Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T01:41:49.386Z Has data issue: false hasContentIssue false
  • English
  • Français

The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes

Published online by Cambridge University Press:  20 August 2015

Yongsam Kim ,
Yunchang Seol ,
Ming-Chih Lai  and
Charles S. Peskin
Yongsam Kim*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Yunchang Seol*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Ming-Chih Lai*
Affiliation:
Department of Applied Mathematics, Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
Charles S. Peskin*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

We extend the immersed boundary (IB) method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble network. In the article [Y. Kim, M.-C. Lai, and C. S. Peskin, J. Comput. Phys. 229:5194-5207,2010], we implemented an IB method for the foam problem in the two-dimensional case, and tested it by verifying the von Neumann relation which governs the coarsening of a two-dimensional dry foam. However, the method implemented in that article had an important limitation; we did not allow for the resolution of quadruple or higher order junctions into triple junctions. A total shrinkage of a bubble with more than four edges generates a quadruple or higher order junction. In reality, a higher order junction is unstable and resolves itself into triple junctions. We here extend the methodology previously introduced by allowing topological changes, and we illustrate the significance of such topological changes by comparing the behaviors of foams in which topological changes are allowed to those in which they are not.

Keywords

65-0465M0676D0576M20Foampermeabilitycapillary-driven motionimmersed boundary methodcoarseningtopological changesT1 and T2 processes
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 2 , August 2012 , pp. 479 - 493
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Glazier, J.A., Gross, S.P., and Stavans, J., Dynamics of two-dimensional soap froths. Phys. Rev. A, 36(1), 1987.Google Scholar
[2]Hilgenfeldt, S., Kraynik, A.M., Koehler, S.A., and Stone, H.A., An accurate von Neumann’s law for three-dimensional foams, Phys. Rev. Lett. 86(12):2685–2688, 2001.Google Scholar
[3]Kermode, J.P. and Weaire, D., 2D-Froth: a program for the investigation of 2-dimensional froths. Computer Physics Communications 60, 75–109, 1990.Google Scholar
[4]Kim, Y. and Peskin, C.S.. 2-D parachute simulation by the Immersed Boundary Method. SIAM J.Sci.Comput. 28(6), 2006.Google Scholar
[5]Kim, Y., Lai, M.-C., and Peskin, C.S., Numerical simulations of two-dimensional foam by the immersed boundary method. J. Comput. Phys. 229:5194–5207, 2010.Google Scholar
[6]Layton, A.T., Modeling water transport across elastic boundaries using an explicit jump method. SIAM J. Sci. Comput. 28(6):2189–2207,2006.Google Scholar
[7]MacPherson, R.D. and Srolovitz, D.J., The von Neumann relation generalized to coarsening of three-dimensional microstructures, Nature, 446(26):1053–1055, 2007.Google Scholar
[8]Mullins, W.W., in Metal Surfaces: Structure, Energetics, and Kinetics. (eds. Robertson, W.D. and Gjostein, N.A.) 17–66(American Society for Metals, Metals Park, Ohio, 1963).Google Scholar
[9]J., von Neumann in Metal Interfaces (ed. Herring, C.) 108–110(American Society for Metals, Cleveland, 1951).Google Scholar
[10]Peskin, C.S., The immersed boundary method. Acta Numerica, 11:479–517, 2002.Google Scholar
[11]Stokie, J.M., Modelling and simulation of porous immersed boundaries. Computers Structures 87(11-12): 701–709, 2009.Google Scholar
[12]Weaire, D. and Hutzler, S., The Physics of Foams. Oxford University Press, 1999.Google Scholar
[13]Weaire, D. and Kermode, J.P., Computer simulation of a two-dimensional soap froth I. Method and motivation. Phil. Mag. B. 48(3), 245–259, 1983.Google Scholar
[14]Weaire, D. and Kermode, J.P., Computer simulation of a two-dimensional soap froth II. Analysis of results. Phil. Mag. B. 50(3), 379–395, 1984.Google Scholar