Lattice Boltzmann method for the heat conduction problem with phase change

An extended lattice Boltzmann (LB) equation was developed for the simulatio n of the phase-change problem governed by the heat conduction equation inco rporated with enthalpy formation. Mathematical consistency between the prop osed extended LB equation and the governing equation was accomplished by th e Chapman-Enskog expansion. Illustrative examples include one-dimensional h alf-space melting and solidification as well as two-dimensional solidificat ion in a corner. Phase change at a single temperature and with a mushy zone are both demonstrated. Two types of boundary condition, prescribed tempera ture and prescribed heat flux, are considered in the illustrative examples. Different thermal diffusivities in the separated phases/zones are accompli shed through varying the relaxation times in the LB equation. All numerical results obtained by the present scheme agree very we with previous analyti cal or numerical results in the literature.