Vertex-Based Simulation of Dry Foam

Foam dynamics is gaining interests within Computational Fluid Dynamics and Computer Graphics. We believe that liquid foam, or froth, is the next evolution in the field of fluid dynamics. Froth is the natural phenomenon of bubbles that arise due to nucleation of gas in liquids. As the physics of foams in two dimensions is better understood this thesis begins the journey of physics-based foam dynamics in Computer Graphics with two-dimensional dry foam. A dry foam is a foam with little or no volume fraction of liquid. From the field of Computational Physics we present the kinetics and dynamics of foams including the vital equilibrium rules that foams comply with. We have implemented a vertex-based method for two-dimensional simulation of dry foam. By design the solver is a nonlinear quasi-static Newton method. We deal with several dynamic processes which include topological changes, gas diffusion, and shear deformation. For animation purposes the numerical model is well behaved and stable and can converge even if the foam is locally ill-defined. This thesis introduces the Ghost Bubble method, a novel contribution to the vertex-based foam model that allows foam simulations with free surfaces and dynamic boundary conditions. A number of improvements to stabilize the numerical model are discussed and implemented and convergence rate analyses are performed against the improved dry foam solver which indicate superlinearity.