Evaluation of force implementation in pseudopotential-based multiphase lattice Boltzmann models

The Lattice Boltzmann method (LBM) has proven to be a promising approach in handling multiphase flow problems. In the most widely applied pseudopotential-based LBM multiphase models, multiphase effects can be added in the form of forces, which is further divided into two aspects of force incorporation scheme and force expression. However, the effect of both aspects on coexistence densities and spurious current has not been evaluated systematically. In this paper, Modified Yuan-type and Zhang-type force expressions are chosen, and then they are incorporated into the lattice Boltzmann equation by the Shan–Chen and exact difference method force incorporation scheme to recover the Carnahan–Starling equation of state (EOS) with an additional surface tension term. Based on the computational results of two phases coexisting at a steady state, it can be observed that the force incorporation scheme affects the coexistence densities implicitly with different relaxation times and does not lead to a large difference in values. Force expression is found to greatly affect the achievable highest density ratio, of which the discrete gradient operator of the pseudopotential plays a crucial role. Spurious current is observed to be related to both the force expression and force incorporation scheme, and in our simulation a different force incorporation scheme brings about a large difference. Moreover, our modification on Yuan-type force expression not only improves the accuracy in capturing coexistence densities at low temperatures, but also provides the possibility of tuning the density ratio and surface tension independently at high density ratios.