An improved Non-Dimensional Lattice Boltzmann Method (NDLBM) is developed and a uniform computational code is compiled to fit into both direct and porous medium model simulations. Comparison studies based on natural convection of 240 cylindrical tube bundle heat exchangers immersed in a thin rectangular solar storage tank show the computational efficiency and accuracy of both direct simulations and porous medium model simulations achieved by using NDLBM. The governing parameters in the macroscopic, microscopic, and mesoscopic length scales corresponding to the enclosure width, tube diameter, and mesh size are obtained. Transient isotherms, streamlines, Nusselt numbers, and CPU time of nine models have been simulated for various pitch, porosity, and distributions of tubes. Given the same grid number and simulation time, the CPU time of the porous medium model simulations by using NDLBM is about 1/60 of that of porous medium simulations by using finite difference based on projection method, and 1/20 of that of the direct simulations with the uniform code based on NDLBM. The porous medium simulations can only obtain Darcy velocity and volume averaged temperature, while the direct simulations can obtain both macroscopic and microscopic velocity and temperature.