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

Fabian Denner, Fabien Evrard, Berend van Wachem

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number111128
JournalJournal of Computational Physics
Volume459
DOIs
StatePublished - Jun 15 2022
Externally publishedYes

Keywords

  • Capillary time-step constraint
  • Coupled algorithm
  • Surface tension
  • Volume-of-fluid method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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