Phase interface effects in the total enthalpy-based lattice Boltzmann model for solid–liquid phase change

In this paper, phase interface effects, including the differences in thermophysical properties between solid and liquid phases and the numerical diffusion across phase interface, are investigated for the recently developed total enthalpy-based lattice Boltzmann model for solid–liquid phase change, which has high computational efficiency by avoiding iteration procedure and linear equation system solving. For the differences in thermophysical properties (thermal conductivity and specific heat) between solid and liquid phases, a novel reference specific heat is introduced to improve the total enthalpy-based lattice Boltzmann model, which makes the thermal conductivity and specific heat decoupled. Therefore, the differences in thermal conductivity and specific heat can be handled by the dimensionless relaxation time and equilibrium distribution function, respectively. As for the numerical diffusion across phase interface, it is revealed for the first time and found to be induced by solid–liquid phase change. To reduce such numerical diffusion, multiple-relaxation-time collision scheme is exploited, and a special value (one fourth) for the so-called “magic” parameter, a combination of two relaxation parameters, is found. Numerical tests show that the differences in thermophysical properties can be correctly handled and the numerical diffusion across phase interface can be dramatically reduced. Finally, theoretical analyses are carried out to offer insights into the roles of the reference specific heat and “magic” parameter in the treatments of phase interface effects.