Forcing scheme in pseudopotential lattice Boltzmann model for multiphase   flows
  The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudo-potential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudo-potential LB model. Firstly, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme and the exact-difference-method (EDM) forcing scheme. The nature of these two schemes and their recovered macroscopic equations will be shown. Secondly, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudo-potential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach for achieving thermodynamic consistency in the pseudo-potential LB model. 
Q. Li, K. H. Luo, and X. J. Li
physics.flu-dyn cond-mat.soft