This paper develops a regularized lattice Boltzmann method for efficiently simulating the flow of N-phase immiscible incompressible fluids based on the phase field model that satisfies conservation and compatibility. By designing auxiliary moments, this method can accurately recover the second-order Allen-Cahn equation and the modified momentum equation. The correctness and effectiveness of the developed N-phase regularized lattice Boltzmann method are validated through numerical simulations of three-phase liquid lens spreading and Kelvin-Helmholtz instability phenomena. Finally, numerical simulations and analyses of three-phase Rayleigh-Taylor instabilities (RTI) were conducted, focusing on the evolution of the phase interface within the Reynolds number range of 500 ≤ Re ≤ 20000 (particularly under high Reynolds number condition of Re = 20000). Quantitative analyses were performed on the amplitude variations of bubbles and spikes at the two interfaces, as well as the changes in dimensionless velocity. We found that as the Reynolds number increases, the phase interface curls up at multiple locations due to Kelvin-Helmholtz instability, making the fluid more prone to dispersion and fragmentation. This study also simulated the evolution of RTI under different interface perturbations. The results indicate that RTI first develops at the perturbed interface, and its evolution gradually triggers instability at another interface.
Xuguang et al. (2025) studied this question.