Interface-resolved simulation of solid-liquid phase change with thermal convection using discrete unified gas kinetic scheme

Abstract

This work presents an interface-resolved model for simulating the solid-liquid phase transition problems. In the method, the natural convection flow is handled by the recently proposed discrete unified gas kinetic scheme (DUGKS). Compared with the conventional lattice Boltzmann equation, DUGKS has more advantages on numerical stability and multiscale computation. On the other hand, the ghost-cell (GC) immersed boundary scheme is applied to capturing the solid-liquid interface of pure material. In contrast to the phase-field or enthalpy-based method, the interface here with zero thickness is resolved and explicitly tracked on the fixed Cartesian grid. It is worth noting that due to the adsorption or release of latent heat, the phase front should be evolved according to the Stefan condition. Since compatible with the GC method, the position of the melting front is directly identified by the intersection point, and the complicated treatment of marker inserting and/or deleting in the previous studies is removed. Three numerical examples, including the one-dimension conduction melting, convection melting in a square cavity and melting in a circular cavity with natural convection are conducted to test the present model. The result demonstrates the accuracy of the method for solid-liquid phase change problems.