Recently it was discovered that altering the shape of the meta stable and unstable branches of an equation of state (EOS) can greatly improve the numerical accuracy of liquid and gas densities in the pseudopotential method. Inspired by this approach we develop an improved approach that is benchmarked for both equilibrium and non-equilibrium situations. We show here that the original approach reduces the method stability in non-equilibrium situations. Here we propose a new procedure to replace the metastable and unstable regions of these EOS by alternative functions. Our approach does not affects the coexistence densities or the speed of sound of the liquid phase while maintaining continuity of the sound speed in the pressure-density curve. Using this approach we were able to reduce the relative error of the planar interface vapor density compared to the thermodynamic consistent value by increasing the vapor phase sound speed. To allow for the benchmarking of dynamic results we also developed a finite difference method (FD) that solves the same macroscopic conservation equation as the pseudopotential lattice Boltzmann method (LBM). With this FD scheme we are able to perform mesh refinement and obtain reference solutions for the dynamic tests. We observed excellent agreement between the FD solutions and our proposed scheme. We also performed a detailed study of the stability of the methods using simulations of a droplet impacting on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remains stable for a density ratio up to $3.38\cdot10^{4}$.
Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows
赝势格子Boltzmann（LB）模型是LB界中用于模拟多相流的流行模型。近年来，基于赝势LB模型和双分布函数LB方法，提出了几种热LB模型来模拟热多相流[G. Házi和A. Márkus，Phys.Rev.E77，026305（2008）; L. Biferale等人，物理修订版信函108，104502（2012）; S. Gong和P. Cheng，Int. J. Heat Mass Transfer 55，4923（2012）]。本文的目的是表明，在热流的赝势LB模拟中，必须消除强迫项对温度方程的影响。首先，通过Chapman-Enskog分析显示了强迫项对温度方程的影响。为了比较，提供了不受强迫项影响的替代治疗。随后，数值研究进行了两个基准测试。数值结果清楚地表明，强迫项效应的存在将导致显着的数值误差的赝势LB模型的热流。
Simulations of inertial liquid-lens coalescence with the pseudopotential lattice Boltzmann method
Forschungszentrum Jülich（于利希研究中心）；Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2)（亥姆霍兹埃尔朗根-纽伦堡可再生能源研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
A quantitative comparison of physical accuracy and numerical stability of Lattice Boltzmann color gradient and pseudopotential multicomponent models for microfluidic applications
Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability
基于改进的赝势LB方法，提出了一种模拟热多相流相变的混合热格子Boltzmann（LB）模型。Li，K. H. Luo和X. J. Li，Phys.Rev.E87，053301（2013）]。本模型不受杂散项所造成的强迫项的影响，这是遇到了一些以前的热LB模型的液-汽相变。利用该模型对汽液沸腾过程进行了模拟。沸腾曲线连同三个沸腾阶段（核态沸腾，过渡沸腾，和膜沸腾）的数值再现在LB社区的第一次。数值结果表明，该模型较好地反映了沸腾传热的基本特征和基本特性，如过渡沸腾过程中瞬态热流密度的剧烈波动和最大传热系数位于比最大热流密度更低的壁面处等。此外，还研究了加热表面润湿性对沸腾传热的影响。结果表明，随着接触角的增大，沸腾的起始温度升高，但临界热流密度降低，沸腾过程在较低的壁厚处进入膜态沸腾，这与实验结果一致。
