×

zbMATH — the first resource for mathematics

A front-tracking method for viscous, incompressible multi-fluid flows. (English) Zbl 0758.76047
Summary: A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. In addition to keeping the density and viscosity stratification sharp, the tracked interface provides a natural way to include surface tension effects. Both two- and three-dimensional, full numerical simulations of bubble motion are presented.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Acrivos, A., The deformation and break-up of single drops in shear fields, (), 1
[2] Anderson, C.R., J. comput. phys., 61, 417, (1985)
[3] Amsden, A.A.; Harlow, F.H., J. comput. phys., 6, 322, (1970)
[4] Baker, G.R.; Moore, D.W., Phys. fluids A, 1, 1451, (1989) · Zbl 0697.76117
[5] Bhaga, D.; Weber, M.E., J. fluid mech., 105, 61, (1981)
[6] Brecht, S.H.; Ferrante, J.R., Phys. fluids A, 1, 1166, (1989)
[7] Boris, J.P., Annu. rev. fluid mech., 21, 345, (1989)
[8] Chern, I.-L.; Glimm, J.; McBryan, O.; Plohr, B.; Yaniv, S., J. comput. phys., 62, 83, (1986)
[9] Chi, B.K.; Leal, L.G., J. fluid mech., 201, 123, (1989) · Zbl 0667.76147
[10] Chorin, A.J., J. comput. phys., 35, 1, (1980)
[11] Christiansen, J.P., J. comput. phys., 13, 363, (1973)
[12] Churchill, S.W., Viscous flows. the practical use of theory, (1988), Butterworths London
[13] Clift, R.; Grace, J.R.; Weber, M.E., Bubbles, drops, and particles, (1978), Academic Press New York/London
[14] Dandy, D.S.; Leal, L.G., J. fluid mech., 208, 161, (1989)
[15] Daly, B.J., Phys. fluids, 10, 297, (1967)
[16] Daly, B.J., J. comput. phys., 4, 97, (1969)
[17] Daripa, P.; Glimm, J.; Lindquist, B.; Maesumi, M.; McBryan, O., On the simulation of heterogeneous petroleum reservoirs, ()
[18] Floryan, J.M.; Rasmussen, H., Appl. mech. rev., 42, 323, (1989)
[19] Fauci, L.J.; Peskin, C.S., J. comput. phys., 77, 80, (1988)
[20] Fogelson, A.L.; Peskin, C.S., J. comput. phys., 79, 50, (1988)
[21] Fritts, M.J.; Boris, J.P., J. comput. phys., 31, 173, (1979)
[22] Fyfe, D.E.; Oran, E.S.; Fritts, M.J., J. comput. phys., 76, 349, (1988)
[23] Glimm, J.; McBryan, O.; Menikoff, R.; Sharp, D.H., SIAM J. sci. slat. comput., 7, 230, (1987)
[24] Glimm, J.; Grove, J.; Lindquist, B.; McBryan, O.; Tryggvason, G., SIAM J. sci. slat. comput., 9, 61, (1988)
[25] Harlow, F.H.; Welch, J.E., Phys. fluids, 8, 2182, (1965)
[26] Hirt, C.W.; Nichols, B.D., J. comput. phys., 39, 201, (1981)
[27] Hyman, J.M., Physica D, 12, 396, (1984)
[28] Koh, C.J.; Leal, L.G., Phys. fluids A, 1, 1309, (1989)
[29] Martinez, M.J.; Udell, K.S., J. fluid mech., 210, 565, (1990)
[30] Meng, J.C.S.; Thomson, J.A.L., J. fluid mech., 84, 433, (1978)
[31] Moretti, G., Annu. rev. fluid mech., 19, 313, (1987)
[32] de Nevers, N.; Wu, J.-L., Aiche j., 17, 182, (1971)
[33] Noh, W.F.; Woodward, P., (), 330
[34] Oran, E.S.; Boris, J.P., Numerical simulations of reactive flow, (1987), Elsevier Amsterdam/New York · Zbl 0466.76098
[35] Peskin, C.S., J. comput. phys., 25, 220, (1977)
[36] Pozrikidis, C., J. fluid mech., 210, 1, (1990)
[37] Rallison, J.M., J. fluid mech., 109, 465, (1981)
[38] Rallison, J.M., Annu. rev. fluid mech., 16, 45, (1984)
[39] Richtmyer, R.D.; Morton, K.W., Difference methods for initialvalue problems, (1967), Interscience New York · Zbl 0155.47502
[40] Ryskin, G.; Leal, L.G., J. fluid mech., 148, 1, (1984) · Zbl 0548.76031
[41] Ryskin, G.; Leal, L.G., J. fluid mech., 148, 19, (1984) · Zbl 0548.76032
[42] Ryskin, G.; Leal, L.G., J. fluid mech., 148, 37, (1984) · Zbl 0548.76033
[43] Stone, H.A.; Bentley, B.J.; Leal, L.G., J. fluid mech., 173, 131, (1986)
[44] Stone, H.A.; Leal, L.G., J. fluid mech., 198, 399, (1989)
[45] Stone, H.A.; Leal, L.G., J. fluid mech., 220, 161, (1990)
[46] Todd, P.H.; McLeod, R.J.Y., Comput. aided design, 18, 33, (1986)
[47] Tryggvason, G., J. comput. phys., 75, 253, (1988)
[48] Tryggvason, G.; Unverdi, S.O., Phys. fluids A, 2, No. 5, 656, (1990)
[49] Wesseling, P., A robust and efficient multigrid method, (), 614, Proceedings, Koln-Porz, 1981
[50] Youngren, G.K.; Acrivos, A., J. fluid mech., 76, 433, (1976)
[51] Yiantsios, S.G.; Higgins, B.G., Phys. fluids A, 1, 1484, (1989)
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.