Breaching the capillary time-step constraint using a coupled VOF method with implicit surface tension

TL;DR

This paper introduces a novel fully-coupled implicit VOF method that allows simulations of interfacial flows with surface tension to use larger time-steps than traditionally limited by the capillary constraint, improving computational efficiency.

Contribution

A new implicit coupled pressure-based algorithm with an algebraic VOF method and implicit surface tension treatment that breaches the capillary time-step constraint in interfacial flow simulations.

Findings

Enables larger time-steps beyond the capillary limit in simulations

Implicit coupling improves numerical stability and accuracy

Applicable to flows with surface tension, density, and viscosity effects

Abstract

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.