Comparative study of free-surface lattice Boltzmann methods: Liquid-fraction-based and phase-field-based methods

We developed a new free-surface lattice Boltzmann method (FS-LBM) based on the phase-field model (phase-field-based FS-LBM), and we compared it with the conventional FS-LBM based on the liquid fraction (liquid-fraction-based FS-LBM). Both methods are variations of LBMs for free-surface flows, i.e., gas–liquid two phase flows with simplified treatment of gas flows. The liquid fraction-based FS-LBM uses the liquid fraction ϵ, similar to the volume-of-fluid method, whereas the proposed phase-field-based FS-LBM calculates the index function ϕ by using the improved lattice kinetic scheme. We compared these methods through the following three test cases: a single stationary droplet, a dam-break flow, and a single rising bubble. In the simulation of a single stationary droplet, we examined the accuracy of the calculation of the interfacial tension, and the results revealed that the liquid-fraction-based FS-LBM is inferior to the phase-field-based FS-LBM due to the low accuracy of curvature calculations. However, by improving the curvature calculation, accurate results could be obtained even with the liquid-fraction-based FS-LBM. In the simulation of a dam-break flow, we examined the numerical stability when the interface moves dynamically, and it was found that there is no significant difference between the two methods. Finally, in the simulation of a single rising bubble, we examined the accuracy and stability in bubbly flows, and it was found that there are significant differences between the two methods in the case where the effect of the interfacial tension is considerable.