zbMATH — the first resource for mathematics

The point-set method: Front-tracking without connectivity. (English) Zbl 0998.76070
Summary: We describe a point-set method for extracting the normal, curvature, and surface area from unordered data points residing on a surface. This capability relaxes front-tracking’s reliance on connectivity between interfacial points, and allows front-tracking to model topological changes at an interface naturally. We use this capability in two- and three-dimensional front-tracking calculations to model coalescence. We also describe a simple projection scheme which allows us to suppress parasitic currents in front-tracking models.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Unverdi, S.O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multifluid flows, J. comput. phys., 100, 25, (1992) · Zbl 0758.76047
[2] Glimm, J.; Grove, J.W.; Li, X.L.; Shyue, K.M.; Zeng, Y.N.; Zhang, Q., 3-dimensional front tracking, SIAM J. sci. comput., 19, 703, (1998)
[3] Glimm, J.; McBryan, O.; Menikoff, R.; Sharp, D.H., Front tracking applied to rayleigh – taylor instability, SIAM J. sci. stat. comput., 7, 230, (1986) · Zbl 0582.76107
[4] Bielert, U.; Sichel, M., Numerical simulation of premixed combustion processes in closed tubes, Combust. flame, 114, 397, (1998)
[5] Bukiet, B., Application of front tracking to two-dimensional curved detonation fronts, SIAM J. sci. stat. comput., 9, 80, (1988) · Zbl 0637.65124
[6] Garaizar, F.X.; Trangenstein, J., Front tracking for shear bands in an antiplane shear model, J. comput. phys., 131, 54, (1997) · Zbl 0873.73077
[7] Tsai, H.L.; Rubinsky, B., A front tracking finite-element study on change of phase interface stability during solidification processes in solutions, J. cryst. growth, 70, 56, (1984)
[8] Unverdi, S.O.; Tryggvason, G., Computations of multifluid flows, Physica D, 60, 70, (1992) · Zbl 0779.76101
[9] Nobari, M.R.; Jan, Y.J.; Tryggvason, G., Head-on collisions of drops: A numerical investigation, Phys. fluids, 8, 29, (1996) · Zbl 1023.76588
[10] S. Nas and G. Tryggvason, Computational investigation of thermal migration of bubbles and drops, in Proceedings ASME Winter Annual Meeting, AMD 174/FED 175 Fluid Mechanics Phenomena in Microgravity, edited by D. A. Sigineret al., pp. 71-83. · Zbl 1136.76584
[11] Esmaeeli, A.; Ervin, E.A.; Tryggvason, G., Numerical simulations of rising bubbles and drops, J. fluid mech., 314, 315, (1996)
[12] Esmaeeli, A.; Tryggvason, G., Direct numerical simulations of bubbly flows. part 1. low Reynolds numbers, J. fluid mech., 377, 313, (1998) · Zbl 0934.76090
[13] Esmaeeli, A.; Tryggvason, G., Direct numerical simulations of bubbly flows. part 2. moderate Reynolds numbers, J. fluid mech., 385, 325, (1999) · Zbl 0945.76087
[14] Juric, D.; Tryggvason, G., A front-tracking method for dendritic solidification, J. comput. phys., 123, 127, (1996) · Zbl 0843.65093
[15] Juric, D.; Tryggvason, G., Computation of boiling flows, Int. J. multiphase flow, 24, 387, (1998) · Zbl 1121.76455
[16] Chang, Y.C.; Hou, T.Y.; Merriman, B.; Osher, S., A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. comput. phys., 124, 449, (1996) · Zbl 0847.76048
[17] A. R. York, Development of modifications to the material point method for the simulation of thin membranes, compressible fluids, and their interactions, Sandia National Laboratory Report SAND97-1893, 1997.
[18] York, A.R.; Sulsky, D.; Schreyer, H.L., The material point method for simulation of thin membranes, Int. J. numer. method eng., 44, 1429, (1999) · Zbl 0971.74079
[19] Hoppe, H., Surface reconstruction from unorganized points, (1994)
[20] G. Tryggvason, B. Bunner, O. Ebrat, and, W. Tauber, Computations of multiphase flows by a finite difference/front tracking method. I. Multi-fluid flows, Lecture notes, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, 1998.
[21] Harlow, F.H.; Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. fluids, 8, 2182, (1965) · Zbl 1180.76043
[22] Swartz, B.K.; Wendroff, B., AZTEC: A front tracking code based on Godunov’s method, Appl. numer. math., 2, 385, (1986) · Zbl 0601.76088
[23] Monaghan, J., Particle methods for hydrodynamics, Comput. phys. rep., 3, 71, (1985)
[24] Burgess, D.; Sulsky, D.; Brackbill, J.U., Mass matrix formulation of the FLIP particle-in-cell method, J. comput. phys., 103, 1, (1992) · Zbl 0761.73117
[25] Brackbill, J.U.; Kothe, D.B.; Zemach, C., A continuum method for modeling surface tension, J. comput. phys., 100, 335, (1992) · Zbl 0775.76110
[26] Sussman, M.; Smereka, P.; Osher, S., A level-set approach for computing solutions to incompressible two-phase flow, J. comput. phys., 114, 146, (1994) · Zbl 0808.76077
[27] Peskin, C.S., Numerical analysis of blood flow in the heart, J. comput. phys., 25, 220, (1977) · Zbl 0403.76100
[28] Baumgardner, J.R.; Frederikson, P.O., Icosahedral discretization of the two-sphere, SIAM J. numer. anal., 22, 1107, (1985) · Zbl 0601.65084
[29] Fyfe, D.E.; Oran, E.S.; Fritts, M.J., Surface tension and viscosity with Lagrangian hydrodynamics on a triangular mesh, J. comput. phys., 76, 349, (1988) · Zbl 0639.76043
[30] Popinet, S.; Zaleski, S., A front-tracking algorithm for accurate representation of surface tension, J. numer. methods fluids, 30, 775, (1999) · Zbl 0940.76047
[31] Lafaurie, B.; Nardone, C.; Scardovelli, R.; Zaleski, S.; Zanetti, G., Modelling merging and fragmentation in multiphase flows with SURFER, J. comput. phys., 113, 134, (1994) · Zbl 0809.76064
[32] J. U. Brackbill, D. Juric, D. Torres, and E. Kallman, Dynamic modeling of microgravity flow, in Proceedings of the Fourth Microgravity Fluid Physics and Transport Phenomena Conference, Cleveland, OH, 1998, 584-589.
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.