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Abstract
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In this paper, the Taylor series expansion and least square-based lattice Boltzmann method (TLLBM) is combined with a local lattice Boltzmann (LB) conjugate heat transfer scheme to simulate different conjugate natural convection problems in a differentially heated enclosure on non-uniform meshes. Four case studies are designed not only to verify the developed basic TLLBM FORTRAN code but also to validate the results of the TLLBM for different conjugate natural convection problems. The convergence study of the presented TLLBM is also carried out and the order of accuracy of the method is reported in different mesh regions. It is concluded that the results of streamlines, isotherms, temperature distributions along a test line, and average Nusselt numbers calculated on the cold and hot walls of the enclosure are compared well with those available in the literature from conventional numerical methods as well as the standard LBM. The computational efficiency of the TLLBM is also examined through comparing the results of simulations on uniform (standard LBM) and non-uniform (TLLBM) meshes in terms of the accuracy and CPU time needed for solutions to converge. It is shown that the TLLBM is able to give accurate results with lower CPU time and mesh sizes than the standard LBM.
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