Three-dimensional phase-field lattice Boltzmann model for incompressible multiphase flows

In this work, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is developed to simulate three-dimensional (3D) multiphase flows with moderate density ratio. Inspired by the work of Liang et al. [H. Liang, B. C. Shi, Z. L. Guo, Z. H. Chai, Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows, Phys. Rev. E, 89(2014) 053320.], a time-dependent source term is added in the LB equation for interface so that the 3D Cahn-Hilliard equation can be recovered precisely. The Navier-Stokes equations are solved by introducing a pressure distribution function, which helps reduce the discretization errors in calculation of density gradient thereby improving the numerical stability for variable density. An interfacial force of potential form is utilized to effectively suppress spurious velocities at the interface and is incorporated into the LB equation as an additional body force. The present 3D model is tested by several classic numerical examples including the solid body rotation, the stationary droplet test, the droplet deformation and breakup in a simple shear flow and the Rayleigh-Taylor instability. Simulation results are shown to be in good agreement with theoretical predictions, available experimental or numerical data, demonstrating a good capability of the present model in capturing the interface, dealing with topological changes, and simulating variable density ratio. In addition, it is interestingly found that the Rayleigh-Taylor instability will be totally suppressed when the Weber number does not exceed a critical value.