On the formulations of interfacial force in the phase-field-based lattice Boltzmann method,International Journal for Numerical Methods in Fluids

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On the formulations of interfacial force in the phase-field-based lattice Boltzmann method
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-02-24 , DOI: 10.1002/fld.4971
Chunhua Zhang ₁ , Zhaoli Guo ₁ , Hong Liang ₂

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Different formulations of interfacial force have been adopted in the existing phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation errors at discrete level. In this article, four-type formulations of interfacial force available in the literature, namely, stress tensor form (STF), chemical potential form (CPF), pressure form, and continuum surface force (CSF) form, are summarized and theoretical analyzed. A systematic study of the performances of all formulations is made by a series of benchmark problems, including stationary droplet, two merging droplets, Capillary wave, rising bubble and drop deformation in shear flow. Numerical results show that CPF is a good choice for small surface deformation problems while STF is preferred for dynamical problems, both STF and CSF presents better numerical stability in terms of Peclet number.

中文翻译：

基于相场的晶格玻尔兹曼方法中界面力的公式化

在现有的基于相场的两相流晶格玻尔兹曼方法中采用了不同的界面力公式。尽管它们在数学上是相同的，但由于离散级别的截断误差，它们的数值性能可能会有所不同。本文总结并理论分析了文献中可用的四种界面力公式，即应力张量形式 (STF)、化学势形式 (CPF)、压力形式和连续表面力 (CSF) 形式。通过一系列基准问题，包括静止液滴、两个合并液滴、毛细管波、上升气泡和剪切流中的液滴变形，对所有配方的性能进行了系统研究。

更新日期：2021-02-24

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