A comparative study of lattice Boltzman and front-trancking finite-difference methods for bubble simulations

This communication describes the results of bubble rise simulations using a lattice Boltzmann method and a front-tracking finite-difference method. The simulations, performed in a 2-D periodic box, consider two specific examples: a steadily rising bubble and a bubble rising in an oscillatory manner with accompanying shape change. We compare the shapes and rise velocities of the steadily rising and oscillating bubbles, the oscillation frequencies and amplitudes, and the bubble shapes at different phases of the oscillations. The simulations reveal that both numerical schemes afford qualitatively similar results, which are within a few percent quantitatively.