The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes (Communications in Computational Physics, 2020)
We extend the immersed boundary (IB) method to simulate the dynamicsof a 2D dry foam by including the topological changes of the bubble network. In thearticle [Y. Kim, M.-C. Lai, and C. S. Peskin, J. Comput. Phys. 229: 5194-5207, 2010], weimplemented an IB method for the foam problem in the two-dimensional case, andtested it by verifying the von Neumann relation which governs the coarsening of atwo-dimensional dry foam. However, the method implemented in that article had animportant limitation; we did not allow for the resolution of quadruple or higher orderjunctions into triple junctions. A total shrinkage of a bubble with more than four edgesgenerates a quadruple or higher order junction. In reality, a higher order junction isunstable and resolves itself into triple junctions. We here extend the methodology previously introduced by allowing topological changes, and we illustrate the significanceof such topological changes by comparing the behaviors of foams in which topologicalchanges are allowed to those in which they are not.