  In order to treat immiscible two-phase flows at large density ratios and high
Reynolds numbers, a three-dimensional code based on the discrete unified gas
kinetic scheme (DUGKS) is developed, incorporating two major improvements.
First, the particle distribution functions at cell interfaces are reconstructed
using a weighted essentially non-oscillatory scheme. Second, the conservative
lower-order Allen-Cahn equation is chosen, instead of the higher-order
Cahn-Hilliard equation, to evolve the free-energy based phase field governing
the dynamics of two-phase interfaces. Five benchmark problems are simulated to
demonstrate the capability of the approach in treating two phase flows at large
density ratios and high Reynolds numbers, including three two dimensional
problems (a stationary droplet, Rayleigh-Taylor instability, and a droplet
splashing on a thin liquid film) and two three-dimensional problems (binary
droplets collision and Rayleigh-Taylor instability). All results agree well
with the previous numerical and the experimental results. In these simulations,
the density ratio and Reynolds number can reach a large value of O(1000). Our
improved approach sets the stage for the DUGKS scheme to handle realistic
two-phase flow problems.
