A discrete unified gas-kinetic scheme for immiscible two-phase flows. (November 2018)

• Record Type: Journal Article
• Authors: Zhang, Chunhua; Yang, Kang; Guo, Zhaoli
• Is Part Of: International journal of heat and mass transfer. Volume 126(2018)Part B
• Page Start: 1326
• Page End: 1336
• Publication Date: 2018-11
• Subjects: Multiphase flow -- Finite-volume method -- Discrete unified gas-kinetic scheme -- Lattice Boltzmann method -- Non-uniform gird; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2018.06.016
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: The proposed model is a finite volume scheme which is easy to perform on irregular meshes. This model can guarantee a low numerical dissipation by coupling the streaming and collision processes. The mesh size and time step are decoupled, and the time step is determined independently by the CFL condition. 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.