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In the present study, a double-population lattice Boltzmann method is applied to the simulation of convection–diffusion phenomena associated with solid–liquid phase transition processes. The research focus is the advancement of the lattice Boltzmann method to complex multitube heat storage system with different numbers and arrangements of tubes. Firstly, a systematic comparison of different lattice Boltzmann models for thermal and flow field in the phase change process is numerically conducted in a square cavity, and the numerical results are validated by the literature data. Then, a comprehensive analysis has been performed in order to investigate the influence of various numbers and arrangements of tubes on the melting dynamics of shell and tube models with different Rayleigh and Stefan numbers. The computational results show how the transient phase-change process, expressed in terms of the volume …