Non-convex profile evolution in two dimensions using volume of fluids

A new Volume of Fluid (VoF) method is applied to the problem surface evolution in two dimensions. The VoF technique is applied to problems that are representative of those that arise in semiconductor manufacturing, specifically photolithography and ion milling. The types of surface motion considered are those whose etch rates vary as a function of both surface position and orientation. Functionality is demonstrated for etch rates that are (non?)-convex in regard to surface orientation. A new method of computing surface curvature using divided differences of the volume fractions is also introduced and applied to the advancement of surfaces as a vanishing diffusive term