Capillary Courant Number for reducing spurious velocities
Functionality to add/problem to solve
Spurious (unphysical) velocities are often a problem in volume of fluid simulations. Dozens of papers are written about techniques to reduce them.
As surface tension is implemented explicitly in interFoam, the time step needs to be limited. It should be limited by the capillary Courant number.
A Capillary Courant number will be useful for everyone who uses interFoam or multiphaseInterFoam, and is working with surface tension. It will be especially usefull when simulating instabilities, because before the instability appears there should usually not be any flow in the fluid.
A Capillary Courant Number should be added to interFoam and multiphaseInterFoam.
What does success look like, and how can we measure that?
The simplest test case would consist of two fluids, one over another. There should not be any flow. Of course, spurious velocities will appear - however, they will be much smaller when using a Capillary Courant number.
Links / references
Personnettaz, P.; Beckstein, P.; Landgraf, S.; Köllner, T.; Nimtz, M.; Weber, N.; Weier, T.: Thermally driven convection in Li||Bi liquid metal batteries, Journal of Power Sources 401(2018) 362-374
The capillary time step is provided at page 36, equation A.1 of the arXiv version.
I can provide the source code for interFoam and multiphaseInterFoam.