A numerical method for two-phase flows with an interface

One of the challenges in modelling multiphase fluid systems is to capture accurately the discontinuous-interface phenomenon. In this paper a numerical model for two-phase flows with a varying density is presented, in which a modified volume of fluid (VOF) method is combined with a semi-implicit algorithm ( ) and a higher-order advection scheme in a collocated grid. The improved volume tracking method allows interfaces to be captured and maintained compactly in one cell, without imposing restrictions on the topological complexity or the number of interfaces that can be represented. The surface tension force is modelled by a continuum surface force approximation. An efficient solver is used for the resulting system of the linear equations. Example problems simulated in this paper are the buoyancy-driven motion of multiple bubbles in a viscous liquid, and bubble-rise towards an interface. The complex topological changes that occur during bubble rise are well predicted. The result is verified by experimental data in the literature.