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In this paper, a phase-field based model under the framework of discreteunified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows isproposed. Two kinetic models are constructed to solve the conservativeAllen-Cahn (A-C) equation that accounts for the interface behavior and theincompressible hydrodynamic equations that govern the flow field, respectively.With a truncated equilibrium distribution function as well as a temporalderivative added to the source term, the macroscopic governing equations can beexactly recovered from the kinetic models through the Chapmann-Enskog analysis.Calculation of source terms involving high-order derivatives existed in thequasi-incompressible model is simplified. A series of benchmark cases includingfour interface-capturing tests and four binary flow tests are carried out.Results compared to that of lattice Boltzmann method (LBM) have been obtained.A convergence rate of second-order can be guaranteed in the test of interfacediagonal translation. The capability of present method in interface trackingthat undergoes a severe deformation has been verified. Stationary bubble andspinodal decomposition problems, both with a density ratio as high as 1000, areconducted and reliable solutions have been provided. The layered Poiseuilleflow with a large viscosity ratio is simulated and numerical results agree wellwith the analytical solutions. Variation of positions of the bubble front andspike tip during the evolution of Rayleigh-Taylor instability (RTI) has beenpredicted precisely. However, the detailed depiction of complicated interfacepatterns appeared in the evolution process is failed, which is mainly caused bythe relatively large numerical dissipation of DUGKS compared to that of LBM. Ahigh-order DUGKS is needed to overcome this problem.

A phase-field model for large-density-ratio two-phase flows based on discrete unified gas-kinetic scheme