  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.
