×

zbMATH — the first resource for mathematics

An improved level set method for incompressible two-phase flows. (English) Zbl 0967.76078
Summary: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of a two-phase flow where the interface can merge/break and the flow can have a high Reynolds number. A distance function formulation of the level set method enables us to compute flows with large density ratios (1000:1) and flows that are surface tenson driven, with no emotional involvement. Recent work has improved the accuracy of the distance function formulation and the accuracy of the advection scheme. We compute flows involving air bubbles and water drops, among others. We validate our code against experiments and theory.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T10 Liquid-gas two-phase flows, bubbly flows
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Sussman, M.; Smereka, P.; Osher, S.J., A level set approach for computing solutions to incompressible two-phase flow, J. comp. phys., 114, 146-159, (1994) · Zbl 0808.76077
[2] Shu, C.W.; Osher, S., Efficient implementation of essentially non-oscillatory shock capturing schemes, II, J. comp. phys., 83, 32-78, (1989) · Zbl 0674.65061
[3] Boulton-Stone, J.M.; Blake, J.R., Gas bubbles bursting at a free surface, J. fluid mech., 254, 437-466, (1993) · Zbl 0780.76011
[4] Unverdi, S.O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multifluid flows, J. comp. phys., 100, 25-37, (1992) · Zbl 0758.76047
[5] Osher, S.; Sethian, J.A., Fronts propagating with curvature-dependent speed: algorithms based on hamilton – jacobi formulations, J. comp. phys., 79, 1, 12-49, (1988) · Zbl 0659.65132
[6] Brackbill, J.U.; Kothe, D.B.; Zemach, C., A continuum method for modeling surface tension, J. comp. phys., 100, 335-353, (1992) · Zbl 0775.76110
[7] Chang, Y.C.; Hou, T.Y.; Merriman, B.; Osher, S., Eulerian capturing methods based on a level set formulation for incompressible fluid interfaces, J. comput. phys., 124, 449-464, (1996) · Zbl 0847.76048
[8] Bell, J.B.; Marcus, D.L., A second-order projection method for variable-density flows, J. comp. phys., 101, 334-348, (1992) · Zbl 0759.76045
[9] M. Sussman and E. Fatemi. An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible flow. SIAM Journal on Scientific Computing. (in press) · Zbl 0958.76070
[10] Harten, A., J. comp. phys., 83, 148-184, (1989)
[11] Rouy, E.; Tourin, A., A viscosity solutions approach to shape-from-shading, SIAM J. numer. anal., 29, 3, 867-884, (1992) · Zbl 0754.65069
[12] Zalesak, S.T., J. comp. phys., 31, 335-362, (1979)
[13] M. Sussman, UCLA, Ph.D. thesis, June 1994
[14] Sussman, M.; Smereka, P., Axisymmetric free boundary problems, J. fluid mechanics, 341, 269-294, (1997) · Zbl 0892.76090
[15] Lundgren, T.S.; Mansour, N.N., Vortex ring bubbles, J. fluid mech., 224, 177, (1991) · Zbl 0717.76119
[16] Hnat, J.G.; Buckmaster, J.D., Spherical cap bubbles and skirt formation, Phys. fluids, 19, 182-194, (1976) · Zbl 0319.76072
[17] Lundgren, T.S.; Mansour, N.N., Oscillations of drops in zero gravity with weak viscous effects, J. fluid mech., 194, 479-510, (1988) · Zbl 0645.76110
[18] Lamb, H., Hydrodynamics, Dover Publications, 1945
[19] Ryskin, G.; Leal, L.G., 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, (1984) · Zbl 0548.76032
[20] Chambers, D., Marcus, D. and Sussman, M., Relaxation spectra of surface waves. In Proceedings of the 1995 International Mechanical Engineering Congress and Exposition, November, 1995
[21] Rienecker, M.M.; Fenton, J.D., A Fourier approximation method for steady water waves, J. fluid mech., 104, 119-137, (1981) · Zbl 0494.76019
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.