Migration-collision scheme of Lattice Boltzmann method for heat conduction problems involving solidification

The phase-change problem is solved by the migration-collision scheme of lattice Boltzmann method. After formula derivation, we find that this method can give a rigorous numerical value for the phase-change temperature, which is of crucial importance. One-dimensional solidification in half-space and two-dimensional solidification in a corner are simulated. The phase change temperature and the liquid-solid interface are both obtained, and the results conform to the analytical solution.