Tomar, G., Gerlach, D., Biswas, G., Alleborn, N., Sharma, A., Durst, F., S.W.J. Welch, and Delgado, A. (2007). Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. J. Comput. Phys., 227: 1267-1285.
390. Tomar, G., Biswas, G., Sharma, A., and Welch, S.W.J. (2008). Multi-mode analysis of bubble growth in saturated film boiling. Phys. Fluids, 20: 092101.
391. Tomar, G., Biswas, G., Sharma, A., and Welch, S.W.J. (2009). Influence of electric field on saturated film boiling. Phys. Fluids, 21: 032107.
392. Tomar, G., Fuster, D., Zaleski, S., and Popinet, S. (2010). Multiscale simulations of primary atomization using Gerris. Comput. Fluids, 39(10): 1864-1874.
393. Tomiyama, A., Zun, I., Sou, A., and Sakaguchi, T. (1993). Numerical analysis of bubble motion with the VOF method. Nucl. Eng. Des., 141: 69-82.
394. Tomiyama, A., Tamai, H., Zun, I., and Hosokawa, S. (2002). Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci., 57: 1849-1858.
395. Tonhardt, R. and Amberg, G. (1998). Phase-field simulations of dendritic growth in a shear flow. J. Cryst. Growth, 194: 406-425.
396. Torres, D.J and Trujillo, M.F. (2006). KIVA-4: an unstructured ALE code for compressible gas flow with sprays. J. Comput. Phys., 219(2): 943-975.
397. Tryggvason, G. and Aref, H. (1983). Numerical experiments on Hele-Shaw flow with a sharp interface. J. Fluid Mech., 136: 1-30.
398. Tryggvason, G. and Aref, H. (1985). Finger interaction mechanisms in stratified Hele-Shaw flow. J. Fluid Mech., 154: 284-301.
399. Tsimplis, M. and Thorpe, S.A. (1989). Wave damping by rain. Nature, 342(6252): 893-895.
400. Udaykumar, H.S., Kan, H.C., Shyy, W., and Tran-Son-Tay, R. (1997). Multiphase dynamics in arbitrary geometries on fixed Cartesian grids. J. Comput. Phys., 137: 366-405.
401. Udaykumar, H.S., Mittal, R., and Shyy, W. (1999). Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids. J. Comput. Phys., 153: 535-574.
402. Udaykumar, H.S., Mittal, R., Rampunggoon, P., and Khanna, A. (2001). A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys., 174: 345-380.
403. Ungar, L.H. and Brown, R.A. (1985). Cellular interface morphologies in direc-tional solidification. IV. The formation of deep cells. Phys. Rev. B, 31: 5931- 5940.
404. Unverdi, S.O. and Tryggvason, G. (1992). A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys., 100: 25-37.
405. van der Vorst, H.A. (1992). Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 13: 631.
406. van der Vorst, H.A. (2003). Iterative Krylov Methods for Large Linear Systems. Cambridge University Press.
407. van Leer, B. (1979). Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys., 32: 101-136.
408. van Sint Annaland, M., Dijkhuizen, W., Deen, N.G., and Kuipers, J.A.M. (2006). Numerical simulation of gas bubbles behaviour using a 3D front tracking method. AIChE J., 52: 99-110.
409. Verschueren, M., van de Vosse, F.N., and Meijer, H.E.H. (2001). Diffuse-interface modelling of thermo-capillary flow instabilities in a Hele-Shaw cell. J. Fluid Mech., 434: 153-166.
410. Viecelli, J.A. (1969). A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique. J. Comput. Phys., 4: 543-551.
411. Villermaux, E. (1998). On the role of viscosity in shear instabilities. Phys. Fluids, 10(2): 368-373.
412. Villermaux, E. and Clanet, C. (2002). Life of a flapping liquid sheet. J. Fluid Mech., 462: 341-363.
413. Villermaux, E., Marmottant, Ph., and Duplat, J. (2004). Ligament-mediated spray formation. Phys. Rev. Lett., 92(7): 074501.
414. Vinje, T. and Brevig, P. (1981). Numerical simulations of breaking waves. Adv. Water Resources, 4: 77-82.
415. Wang, S.K., Lee, S.J., Jones, O.C., Jr. and Lahey, R.T. Jr. (1987). 3-D turbulence structure and phase distribution in bubbly two-phase flows. Int. J. Multiphase Flow, 13: 327-343.
416. Wang, Y., Lu, X., Zhuang, L., Tang, Z., and Hu, W. (2004). Numerical simulation of drop Marangoni migration under microgravity. Acta Astronaut., 54: 325-335.
417. Wanga, J., Lua, P., Wanga, Z., Chao, C., and Maoa, Z.-S. (2008). Numerical sim-ulation of unsteady mass transfer by the level set method. Chem. Eng. Sci., 63: 3141-3151.
418. Weatherburn, C.E. (1927). Differential Geometry of Three Dimensions, Vol. I. Cambridge University Press, Cambridge.
419. Welch, S.W.J. (1995). Local simulation of two-phase flows including interface tracking with mass transfer. J. Comput. Phys., 121: 142-154.
420. Welch, S.W.J. and Biswas, G. (2007). Direct simulation of film boiling including electrohydrodynamic forces. Phys. Fluids, 19: 012106.
421. Welch, S.W.J. and Wilson, J. (2000). A volume of fluid based method for fluid flows with phase change. J. Comput. Phys., 160: 662-682.
422. Werder, T., Walther, J.H., and Koumoutsakos, P. (2005). Hybrid atomistic-continuum method for the simulation of dense fluid flow. J. Comput. Phys., 205: 373-390.
423. Wesseling, P. (1992). An Introduction to Multigrid Methods. Wiley, New York.
424. Wesseling, P. (2001). Principles of Computational Fluid Dynamics. Springer-Verlag Berlin.
425. Wheeler, A.A., Murray, B.T., and Schaefer, R.J. (1993). Computations of dendrites using a phase-field model. Phys. D, 66: 243-262.
426. Wheeler, A.A., Ahmad, N.A., Boettinger, W.J., Braun, R.J., McFadden, G.B., and Murray, B.T. (1995). Recent development in phase-field models of solidification. Adv. Space Res., 16: 163-172.
427. Worthington, A.M. (1908). A Study of Splashes. Longmans, Green and Co., London.
428. Xue, M., Xu, H.B., Liu, Y.M., and Yue, D.K.P. (2001). Computations of fully nonlinear three-dimensional wave-wave and wave-body interactions. Part 1. Dynamics of steep three-dimensional waves. J. Fluid Mech., 438: 11-39.
429. Yabe, T., Xiao, F., and Utsumi, T. (2001). The constrained interpolation profile (CIP) method for multi-phase analysis. J. Comput. Phys., 169: 556-593.
430. Yanenko, N.N. (1971). The Method of Fractional Steps for Solving Multidimen-sional Problems of Mathematical Physics in Several Variables. Springer-Verlag, Berlin.
431. Yang, C. and Maoa, Z.-S. (2005). Numerical simulation of interphase mass transfer with the level set approach. Chem. Eng. Sci., 60: 2643-2660.
432. Yang, X., Feng, J.J., Liu, C., and Shen, J. (2006a). Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. J. Comput. Phys., 218(1): 417-428.
433. Yang, X., James, A.J., Lowengrub, J., Zheng, X., and Cristini, V. (2006b). An adaptive coupled level-set/volume-of-fluid interface capturing method for un-structured triangular grids. J. Comput. Phys., 217: 364-394.
434. Yang, Y. and Udaykumar, H.S. (2005). Sharp interface Cartesian grid method III: solidification of pure materials and binary solutions. J. Comput. Phys., 210: 55-74.
435. Yarin, A.L. (2006). Drop impact dynamics: splashing, spreading, receding, bounc-ing. Annu. Rev. Fluid Mech., 38: 159-192.
436. Yarin, A.L. and Weiss, D.A. (1995). Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J. Fluid Mech., 283: 141-173.
437. Yecko, P. and Zaleski, S. (2005). Transient growth in two-phase mixing layers. J. Fluid Mech., 528: 43-52.
438. Yecko, P., Zaleski, S., and Fullana, J.-M. (2002). Viscous modes in two-phase mixing layers. Phys.Fluids, 14: 4115-4122.
439. Youngren, G.K. and Acrivos, A. (1976). On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech., 76: 433.
440. Youngs, D.L. (1982). Time dependent multimaterial flow with large fluid distor-tion. In Numerical Methods for Fluid Dynamics (eds. K.M. Morton and M.J. Baines) Academic Press, New York, pp. 27-39.
441. Youngs, D.L. (1984). An interface tracking method for a 3D Eulerian hydrody-namics code. Technical report, AWRE. Technical Report 44/92/35.
442. Yu, D. and Tryggvason, G. (1990). The free surface signature of unsteady, two-dimensional vortex flows. J. Fluid Mech., 218: 547-572.
443. Yu, P.-W., Ceccio, S.L., and Tryggvason, G. (1995). The collapse of a cavitation bubble in shear flows - a numerical study. Phys. Fluids, 7: 2608-2616.
444. Zaleski, S., Zanetti, G., Scardovelli, R., et al. (1992-2008). SURFER code. The code is covered by the GNU Public Licence and may be downloaded from http://www.lmm.jussieu.fr/?zaleski.
445. Zeff, B.W., Kleber, B., Fineberg, J., and Lathrop, D.P. (2000). Singularity dynamics in curvature collapse and jet eruption on a fluid surface. Nature, 403: 401-404.
446. Zenit, R., Koch, D.L., and Sangani, A.S. (2001). Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J. Fluid Mech., 429: 307-342.
447. Zhang, D.Z. and Prosperetti, A. (1994). Ensemble phase-averaged equations for bubbly flows. Phys. Fluids, 6: 2956-2970.
448. Zhang, J., Eckmann, D.M., and Ayyaswamy, P.S. (2006). A front tracking method for a deformable intravascular bubble in a tube with soluble surfactant transport. J. Comput. Phys., 214: 366-396.
449. Zhou, H. and Pozrikidis, C. (1993). The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech., 255: 103-127.
450. Zinchenko, A.Z. and Davis, R.H. (2000). An efficient algorithm for hydrodynami-cal interaction of many deformable drops. J. Comput. Phys, 157: 539-587.