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The pseudopotential lattice Boltzmann (LB) model is a popular model in the LBcommunity for simulating multiphase flows. Recently, several thermal LB models,which are based on the pseudopotential LB model and constructed within theframework of the double-distribution-function LB method, were proposed tosimulate thermal multiphase flows [G. H\'azi and A. M\'arkus, Phys. Rev. E 77,026305 (2008); L. Biferale et al., Phys. Rev. Lett. 108, 104502 (2012); S. Gongand P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)]. The objective of thepresent paper is to show that the effect of the forcing term on the temperatureequation must be eliminated in the pseudopotential LB modeling of thermalflows. First, the effect of the forcing term on the temperature equation isshown via the Chapman-Enskog analysis. For comparison, alternative treatmentsthat are free from the forcing-term effect are provided. Subsequently,numerical investigations are performed for two benchmark tests. The numericalresults clearly show that the existence of the forcing-term effect will lead tosignificant numerical errors in the pseudopotential LB modeling of thermalflows.

Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows