Modified phase-field-based lattice Boltzmann model for incompressible multiphase flows,Physical Review E

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Modified phase-field-based lattice Boltzmann model for incompressible multiphase flows
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-17 , DOI: 10.1103/physreve.104.035305
Xingchun Xu ₁ , Yanwei Hu ₂ , Bing Dai ₁ , Lei Yang ₁ , Jiecai Han ₁ , Yurong He ₂ , Jiaqi Zhu _{1,

3}

Affiliation

Based on the phase-field theory, a multiple-relaxation-time (MRT) lattice Boltzmann model is proposed for the immiscible multiphase fluids. In this model, the local Allen-Chan equation is chosen as the target equation to capture the phase interface. Unlike previous MRT schemes, an off-diagonal relaxation matrix is adopted in the present model so that the target phase-field equation can be recovered exactly without any artificial terms. To check the necessity of removing those artificial terms, comparative studies were carried out among different MRT schemes with or without correction. Results show that the artificial terms can be neglected at low March number but will cause unphysical diffusion or interface undulation instability for the relatively large March number cases. The present modified model shows superiority in reducing numerical errors by adjusting the free parameters. As the interface transport coupled to the fluid flow, a pressure-evolution lattice Boltzmann equation is adopted for hydrodynamic properties. Several benchmark cases for multiphase flow were conducted to test the validity of the present model, including the static drop test, Rayleigh-Taylor instability, and single rising bubble test. For the rising bubble simulation at high density ratios, bubble dynamics obtained by the present modified MRT lattice Boltzmann model agree well with those obtained by the FEM-based level set and FEM-based phase-field models.

中文翻译：

不可压缩多相流的基于修正相场的晶格 Boltzmann 模型

基于相场理论，提出了不混溶多相流体的多重弛豫时间（MRT）格子Boltzmann模型。在该模型中，选择局部 Allen-Chan 方程作为目标方程来捕获相界面。与以前的 MRT 方案不同，本模型采用了非对角松弛矩阵，因此可以在没有任何人工项的情况下准确地恢复目标相场方程。为了检查去除这些人为术语的必要性，对不同的 MRT 方案进行了比较研究，有无修正。结果表明，人工项在较低的 March 数情况下可以忽略，但在较大的 March 数情况下会导致非物理扩散或界面波动不稳定。本修正模型通过调整自由参数显示出在减少数值误差方面的优越性。由于界面传输与流体流动耦合，因此流体动力学特性采用压力演化晶格玻尔兹曼方程。进行了多相流的几个基准案例来测试本模型的有效性，包括静态跌落测试、瑞利-泰勒不稳定性和单上升气泡测试。对于高密度比下的上升气泡模拟，由当前改进的 MRT 晶格 Boltzmann 模型获得的气泡动力学与基于 FEM 的水平集和基于 FEM 的相场模型获得的动力学非常吻合。进行了多相流的几个基准案例来测试本模型的有效性，包括静态跌落测试、瑞利-泰勒不稳定性和单上升气泡测试。对于高密度比下的上升气泡模拟，由当前改进的 MRT 晶格 Boltzmann 模型获得的气泡动力学与基于 FEM 的水平集和基于 FEM 的相场模型获得的动力学非常吻合。进行了多相流的几个基准案例来测试本模型的有效性，包括静态跌落测试、瑞利-泰勒不稳定性和单上升气泡测试。对于高密度比下的上升气泡模拟，由当前改进的 MRT 晶格 Boltzmann 模型获得的气泡动力学与基于 FEM 的水平集和基于 FEM 的相场模型获得的动力学非常吻合。

更新日期：2021-09-17

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