A discrete unified gas-kinetic scheme for immiscible two-phase flows

Abstract In this work, a discrete unified gas-kinetic scheme (DUGKS) is proposed for two-phase flows. In the framework of DUGKS, two kinetic equations are used to solve the quasi-incompressible phase-field governing equations (Yang and Guo, 2016), one of the kinetic models is developed for the Chan-Hilliard (CH) equation and the other is for the Navier-Stokes equations. The DUGKS can correctly recover the quasi-incompressible phase-field governing equations through the Chapman-Enskog analysis. Unlike previous phase-field-based lattice Boltzmann equation (LBE) models, the Courant-Friedricks-Lewy (CFL) condition in DUGKS is adjustable which can increase numerical stability. Furthermore, with the finite-volume formulation the model can be easily implemented on non-uniform meshes which can improve numerical precision. The proposed model is validated by simulating several benchmark problems, including a stationary drop, the layered Poiseuille flow, a rising bubble in the liquid and the Rayleigh-Taylor instability and some comparisons with the quasi-incompressible LBE model are presented. Numerical results show that the present model is capable of dealing with a wider range of viscosity and density ratios than the quasi-incompressible LBE model. In particular, the numerical accuracy can be improved by using non-uniform meshes. Overall, the present model is a promising tool for numerical simulation of two-phase flows.