The Voronoi Implicit Interface Method and Computational Challenges in Multiphase Physics

We review some of the motivation and development of the Voronoi Implicit Interfaces Method (VIIM), first introduced in [10], for tracking multiple interacting and evolving regions, whose motion is determined by complex physics that include hydrodynamic, elastic, and geometric forces. The method automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions, and topological changes in the system occur naturally, with no surgery required.