Breaching the capillary time-step constraint

The capillary time-step constraint is the dominant limitation on the applicable time-step for most simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a fully-coupled algorithm based on an algebraic Volume-of-Fluid (VOF) method, whereby the advection of the interface is solved together with the momentum and continuity equations of the interfacial flow in a single system of linearised equations. Surface tension is represented by an implicit formulation of the Continuum Surface Force (CSF) model, in which both the interface curvature and the gradient of the colour function are treated implicitly with respect to the colour function. Hence, this numerical framework features an implicit coupling of pressure, velocity and the VOF colour function in each governing equation. Results of representative test-cases are presented, which demonstrate that this new numerical framework makes it possible to apply time-steps larger than the capillary time-step constraint, as long as other relevant time-step constraints are respected.