Browsing by Author "Peskin, Charles S."

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Numerical simulations of three-dimensional foam by the immersed boundary method
(2014-07-15)
Kim, Yongsam
;
Lai, Ming-Chih
;
Peskin, Charles S.
;
Seol, Yunchang
;
應用數學系
In this paper, we extend (Kim et al., 2010 [13]) to the three-dimensional dry foam case, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquid-film internal boundaries that partitions the gas into discrete cells or bubbles. The liquid-film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an immersed boundary method that takes into account the non-equilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquid-film boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the three-dimensional framework, and test it by verifying the 3D generalization of the von Neumann relation, which governs the coarsening of a three-dimensional dry foam. (C) 2014 Elsevier Inc. All rights reserved.
The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes
(2012-08-01)
Kim, Yongsam
;
Seol, Yunchang
;
Lai, Ming-Chih
;
Peskin, Charles S.
;
數學建模與科學計算所(含中心)
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.