Well-balanced discrete unified gas-kinetic scheme for two-phase systems

Abstract

In this paper, a well-balanced discrete unified gas-kinetic scheme (WB-DUGKS) is developed to capture the physical equilibrium state for two-phase fluid systems. Based on the strategies adopted in the well-balanced lattice Boltzmann equation (WB-LBE) [Z. Guo, “Well-balanced lattice Boltzmann model for two-phase systems,” Phys. Fluids 33, 031709 (2021)], a novel equilibrium distribution function and a modified force term are employed in the DUGKS framework. Unlike the LBE model, the time step in DUGKS is decoupled from the mesh size such that the numerical stability can be enhanced. First, the well-balanced properties of the method are validated by simulating a stationary droplet. The numerical results show that the WB-DUGKS can successfully reach an equilibrium state and exhibits superior numerical stability at low viscosity compared with the WB-LBE model. Then, the dynamic process of the coalescence of two droplets is simulated. The time scaling predicted by the present model is in good quantitatively agreement with the previous numerical results and experimental data. Overall, the proposed model provides a promising tool for simulating two-phase systems.