An improved lattice Boltzmann method for incompressible two-phase flows with large density differences

Abstract

We propose a new lattice Boltzmann method (LBM) for two-phase fluid flows with high density ratios by improving Inamuro et al.’s method [13] without solving the pressure Poisson equation. In the proposed method, we use the lattice kinetic scheme (LKS, an extended scheme of LBM) in the same way as Inamuro et al.’s method. The velocity and pressure fields are computed by using a single equilibrium distribution function and by adjusting the speed of sound in a high density region to satisfy the incompressible continuity equation even for high density ratios. In addition, an improved LKS is used for eliminating dissipation errors, and the continuous surface force (CSF) model is used for modeling interfacial tension of thin interfaces accurately. In order to show the validity of the method, we apply the method to the simulations of a stationary drop, binary droplet collision, rising bubbles, and the impact of a drop on a thin liquid film (a milk crown). In a stationary drop, pressure and density profiles are computed, and the effect of sound speed on time evolution of the pressure field in the drop is illustrated. The stable computations can be performed for high density ratios up to 855. In the simulations of a binary droplet collision and rising bubbles, the computed results by the proposed method are compared with those by Inamuro et al.’s method in good agreement. Also, the computation time of the proposed method is about 50 times faster than that of Inamuro et al.’s method . In the simulation of a milk crown, the time evolution of the crown radius is in good agreement with theoretical predictions.