Numerical Simulation of Solid Melting with Natural Convection Using the Double Lattice Boltzmann Method

A double lattice Boltzmann method (LBM) using the D2Q9 model was applied to simulate solid melting with natural convection and heat transfer that may occur in nuclear and diverse energy systems. The method applied multi-relaxation time LBM (MRT-LBM) to the fluid-flow field in the liquefied region and single-relaxation-time LBM (SRT-LBM) to the energy field over the entire domain, regardless of phase states. The liquid fraction and solid–liquid interface were estimated using an enthalpy–porosity formulation based on temperature, while detailed mushy-zone modeling was omitted to reduce computational cost. A bounce-back treatment was applied at solid boundaries and phase interfaces. Comparison and validation against gallium melting experiments and previous finite element and finite volume calculations showed that the proposed model efficiently tracks melt-front evolution and captures the dominant convection pattern without complex adaptive-grid or level-set techniques. The results demonstrate good agreement with benchmark data and indicate that the double LBM framework is suitable for engineering simulations of convection-driven melting in energy system geometries.