One attractive feature of the original pseudopotential method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function. In order to improve the method, regarding thermodynamic consistency and control of surface tension, different approaches were developed in the literature, such as multirange interactions potential and modified forcing schemes. In this work, a strategy to combine these enhancements with an appropriate interaction force field using only nearest-neighbor interactions is devised, starting from the desired pressure tensor. The final step of our procedure is implementing this external force by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Static tests showed that current procedure is suitable to control the surface tension and phase densities. Based on thermodynamic principles, it is devised a solution for phase densities in a droplet, which states explicitly dependence on the surface tension and interface curvature. A comparison with numerical results suggest a physical inconsistency in the pseudopotential method. This fact is not commonly discussed in the literature, since most of studies are limited to the Maxwell equal area rule. However, this inconsistency is shown to be dependent on the equation of state (EOS), and its effects can be mitigated by an appropriate choice of Carnahan-Starling EOS parameters. Also, a droplet oscillation test was performed, and the most divergent solution under certain flow conditions deviated 7.5% from the expected analytical result. At the end, a droplet impact test against a solid wall was performed to verify the method stability, and it was possible to reach stable simulation results with density ratio of almost 2400 and Reynolds number of $\text{Re}=373$. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behavior.

中文翻译：

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伪势格玻尔兹曼法的力法

原始伪电势方法的一个吸引人的特征在于其简单性，即可以根据最近邻电势函数来添加力。为了改进该方法，关于热力学一致性和表面张力的控制，文献中开发了不同的方法，例如多范围相互作用势和改进的强迫方案。在这项工作中，从所需的压力张量开始，设计了一种仅使用最近邻相互作用将这些增强功能与适当的相互作用力场相结合的策略。我们程序的最后一步是通过使用经典的Guo强迫方案来实现这种外力。进行了有关静态和动态流动条件的数值测试。静态测试表明，目前的方法适合控制表面张力和相密度。基于热力学原理，为液滴中的相密度设计了一种解决方案，该解决方案明确指出了表面张力和界面曲率的依赖性。与数值结果的比较表明，伪电势方法存在物理矛盾。由于大多数研究仅限于麦克斯韦等面积法则，因此在文献中并未对此事实进行普遍讨论。然而，这种不一致性被示出依赖于状态（EOS）的方程，其效果可以通过的卡纳汉-斯塔林EOS参数的适当选择来减轻。另外，还进行了液滴振荡测试，在某些流动条件下，最发散的溶液偏离了预期的分析结果7.5％。在最后，$\text{回覆}=373$。观察到的结果证实了所提出的方法能够复制所需的宏观多相行为。