School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan, 430074, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China.
Phys Rev E. 2023 Mar;107(3-2):035308. doi: 10.1103/PhysRevE.107.035308.
In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.
在这项工作中，我们开发了一种改进的基于相场的格子玻尔兹曼（LB）方法，其中使用混合 Allen-Cahn 方程（ACE）和灵活的权重代替全局权重来抑制数值弥散并消除粗化现象。然后采用两种 LB 模型分别求解混合 ACE 和纳维-斯托克斯方程。通过 Chapman-Enskog 分析，本 LB 模型可以正确恢复混合 ACE，并且可以显式计算用于标记不同相的宏观序参量。最后，通过五个测试验证了本 LB 方法的有效性，包括圆形界面的对角平移、两个不同半径的静止气泡、在重力作用下上升的气泡、二维和三维的瑞利-泰勒不稳定性以及三维的 Plateau-Rayleigh 不稳定性。数值结果表明，本 LB 方法在减少数值弥散和粗化现象方面具有优异的性能。
