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

A double lattice Boltzmann method (LBM) based on the D2Q9 model was developed to simulate natural convection melting and heat transfer in energy systems, including nuclear systems. Fluid flow in the liquid region was solved using the multi-relaxation-time LBM (MRT-LBM), whereas the energy equation was treated with the single-relaxation-time LBM (SRT-LBM) over the entire domain. Phase change was modeled through an enthalpy–porosity formulation, with the liquid fraction and solid–liquid interface determined from local enthalpy, while explicit mushy-region resolution was avoided to improve computational efficiency. Bounce-back treatment represented solid boundaries and the evolving interface. The model was validated against gallium-melting experiments and previous finite element and finite volume computations. The predicted melt-front evolution and convection behavior agreed well with benchmark data, confirming that the proposed framework can capture coupled fluid motion and heat transfer during melting without adaptive meshes or level-set methods.