Three–dimensional lattice Boltzmann models for solid–liquid phase change

A single–relaxation–time (SRT) and a multiple–relaxation–time (MRT) lattice Boltzmann (LB) models are proposed for three–dimensional (3 D) solid–liquid phase change. The enthalpy conservation equation can be recovered from the present models. The reasonable relationship of the relaxation times in the MRT model is discussed. One–dimensional (1 D) melting with analytical solution is calculated by the SRT and MRT models for validation. Moveover, 1 D solidification with analytical solution is simulated by using the MRT model. ​Compared with the SRT model, the MRT one is more accurate to capture the phase interface. The MRT model is also verified with other published two–dimensional (2 D) analytical and numerical results. The validations suggest that the present MRT approach is qualified to simulate the 3 D solid–liquid phase change process. Furthermore, the influences of Rayleigh number and Prandtl number on the 3 D melting are investigated.