A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow

A new approach based on volume preserving motion by mean curvature for treating surface tension in two-phase flows is introduced. Many numerical tests and a theoretical justification are included which provide evidence regarding the efficacy of the new approach. For many flows, which exhibit stiff surface tension effects, the new approach gives a factor of at least three and sometimes five or more speed-up for a given accuracy. The new method is easy to implement in the context of (1) level set methods, or coupled level set and volume-of-fluid methods, (2) complicated interfaces separating gas from liquid, and (3) three dimensional axisymmetric, or fully three dimensional adaptive mesh refinement.