A high‐order phase‐field based lattice Boltzmann model for simulating complex multiphase flows with large density ratios

Abstract

SummaryBased on phase‐field theory, we develop a simple and robust single relaxation time (SRT) lattice Boltzmann (LB) model for simulating complex multiphase flows with large density ratios (up to 2000). The approach utilizes two LB equations (LBE), one is used to describe the interface behavior and the other is used to calculate the hydrodynamic properties. To improve the accuracy and stability in capturing interface, the high‐order LB model derived through the fourth‐order Chapman‐Enskog expansion analysis is applied to Cahn‐Hilliard equation. For solution of the flow field, a modified particle distribution function in the pressure‐velocity formulation is constructed to correctly consider the effect of local density variation and continuous pressure field. With such improvement, the proposed multiphase LB model is able to maintain numerical stability for the problem with very large density ratio, lower relaxation parameter and complex interface. For validation, a series of benchmark cases are carried out. Specially, the full potential of the proposed model is validated by bubble bursting at a free surface, bubble rising and droplet splashing with a density ratio of 2000. In all test cases, the obtained numerical results agree well with the reference data or the analytical solutions.