Advances of Phase-Field Model in the Numerical Simulation of Multiphase Flows: A Review

The phase-field model (PFM) is gaining increasing attention in the application of multiphase flows due to its advantages, in which the phase interface is treated as a narrow layer and phase parameters change smoothly and continually at this thin layer. Thus, the construction or tracking of the phase interface can be avoided, and the bulk phase and phase interface can be simulated integrally. PFM provides a useful alternative that does not suffer from problems with either the mass conservation or the accurate computation of surface tension. In this paper, the state of the art of PFM in the numerical modeling and simulation of multiphase flows is comprehensively reviewed. Starting with a brief description of historical developments in the PFM, we continue to take a tour into the basic concepts, fundamental theory, and mathematical models. Then, the commonly used numerical schemes and algorithms for solving the governing systems of PFM in the application of multiphase flows are presented. The various applications and representative results, especially in non-match density scenarios of multiphase flows, are reviewed. The primary challenges and research focus of PFM are analyzed and summarized as well. This review is expected to provide a valuable reference for PFM in the application of multiphase flows.