A generalized conservative phase-field simplified lattice Boltzmann method for miscible and immiscible ternary flows with large density ratio

In this paper, a generalized conservative phase-field simplified lattice Boltzmann method is proposed, which is suitable for both miscible and immiscible ternary flow problems. This method extends our earlier simplified multiphase lattice Boltzmann method (SMLBM) (Chen et al., 2018a) for two-phase flows to the ternary flows by using a generalized conservative equation with Lagrange multiplier to control the evolution of the interface and ensures the conservations of the volume and total mass of each phase. Moreover, the good stability of the SMLBM is utilized for solving the interface problems with large gradients induced by large density ratios between different fluid components. To validate the present method, several ternary flow examples are simulated. The numerical results show that the method can effectively simulate the ternary flows with a density ratio up to 1200 and can be applied to accurately simulate the miscible ternary flows with satisfying the reduction consistency conditions.