Double Bubbles Sans Toil and Trouble: Discrete Circulation-Preserving Vortex Sheets for Soap Films and Foams

摘要

Simulating the delightful dynamics of soap films, bubbles, and foamsrnhas traditionally required the use of a fully three-dimensional manyphasernNavier-Stokes solver, even though their visual appearance isrncompletely dominated by the thin liquid surface. We depart from earlierrnwork on soap bubbles and foams by noting that their dynamicsrnare naturally described by a Lagrangian vortex sheet model in whichrncirculation is the primary variable. This leads us to derive a novelrncirculation-preserving surface-only discretization of foam dynamicsrndriven by surface tension on a non-manifold triangle mesh. We representrnthe surface using a mesh-based multimaterial surface trackerrnwhich supports complex bubble topology changes, and evolve thernsurface according to the ambient air flow induced by a scalar circulationrnfield stored on the mesh. Surface tension forces give rise torna simple update rule for circulation, even at non-manifold Plateaurnborders, based on a discrete measure of signed scalar mean curvature.rnWe further incorporate vertex constraints to enable the interactionrnof soap films with wires. The result is a method that is at oncernsimple, robust, and efficient, yet able to capture an array of soaprnfilms behaviors including foam rearrangement, catenoid collapse,rnblowing bubbles, and double bubbles being pulled apart.