Summary
In this paper we present a 2D Volume of Fluid two phase flow model with surface tension. The model is based on the incompressible Navier -Stokes equations, it uses implicit time stepping, unstructured grids and staggered finite volumes. A cubic spline interface interpolant which preserves the volume fraction distribution is introduced. Interface adaptive and/or interface aligned deformable grids are reconstructed in each time step with help of either a linear or spline interface approximation. Anomalous currents around bubbles are significantly reduced with help of cubic spline interpolants. The simulations of buoyant bubbles are compared with known theoretical, numerical and experimental results.
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References
R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst. Templates for the solution of linear systems: Building blocks for iterative methods. SIAM, 1994.
D. Bhaga and M. E. Weber. Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech., 105:61, 1992.
R. Clift, J. R. Grace, and M. E. Weber. Bubbles, Drops, and Particles. Academic Press, 1978.
R. Collins. A simple model of the plane gas bubble in a finite liquid. J.Fluid Mech., 22:763, 1965.
B. J. Daly. A technique for including surface tension effects in hydrodynamic calculations. J. Comput. Phys., 4:97, 1969.
D. E. Fyfe, E.S. Oran, and M. J. Fritts. Surface tension and viscosity with lagrangian hydrodynamics on a triangular mesh. J. Comput. Phys., 76:394, 1988.
L. Ginzburg and G. Wittum. Two-phase flows on unstructured grids with spline volume tracking. J. Comput. Phys., 2001.
D. Gueyffier, J. Lie, A. Nadim, R. Scardovelli, and S. Zaleski. Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys., 152:423, 1999.
J. G. Hnat and J. D. Buckmaster. Spherical cap bubbles and skirt formation. Phys. Fluids, 19:182, 1976.
B. Lafaurie, C. Nardone, R. Scardovelli, and S. Zaleski. Modeling merging and fragmentation in multiphase flows with surfer. J. Comput. Phys., 113:134, 1994.
J. Li. Calcul d’ interface affine par morceaux. C.R.Acad.Sci.Paris, 320, série IIb:391, 1995.
S. Popinet and S. Zaleski. A front-tracking algorithm for accurate representation of surface tension. Int. J. Numer. Meth. Fluids, 30:775, 1999.
W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannnery.Numerical Recipes in C. Cambridge, 1992.
W. J. Rider and D. B. Kothe. Reconstructing volume tracking. J. Comput. Phys., 141:112, 1998.
G. Ryskin and L. G. Leal. 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, 1984.
R. Scardovelli and S. Zaleski. Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech., 31:567, 1999.
G. L. Sleijpen, H. A. vander Vorst, and D. R. Fokkema. Bicgstab(1) and other hybrid bi-cg methods. Numerical Algorithms, 7:75, 1994.
M. Sussmann and S. Osher P. Smereka. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys., 114:146, 1994.
M. Sussmann and P. Smereka. Axisymmetric free boundary problems. J. Fluid Mech., 341:269, 1997.
S. H. Unverdi and G. Tryggvason. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys., 100:25, 1992.
D. L. Youngs. Time-dependent multi-material flow with large fluid distortion. (In Numerical Methods fbr Fluid Dynamics),1986.
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© 2003 Springer-Verlag Berlin Heidelberg
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Ginzburg, I., Wittum, G., Zaleski, S. (2003). Adaptive Multigrid Computations of Multiphase Flows. In: Hirschel, E.H. (eds) Numerical Flow Simulation III. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45693-3_5
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DOI: https://doi.org/10.1007/978-3-540-45693-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53653-3
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