Abstract
A survey of fixed-grid methods for the calculation of free-surface flows is presented. These methods are based on a single-fluid formulation that is described first. Then concise overviews of the volume-of-fluid, level-set, and front-tracking algorithms are given.
Supported by NASA
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, D.M., McFadden, G.B. & Wheeler, A.A., 1998, Diffuse-interface methods in fluid mechanics, Annu. Rev. Fluid Mech. 30, 139–165.
Athanasopoulos, I., Makrakis, G. & Rodrigues, J.F. editors, 1999, Free Boundary Problems: Theory and Applications, CRC Press.
Bell, J.B., Colella, P. & Glaz, H.M., 1989, A second-order projection method for the incompressible Navier-Stokes equations, J. Comp. Phys., 85, 257–283.
Brackbill, J.U., Kothe, D.B., & Zemach, C., 1992, A continuum method for modeling surface tension, J. Comp. Phys., 100, 335–354.
Bussmann, M., Mostaghimi, J., & Chandra, S., 1999, On a three-dimensional volume tracking model of droplet impact, Phys. Fluids, 11, 1406–1417.
Chang, Y.C., Hou, T.Y., Merriman, B., & Osher, S., 1996, A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comp. Phys., 124, 449–164.
Chen, S. & Doolen, G.D., 1998, Lattice Boltzmann methods for fluid flows, Annu. Rev. Fluid Mech. 30, 329–364.
Chorin, A.J., 1985, Curvature and solidification, J. Comp. Phys., 57, 472.
Duraiswami, R. & Prosperetti, A., 1992, Orthogonal mapping in two dimensions, J. Comput. Phys. 98, 254–268.
Esmaeeli, A. & Tryggvason, G., 1998, Direct numerical simulation of bubbly flows. Part I. Low Reynolds number arrays, J. Fluid Mech., 377, 313–345.
Esmaeeli, A. & Tryggvason, G., 1999, Direct numerical simulation of bubbly flows. Part II. Moderate Reynolds number arrays, J. Fluid Mech., 385, 325–358.
Glimm, J., Marchesin, D. & McBryan, O., 1981, A numerical method for two-phase flow with an unstable interface, J. Comp. Phys. 39, 179–200.
Glimm, J., Grove, J.W., Li, X.L., Young, R., Zhang, Q. & Zeng, Y., 1998, Three-dimensional front tracking, J. Sci. Comp. 19, 703–727.
He, X.Y., Chen, S. & Zhang, R.Y., 1999, A lattice Boltzmann scheme for incompressible multiphase flow and its application to the simulation of Rayleigh-Taylor instability, J. Comp. Phys. 152, 642–663.
Hirt, C.W. & Nichols, B.D., 1981, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comp. Phys., 39, 201–225.
Jacqmin, D., 1999, Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comp. Phys. 155, 96–127.
Jacqmin, D., 2000, Contact-line dynamics of a diffuse fluid interface, J. Fluid Mech. 402, 57–88.
Juric, D. & Tryggvason, G., 1996, A front tracking method for dendritic solidification, J. Comput. Phys., 123, 127–148.
Juric, D. & Tryggvason, G., 1998, Computation of boiling flows, Int J. Multiphase Flow, 24, 387–410.
Kang, I.S. & Leal, L.G., 1987, Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. I. Finite-difference scheme and its application to the deformation of a bubble in a uniaxial straining flow, Phys. Fluids 30, 1929–1940.
Kemmer, N., 1977, Vector Analysis: A Physicist’s Guide to the Mathematics of Fields in Three Dimensions, Cambridge U.R., Cambridge, U.K.
Kothe, D.B. & Mjolsness, R.C., 1992, RIPPLE: A new method for incompressible flows with free surfaces, AIAA J., 30, 2694–2700.
Landau, L. & Lifshitz, E.M., 1959, Statistical Physics, Pergamon Press.
Liao, G., Liu, F., de la Pena, G.C., Peng, D. & Osher, S. 2000, Level-set-based deformation methods for adaptive grids, J. Comp. Phys. 159, 103–122.
Lowengrub, J.S. & Truskinovsky, L., 1998, Cahn-Hilliard fluids and topological transitions, Proc. R. Soc. Lond. A454, 2617–2654.
Nobari, M.R.H., Jan, Y.J., & Tryggvason, G., 1996, Head-on collision of drops — A numerical investigation, Phys. Fluids, 8, 29–42.
Nobari, M.R.H. & Tryggvason, G., 1996, Numerical simulations of three-dimensional drop collisions, AIAA J., 34, 750–755.
Poo, J.Y. & Ashgriz, N., 1989, A computational method for determining curvatures, J. Comp. Phys., 84, 483.
Popinet, S. & Zaleski, S., 1999, A front-tracking algorithm for accurate representation of surface tension, Int. J. Numer. Meth. Fluids 30, 775–793.
Puckett, E.G., Almgren, A.S., Bell, J.B., Marcus, D.L., & Rider, W.J., 1997, A high-order projection method for tracking fluid interfaces in variable density incompressible flows, J. Comp. Phys., 130, 269–282.
Rider, W.J. & Kothe, D.B., 1998, Reconstructing volume tracking, J. Comp. Phys., 141, 112–152.
Rudman, M., 1997, Volume-tracking methods for interfacial flow calculations, Int. J. Numer. Methods Fluids, 24, 671–691.
Ryskin, G. & Leal, L.G., 1984, Numerical solution of free-boundary problems in fluid mechanics. Part I. The finite-difference technique, J. Fluid Mech. 148, 1–17.
Scardovelli, R. & Zaleski, S., 1999, Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Dyn., 31, 567–603.
Sethian, J.A., 1996, Level Set Methods, Cambridge U.P., Cambridge, UK.
Son, G. & Dhir, V.K., 1998, Numerical simulation of film boiling near critical pressures with a level set method, J. Heat Transfer, 120, 183–192.
Sussman, M. & Fatemi, E., 1999, An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20, 1165–1191.
Sussman, M. & Smereka, P., 1997, Axisymmetric free boundary problems, J. Fluid Mech., 341, 269–294.
Sussman, M., Smereka, P., & Osher, S., 1994, A level set approach for computing solutions to incompressible two-phase flow, J. Comp. Phys., 114, 146–159.
Sussman, M., Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H. & Welcome, M.L., 1999, An adaptive level set approach for incompressible two-phase flows, J. Comp. Phys., 148, 81–124.
Takagi, S., Prosperetti, A. & Matsumoto, Y., 1994, Drag coefficient of a gas bubble in an axisymmetric shear flow, Phys. Fluids 6, 3186–3188.
Tezduyar, T., Aliabadi, S. & Behr, M., 1998, Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces, Comp. Meth. Appl. Mech. Eng. 155, 235–248.
Thompson, J.F., Warsi, Z.V.A. & Wayne, C.W., 1985 Numerical Grid Generation: Foundations and Applications, North-Holland.
Thompson, J.F., Soni, B. & Weatherill, N., 1998, Handbook of Grid Generation, CRC Press.
Tsai, W.T. & Yue, D.K.P., 1996, Computation of nonlinear free-surface flows, Annu. Rev. Fluid Mech. 28, 249–278.
Unverdi, S.O. & Tryggvason, G., 1992, A front-tracking method for viscous, incompressible multi-fluid flows, J. Comp. Phys., 100, 25–37.
Williams, M.W., Kothe, D.B., & Puckett, E.G., 1998, Accuracy and convergence of continuum surface tension models, available from http://math.math.ucdavis.edu /egp/.
Wren, G.P., Ray, S.E., Aliabadi, S.K. & Tezduyar, T.E., 1997, Simulation of flow problems with moving mechanical components, fluid-structure interactions and two-fluid interfaces, Int. J. Numer. Methods Fluids 24, 1433–1448.
Yabe, T., Hoshino, H. & Tsuchiya, T., 1991, Two- and three-dimensional behavior of Rayleigh-Taylor and Kelvin-Helmholtz instabilities, Phys. Rev. A44, 2756–2758.
Yabe, T., 1998, A numerical procedure CIP to solve all phases of matter together, in Six-teenth International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics Vol. 575, C.H. Bruneau editor, Springer, pp. 439–457.
Zaleski, S., Li, J., Succi, S., Scardovelli, R., & Zanetti, G., 1995, Direct numerical simulation of flows with interfaces, in Proceedings of the 2nd International Conference on Multiphase Flow, Serizawa, A., Fukano, T., & Bataille, J., eds., Kyoto, ICMF95, PT2–1 -PT2–12.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Wien
About this paper
Cite this paper
Prosperetti, A. (2002). Navier-Stokes Numerical Algorithms for Free-Surface Flow Computations: An Overview. In: Rein, M. (eds) Drop-Surface Interactions. CISM International Centre for Mechanical Sciences, vol 456. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2594-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2594-6_8
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83692-7
Online ISBN: 978-3-7091-2594-6
eBook Packages: Springer Book Archive