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

TL;DR

This paper demonstrates that the forcing term in pseudopotential lattice Boltzmann models significantly affects thermal flow simulations, and eliminating it improves accuracy in modeling multiphase thermal flows.

Contribution

The study reveals the necessity to remove the forcing term's effect on the temperature equation in pseudopotential LB models for thermal flows, providing analysis and alternative methods.

Findings

Forcing term impacts temperature equation accuracy

Eliminating the forcing term reduces numerical errors

Numerical tests confirm improved model fidelity

Abstract

The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB community for simulating multiphase flows. Recently, several thermal LB models, which are based on the pseudopotential LB model and constructed within the framework of the double-distribution-function LB method, were proposed to simulate 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. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)]. The objective of the present paper is to show that the effect of the forcing term on the temperature equation must be eliminated in the pseudopotential LB modeling of thermal flows. First, the effect of the forcing term on the temperature equation is shown via the Chapman-Enskog analysis. For comparison, alternative treatments that are free from the forcing-term effect are provided. Subsequently, numerical investigations are performed for two benchmark tests. The numerical results clearly show that the existence of the forcing-term effect will lead to significant numerical errors in the pseudopotential LB modeling of thermal flows.