Phase-field lattice Boltzmann model for two-phase flows with large density ratio

In this work, a lattice Boltzmann (LB) model based on the phase-field method is proposed for simulating large density ratio two-phase flows. An improved multiple-relaxation-time (MRT) LB equation is first developed to solve the conserved Allen-Cahn (AC) equation. By utilizing a nondiagonal relaxation matrix and modifying the equilibrium distribution function and discrete source term, the conserved AC equation can be correctly recovered by the proposed MRT LB equation with no deviation term. Therefore, the calculations of the temporal derivative term in the previous LB models are successfully avoided. Numerical tests demonstrate that satisfactory accuracy can be achieved by the present model to solve the conserved AC equation. What is more, the discrete force term of the MRT LB equation for the incompressible Navier-Stokes equations is also simplified and modified in the present work. An alternative scheme to calculate the gradient terms of the order parameter involved in the discrete force term through the nonequilibrium part of the distribution function is also developed. To validate the ability of the present LB model for simulating large density ratio two-phase flows, series of benchmarks, including two-phase Poiseuille flow, droplet impacting on thin liquid film, and planar Taylor bubble are simulated. It is found that the results predicted by the present LB model agree well with the analytical, numerical, and experimental results.