An extension of the discrete unified gas-kinetic scheme to gas–liquid phase change problems

In this work, an extension of the discrete unified gas-kinetic scheme (DUGKS) to gas–liquid phase change problems is proposed based on the conservative Allen–Cahn phase-field model. The kinetic framework of the DUGKS for gas–liquid phase change problems comprises three components: the conservative Allen–Cahn phase-field equation to describe the interface evolution, the Navier–Stokes equations for fluid flow, and the energy equation for the temperature field. To model the phase change, a source term is introduced based on the heat conduction balance across the interface. By applying Chapman–Enskog analysis, these kinetic equations can be correctly recovered to the corresponding macroscopic equations. The DUGKS approach, which integrates the strengths of the lattice Boltzmann method and the finite volume method, can capture the non-equilibrium phenomenon of phase change more precisely and simulate under the non-uniform mesh with high accuracy. The main contribution of this work lies in formulating a gas–liquid phase change phase-field model by embedding a physically consistent source term into the conservative Allen–Cahn equation under the framework of the DUGKS, enabling an accurate description of the interfacial dynamics during phase change. Including one-dimensional Stefan problem, the evaporation of the stationary droplet, the falling evaporating droplet under gravity in a container, and the saturated film boiling, four benchmark cases are conducted to validate the proposed models and methods. It is demonstrated that the present method can accurately capture the interface dynamics and simulate the gas–liquid phase change problems.