On the re-initialization of fluid interfaces in diffuse interface method

In this paper, a re-initialization method of fluid interfaces is introduced into the Cahn-Hilliard (C-H) model for reducing the continuous numerical and modeling diffusion in the simulation of complex multiphase flows. In this method, the re-initialization process is achieved through three simple steps. Specifically, the order parameter C obtained from the C-H model is first transformed into a roughly estimated distance function d. After that, correction of d is made by using the Hamilton-Jacobian equation. Finally, reconstruction of the fluid interface is then performed to enforce the profile of C to its equilibrium state. The re-initialization of the fluid interface is only required to be implemented occasionally so that the overall computational efficiency is comparable with the original C-H model. In addition to the phase field, the flow field is solved by using the recently-proposed multiphase lattice Boltzmann flux solver. Numerical validations of the proposed method have been carried out by simulating a shearing droplet, Rayleigh-Taylor instability of binary-layered fluids and droplet splashing on a thin film. Good agreements have been achieved with the data published in the literature. The obtained results also show that the present method not only reduces numerical and modeling diffusion substantially but also is able to accurately capture small yet important interfacial structures, such as entrapped air bubbles for the droplet splashing on a thin film.