An efficient phase-field-based multiple-relaxation-time lattice Boltzmann model for three-dimensional multiphase flows

In this paper, an efficient phase-field-based lattice Boltzmann (LB) model with multiple-relaxation-time (MRT) collision operator is developed for the simulation of three-dimensional multiphase flows. This model is an extension of our previous two-dimensional model (Liang et al., 2014) to the three dimensions using the D3Q7 (seven discrete velocities in three dimensions) lattice for the Cahn-Hilliard equation and the D3Q15 lattice for the Navier-Stokes equations. Due to the less lattice-velocity directions used, the computational efficiency can be significantly improved in the study of three-dimensional multiphase flows, and simultaneously the present model can recover the Cahn-Hilliard equation and the Navier-Stokes equations correctly through the Chapman-Enskog procedure. We compare the present MRT model with its single-relaxation-time version and the previous LB model by using two benchmark interface-tracking problems, and numerical results show that the present MRT model can achieve a significant improvement in the accuracy and stability of the interface capturing. The developed model can also be able to deal with multiphase fluids with high viscosity ratio, which is demonstrated by the simulation of the layered Poiseuille flow and Rayleigh-Taylor instability at various viscosity ratios. The numerical results are found to be in good agreement with the analytical solutions or some available results. In addition, it is also found that the instability induces a more complex structure of the interface at a low viscosity.