An optimal two-relaxation-time lattice Boltzmann equation for solid-liquid phase change: The elimination of unphysical numerical diffusion

This paper proposes an optimal two-relaxation-time (OTRT) lattice Boltzmann equation (LBE) for solid-liquid phase change. By using the Chapman-Enskog expansion, the OTRT LBE can recover the enthalpy-based energy governing equation up to second-order accuracy. Moreover, a detailed theoretical analysis proves that by keeping an optimal relation between the two relaxation times, the OTRT LBE can effectively eliminate the unphysical numerical diffusion of arbitrary DmQn (m dimensions and n discrete velocities) lattice Boltzmann models for both one-phase and two-phase melting problems. Five test cases including one-dimensional to three-dimensional solid-liquid phase change problems are calculated to validate the OTRT LBE. The results show that OTRT LBE can effectively eliminate the unphysical numerical diffusion induced by the discontinuous heat flux across the phase interface, for one-dimensional to three-dimensional solid-liquid phase change problems.