Force Method in a Pseudo-potential Lattice Boltzmann Model

TL;DR

This paper analyzes and compares different force schemes in a pseudo-potential lattice Boltzmann model, selecting the most accurate one to enhance simulation precision for large density ratios and discussing methods to further improve model accuracy.

Contribution

The study evaluates various force schemes in a pseudo-potential lattice Boltzmann model and applies the most accurate scheme to improve large density ratio simulations.

Findings

Guo et al.'s force scheme improves model accuracy

Errors are correlated with spurious velocities on interfaces

Rescaling the equation of state and multi-relaxation time enhance accuracy

Abstract

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.