Lattice Boltzmann model for interface capturing of multiphase flows based on Allen–Cahn equation

A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen–Cahn equation (ACE). By adopting the improved form of a relaxation matrix and an equilibrium distribution function, the time derivative ∂t (ϕ u ) induced by recovering the diffusion term in ACE is eliminated. The conducted Chapman–Enskog analysis demonstrates that the correct conservative ACE is recovered. Four benchmark cases including Zalesak’s disk rotation, vortex droplet, droplet impact on thin film, and Rayleigh–Taylor instability are investigated to validate the proposed model. The numerical results indicate that the proposed model can accurately describe the complex interface deformation.