Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow

The application of the lattice Boltzmann method in two-phase flows is often restricted by the numerical instability at low viscosities. In this work, a multirelaxation-time (MRT) lattice Boltzmann model (LBM) is developed using the interaction potential approach. With the MRT collision term and a general force term, the new MRT model is able to significantly enhance the numerical stability at low viscosities, without appreciable increase in computation time or memory use. Advanced force formulation using the multirange potential can also be readily incorporated into the current MRT scheme. Numerical tests are first performed in two dimensions under equilibrium conditions. The MRT model is able to reduce the lowest stable viscosity by an order of magnitude compared to the single relaxation time LBM. In addition, the spurious velocity at the gas-liquid interface can also be significantly decreased by tuning the adjustable relaxation parameters. Then two sets of three-dimensional simulations are conducted to investigate the buoyant rise of a gas bubble in a low-viscosity liquid. In particular, millimeter air bubble in water, which is difficult for traditional two-phase LBM due to both low viscosity and high-surface tension, is successfully simulated using the MRT technique developed in this study. The simulated bubble shape and velocity are compared with the experimental results and empirical correlations in the literature, and the satisfactory agreement proves the validity of the MRT-LBM for two-phase flows.