The lack of thermodynamic consistency is a well-recognized problem in the single-component pseudopotential lattice Boltzmann models which prevents them from replicating accurate liquid and vapor phase densities; i.e., current models remain unable to exactly match coexisting density values predicted by the associated thermodynamic model. Most of the previous efforts had attempted to solve this problem by introducing tuning parameters, whose determination required empirical trial and error until acceptable thermodynamic consistency was achieved. In this study, we show that the problem can be alternatively solved by properly designing customized equations of state (EOSs) that replace any cubic EOS of choice during the computation of effective mass used in Shan-Chen forces. A two-parameter cubic-shaped customized EOS is introduced. Contrary to previous efforts, customization parameters in the new EOS are nonempirical and are rather derived from solving the integral mechanical stability equation, which neglects the need for any type of tuning for the attainment of rigorous thermodynamic consistency. The proposed approach reduces the errors of the coexisting densities and saturated pressure in the simulation to a maximum of $0.01\%$ within the liquid-vapor density ratio range from $O\left(1\right)$ to $O\left({10}^4\right)$, which had not been achieved in any of the previous tuning-based efforts. A straightforward way for achieving the desired surface tension via the customized EOS is also provided.

中文翻译：

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通过自定义状态方程，在单组分伪势格Boltzmann模型中达到严格的热力学一致性和表面张力。

缺乏热力学一致性是单组分伪势格子Boltzmann模型中公认的问题，它阻止了它们复制精确的液相和气相密度。也就是说，当前模型仍然无法精确匹配由相关热力学模型预测的共存密度值。以前的大多数努力都试图通过引入调整参数来解决此问题，调整参数的确定需要经验试验和误差，直到获得可接受的热力学一致性为止。在这项研究中，我们表明，可以通过适当设计定制的状态方程（EOS）来解决问题，该方程可以替代在计算Shan陈力中使用的有效质量时选择的任何立方EOS。介绍了一种两参数立方定制的EOS。与以前的努力相反，新EOS中的自定义参数是非经验性的，而是从求解整体机械稳定性方程式得出的，该方程式忽略了为实现严格的热力学一致性而进行任何类型的调整的需求。所提方法将模拟中共存密度和饱和压力的误差减小到最大$0.01％$ 液汽密度比在 $Ø（\mathrm{1个}）$ 至 $Ø（{10}^4）$，这在以前的任何基于调优的工作中都没有实现。还提供了一种通过定制的EOS实现所需表面张力的直接方法。