Lattice Boltzmann method for the heat conduction problem with phase change

An extended lattice Boltzmann (LB) equation was developed for the simulation of the phase-change problem governed by the heat conduction equation incorporated with enthalpy formation. Mathematical consistency between the proposed extended LB equation and the governing equation was accomplished by the Chapman-Enskog expansion. Illustrative examples include one-dimensional half-space melting and solidification as well as two-dimensional solidification in a corner. Phase change at a single temperature and with a mushy zone are both demonstrated. Two types of boundary condition, prescribed temperature and prescribed heat flux, are considered in the illustrative examples. Different thermal diffusivities in the separated phases/zones are accomplished through varying the relaxation times in the LB equation. All numerical results obtained by the present scheme agree very we with previous analytical or numerical results in the literature.