Force method in a pseudo-potential lattice Boltzmann model

Single component pseudo-potential lattice Boltzmann models have been widely studied due to their simplicity and stability in multiphase simulations. While numerous models have been proposed, comparative analysis and advantages and disadvantages of different force schemes are often lacking. A pseudo-potential model to simulate large density ratios proposed by Kupershtokh et al. [1] 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. [2] is selected and applied to improve the accuracy of Kupershtokh et al.'s model. Results obtained using the modified Kupershtokh et al.'s model [1] for different value of τ are compared with those obtained using Li et al.'s model [3]. Effect of relaxation time τ 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 [2]. However, the errors and τ'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 τ, 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 of the density ratios.