Fully-Coupled Balanced-Force VOF Framework for Arbitrary Meshes with Least-Squares Curvature Evaluation from Volume Fractions

A fully-coupled balanced-force numerical framework for two-phase flows with surface tension on arbitrary collocated meshes is presented, including a novel method to evaluate the curvature from volume fractions. The presented framework reduces the imbalances at the interface to solver tolerance and provides stable and reliable results for density ratios of 10⁶ and larger. The new method to evaluate the curvature is based on a least-squares fit, providing better or equal accuracy compared to implementations found in the literature, which are generally limited to structured meshes, and the accuracy on Cartesian and tetrahedral meshes is shown to be comparable.