Interface-capturing lattice Boltzmann equation model for two-phase flows
Interface-capturing lattice Boltzmann equation model for two-phase flows
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DOI：
10.1103/physreve.91.013302
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发表时间：
2015-01-07
影响因子：
2.4
通讯作者：
Guo, Zhaoli
中科院分区：
文献类型：
--
作者：
Lou, Qin;Guo, Zhaoli
在这项工作中，界面捕获格子玻尔兹曼方程（LBE）模型提出的两相流。在模型中，Lax-Wendroff传播方案和适当选择的平衡分布函数。采用Lax-Wendroff格式提供可调的Courant-Friedrichs-Lewy（CFL）数，并给出平衡分布以消除弛豫时间对CFL数的依赖性.结果，可以通过减少CFL数来准确地捕获界面。通过直接求解具有平坦界面的两相系统的LBE，导出了化学势梯度的理论表达式。结果表明，化学势的梯度与CFL数的平方成正比，这解释了为什么该模型能够在小CFL数下自然地捕捉到界面，以及为什么标准LBE模型存在较大的界面误差.数值试验，包括一维平坦界面问题，二维圆形液滴问题，和三维球形液滴问题，表明所提出的LBE模型表现良好，可以捕捉到一个尖锐的界面与适当的CFL数.
In this work, an interface-capturing lattice Boltzmann equation (LBE) model is proposed for two-phase flows. In the model, a Lax-Wendroff propagation scheme and a properly chosen equilibrium distribution function are employed. The Lax-Wendroff scheme is used to provide an adjustable Courant-Friedrichs-Lewy (CFL) number, and the equilibrium distribution is presented to remove the dependence of the relaxation time on the CFL number. As a result, the interface can be captured accurately by decreasing the CFL number. A theoretical expression is derived for the chemical potential gradient by solving the LBE directly for a two-phase system with a flat interface. The result shows that the gradient of the chemical potential is proportional to the square of the CFL number, which explains why the proposed model is able to capture the interface naturally with a small CFL number, and why large interface error exists in the standard LBE model. Numerical tests, including a one-dimensional flat interface problem, a two-dimensional circular droplet problem, and a three-dimensional spherical droplet problem, demonstrate that the proposed LBE model performs well and can capture a sharp interface with a suitable CFL number.