A variational volume-of-fluid (VOF) approach to curvature-driven flows

We introduce a variational volume-of-fluid methodology for evolving interfaces by curvature driven flow. The approach makes use of the traditional directionally split scheme to advect the fluid interface. Canonical two and three-dimensional geometries are tested with the formulation and the results are shown to match the physical behavior predicted by level-set methods with the additional advantage of interface sharpness and the lack of the need for interface “surgery”. The advecting velocities are also modified with a minimum curvature constraint for the same initial geometries and mass is shown to be conserved after minimum curvature is reached.

This work is supported by the Office of Naval Research (ONR).