A continuum method for modeling surface tension. (English) Zbl 0775.76110

Summary: A new method for modeling surface tension effects on fluid motion has been developed. Interfaces between fluids of different properties, or “colors”, are represented as transition regions of finite thickness, across which the color variable varies continuously. At each point in the transition region, a force density is defined which is proportional to the curvature of the surface of constant color at that point. It is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero. The continuum method eliminates the need for interface reconstruction, simplifies the calculation of surface tension, enables accurate modeling of two- and three-dimensional fluid flows driven by surface forces, and does not impose any modeling restrictions on the number, complexity, or dynamic evolution of fluid interfaces having surface tension. Computational results for two-dimensional flows are given to illustrate the properties of the method.


76M20 Finite difference methods applied to problems in fluid mechanics
76D45 Capillarity (surface tension) for incompressible viscous fluids
76B45 Capillarity (surface tension) for incompressible inviscid fluids


Full Text: DOI


[1] Nelleon, M., Mechanics and Properties of Matter (1952), Heineman: Heineman London, Chap. VI
[2] Levich, V. G., Physicochemical Hydrodynamics (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[3] Lamb, H., Hydrodynamics (1932), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · JFM 26.0868.02
[4] Ostrach, S., Annu. Rev. Fluid. Mech., 14, 313 (1982)
[5] Myshkis, A. D.; Babskii, V. G.; Kopachevskii, N. D.; Slobozhanin, L. A.; Tyuptsov, A. D., Low-Gravity Fluid Mechanics (1987), Springer-Verlag: Springer-Verlag New York
[6] Drazin, P. G.; Reid, W. H., Hydrodynamic Stability (1981), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · Zbl 0449.76027
[7] Oguz, H. N.; Sadhal, S. S., J. Fluid. Mech., 194, 563 (1988)
[8] Gaver, D. P.; Grotberg, J. B., J. Fluid. Mech., 213, 127 (1990)
[9] Batchelor, G. K., An Introduction to Fluid Dynamics (1967), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · Zbl 0152.44402
[10] Pruppacher, H. R.; Klett, J. D., Microphysics of Clouds and Precipitation (1978), Reidel: Reidel Dordrecht
[11] Oran, E. S.; Boris, J. P., Numerical Simulation of Reactive Flow (1987), Elsevier: Elsevier New York · Zbl 0762.76098
[12] Landau, L. D.; Lifshitz, E. M., Fluid Mechanics (1959), Pergamon: Pergamon New York · Zbl 0146.22405
[13] Levich, V. G.; Krylov, V. S., Annu. Rev. Fluid Mech., 1, 293 (1969)
[14] Kenning, D. B.R., Appl. Mech. Rev., 21, 1101 (1968)
[15] Yih, C.-S., Phys. Fluids, 11, 477 (1968)
[16] Yih, C.-S., Phys. Fluids, 12, 1982 (1969)
[17] Adler, J.; Sowerby, L., J. Fluid Mech., 42, 549 (1970)
[18] Greenspan, H. P., Stud. Appl. Math., 57, 45 (1977)
[19] de Boor, C., A Practical Guide to Splines (1967), Springer-Verlag: Springer-Verlag New York
[20] Mansour, N. G.; Lundgren, T. S., Phys. Fluids A, 2, 1141 (1990)
[21] Harlow, F. H.; Welch, J. E., Phys. Fluids, 8, 2182 (1965)
[22] Hirt, C. W.; Amsden, A. A.; Cook, J. L., J. Comput. Phys., 14, 227 (1974)
[23] Kafka, F. Y.; Dussan, E. B., J. Fluid Mech., 95, 539 (1979)
[24] Elmore, W. C.; Heald, M. A., Physics of Waves (1969), McGraw-Hill: McGraw-Hill New York
[25] Nichols, B. D.; Hirt, C. W.; Hotchkiss, R. S., SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries, (LA-8355 (1980), Los Alamos National Laboratory), (unpublished)
[26] Hirt, C. W.; Nichols, B. D., J. Comput. Phys., 39, 201 (1981)
[27] Kothe, D. B.; Mjolsness, R. C.; Torrey, M. D., RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces, (LA-12007-MS (1991), Los Alamos National Laboratory), (unpublished) · Zbl 0762.76074
[28] Torrey, M. D.; Mjolsness, R. C.; Stein, L. R., NASA-VOF3D: A Three-Dimensional Computer Program for Incompressible Flows with Free Surfaces, (LA-11009-MS (1987), Los Alamos National Laboratory), (unpublished)
[29] Daly, B. J., Phys. Fluids, 12, 1340 (1969)
[30] Hotchkiss, R. S., Simulation of Tank Draining Phenomena with the NASA SOLA-VOF Code, (LA-8163-MS (1979), Los Alamos National Laboratory), (unpublished)
[31] Brackbill, J. U., Methods Comput. Phys., 16, 1 (1976)
[34] Brackbill, J. U.; Ruppel, H. M., J. Comput. Phys., 65, 314 (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.