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Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions

Front tracking provides sharp resolution of wave fronts through the active tracking of interfaces between distinct materials. A major challenge to this method is to handle changes in the interface topology. We describe two algorithms, implemented in the front tracking code FronTier, to model dynamic changes in three-dimensional interfaces. The two methods can be combined to give a hybrid method that is superior to each individual method. The success of these algorithms is shown by simulations of Rayleigh--Taylor instability, which is an interfacial instability driven by an acceleration directed across a material interface. Our numerical results are validated by comparing the numerical computation of the velocity of a single rising bubble with an analytic model for the bubble velocity.