  Single component pseudo-potential lattice Boltzmann models have been widely
studied due to their simplicity and stability in multiphase simulations. While
numerous model have been proposed, comparative analysis and advantages and
disadvantages of different force schemes is often lacking. A pseudo-potential
model to simulate large density ratios proposed by Kupershtokh et al. is
analyzed in detail in this work. Several common used force schemes are utilized
and results compared. Based on the numerical results, the relatively most
accurate force scheme proposed by Guo et al. is selected and applied to improve
the accuracy of Kupershtokh et al.'s model. Results obtained using the modified
Kupershtokh et al.'s model for different value of are compared with those
obtained using Li et al.'s model. Effect of relaxation time on the accuracy of
the results is reported. Moreover, it is noted that the error in the density
ratio predicted by the model is directly correlated with the magnitude of the
spurious velocities on (curved) interfaces. Simulation results show that, the
accuracy of Kupershtokh et al.'s model can be improved with Guo et al.'s force
scheme. However, the errors and relax time's effects are still noticeable when
density ratios are large. To improve the accuracy of the pseudo-potential model
and to reduce the effects of the relax time, two possible methods were
discussed in the present work . Both, a rescaling of the equation of state and
multi-relaxation time, are applied and are shown to improve the prediction
accuracy of the density ratios.
