Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows

Abstract

Motivated by the need for three-dimensional methods for interface calculations that can deal with topology changes, we describe a numerical scheme, built from a volume-of-fluid interface tracking technique that uses a piecewise-linear interface calculation in each cell. Momentum balance is computed using explicit finite volume/finite differences on a regular cubic grid. Surface tension is implemented by the continuous surface stress or continuous surface force method. Examples and verifications of the method are given by comparing simulations to analytical results and experiments, for sedimenting droplet arrays and capillary waves at finite Reynolds number. In the case of a pinching pendant drop, both three-dimensional and axisymmetric simulations are compared to experiments. Agreement is found both before and after the reconnections.