The recently proposed simplified thermal lattice Boltzmann method (STLBM) is a promising solution to challenging flow problems at high Reynolds/Rayleigh numbers. The double-distribution-function (DDF) strategy employed in the construction of STLBM schemes allows the application of different lattice velocity models that would certainly bring fluctuations to numerical performance. A comprehensive investigation into this issue is absent in the literature, which motivates the present work. This study is initiated by the von Neumann stability analysis which gives a theoretical glance at the numerical stability of the STLBM with different lattice velocity models at extreme conditions of low relaxation parameters. Benchmark examples are then presented to showcase the practical performance. The theoretical analysis and the numerical test mutually demonstrate that the STLBM can maintain good numerical stability with different lattice velocity models. In addition, numerical studies of the convergence, the accuracy, and the computational efficiency of the STLBM with different lattice velocity models are carried out. It is found that using lattice velocity models with fewer directions can reduce 14-16% computational time in each iteration. But the total computation time is also related to the convergence speed which can be altered by specific lattice velocity model. Finally, a guideline for the selection of lattice velocity model in different thermal flow problems is provided.

Thermal flow; Lattice Boltzmann method; Stability; Lattice velocity model