  The capillary time-step constraint is the dominant limitation on the
applicable time-step in many simulations of interfacial flows with surface
tension and, consequently, governs the execution time of these simulations. We
propose a fully-coupled pressure-based algorithm based on an algebraic
Volume-of-Fluid (VOF) method in conjunction with an implicit linearised surface
tension treatment that can breach the capillary time-step constraint. 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,
providing an implicit coupling between pressure, velocity and the VOF colour
function used to distinguish the interacting fluids. Surface tension is treated
with an implicit formulation of the Continuum Surface Force (CSF) model,
whereby both the interface curvature and the gradient of the colour function
are treated implicitly with respect to the colour function. The presented
results demonstrate that a time-step larger than the capillary time-step can be
applied with this new numerical framework, as long as other relevant time-step
restrictions are satisfied, including a time-step restriction associated with
surface tension, density as well as viscosity.
