A discrete kinetic scheme for simulating anisotropic liquid-solid phase change with thermal flows

A discrete kinetic scheme is proposed to evaluate anisotropic liquid-solid phase change. Based on finite-volume type discretization, the scheme has favorable stability and accuracy and is flexible to apply in non-structure meshes. Furthermore, it is coupled with the Boltzmann-Shakhov equation through the thermal effect and diffuse interface based fluid-solid interaction to model phase change under various hydrodynamic conditions. Simulations of anisotropic dendrite growth with and without thermal flows are presented and compared. It is evident that the present scheme is competent in capturing motion of complex interface accompanied by thermal and hydrodynamic interactions between solid and liquid phases.