A lattice Boltzmann (LB) model is proposed to track the interface of binary fluid system based on the conservative-form Allen-Cahn (A-C) equation for phase field. Utilizing an equilibrium distribution function and a modified LB equation, this model is able to correctly recover the conservative A-C equation through the Chapman-Enskog analysis. A series of two-dimensional (2D) and three-dimensional (3D) phase-capturing benchmark tests have been conducted for validation, which include the diagonal translation of a circular interface, the rigid-body rotation of a Zalesak disk, and the deformation of 2D circular interface and 3D spherical interface in shear flows, all illustrating better accuracy and stability of the proposed model than the previous models tested. By coupling the incompressible hydrodynamic equation, a stationary droplet, a spinodal decomposition, and the Rayleigh-Taylor instability are simulated as well, showing the satisfying performance of the model in dealing with complex interfaces of binary fluid systems.

中文翻译：

---

基于Allen-Cahn方程的二元流体系统界面跟踪的相场格子Boltzmann模型

提出了一种格子Boltzmann（LB）模型，该模型基于相场的保守形式Allen-Cahn（AC）方程来跟踪二元流体系统的界面。利用平衡分布函数和修正的LB方程，该模型能够通过Chapman-Enskog分析正确地恢复保守的AC方程。为了验证，已进行了一系列的二维（2D）和三维（3D）相位捕获基准测试，包括圆形界面的对角平移，Zalesak圆盘的刚体旋转以及变形2D圆形界面和3D球形界面在剪切流中的分布，都说明了该模型比以前测试的模型具有更好的精度和稳定性。通过耦合不可压缩的流体动力学方程，固定液滴