Multiple-relaxation-time lattice-Boltzmann model for multiphase flow

The lattice-Boltzmann method has shown promise in simulating multiphase flows. However, when using the Bhatnagar-Gross-Krook (BGK) collision operator and polynomial equilibria, numerical stability problems have been shown to occur as the relaxation time is decreased. Some authors have suggested the use of multiple-relaxation-time (MRT) models in lieu of the BGK collision operator, which employs a single relaxation time, to enhance numerical stability. In this paper, a MRT lattice-Boltzmann model for multiphase flow is developed and evaluated for accuracy in several test problems including oscillating liquid cylinders and capillary waves. It is shown that the MRT model is able to achieve numerically stable results at lower viscosities relative to the corresponding BGK model.