Abstract
In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.
Highlights
In the past three decades, the lattice Boltzmann (LB) method [1,2,3,4,5,6,7,8,9,10,11], which originates from the lattice gas automaton (LGA) method [12], has been developed into an efficient numerical approach for simulating fluid flow and heat transfer
Different from conventional numerical methods, which are based on the direct discretization of macroscopic governing equations, the LB method is built on the mesoscopic kinetic equation
The previous three-dimensional color-gradient LB models usually suffer from the lack of Galilean invariance and considerable numerical errors because of the error terms in the recovered macroscopic equations
Summary
In the past three decades, the lattice Boltzmann (LB) method [1,2,3,4,5,6,7,8,9,10,11], which originates from the lattice gas automaton (LGA) method [12], has been developed into an efficient numerical approach for simulating fluid flow and heat transfer. In the colorgradient LB method, two distribution functions are introduced to represent two different fluids and a color-gradient-based perturbation operator is employed to generate the surface tension as well as a recoloring step for separating different phases or components. Through the Chapman-Enskog analysis, Huang et al [28] showed that some error terms exist in the macroscopic momentum equation recovered from the color-gradient twophase LB method. They demonstrated that for two-phase flows with different densities the error terms significantly affect the numerical accuracy.
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