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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (5): 495-505.doi: 10.3969/j.issn.1005-3085.2016.05.005

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广义Ginzburg-Landau方程的格子Boltzmann模型

李精伟,  刘德民,  张国梁,  林玉婷   

  1. 新疆大学数学与系统科学学院，乌鲁木齐 830046
  • 收稿日期:2015-04-13 接受日期:2015-12-21 出版日期:2016-10-05 发布日期:2016-12-15
  • 基金资助:
    国家自然科学基金 (11461068)；新疆大学创新训练计划项目 (XJU-SRT-14049)；新疆大学科研基金 (BS110101).

Lattice Boltzmann Model for the Generalized Ginzburg-Landau Equation

LI Jing-wei,  LIU De-min,  ZHANG Guo-liang,  LIN Yu-ting   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046
  • Received:2015-04-13 Accepted:2015-12-21 Online:2016-10-05 Published:2016-12-15
  • Supported by:
    The National Natural Science Foundation of China (11461068); the Innovation Training Project of Xinjiang University (XJU-SRT-14049); the Scientific Research Foundation of Xinjiang University (BS110101).

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摘要： 本文为了求解广义Ginzburg-Landau方程，提出了带有附加项的五点单弛豫格子Boltzmann模型．首先通过使用Chapman-Enskog展开和Taylor展开，得到了一系列不同时间尺度的偏微分方程和平衡态分布函数的高阶矩．然后我们利用平衡态分布函数的矩方程构造了具有截断误差的格子Boltzmann模型，得到了数值耗散项，并应用Hirt启示性稳定化方法得到模型的稳定条件．最后，我们给出了广义Ginzburg-Landau方程的数值例子．数值结果表明这种方法可以用来模拟广义Ginzburg-Landau方程．

关键词: 广义Ginzburg-Landau方程, 格子Boltzmann模型, Chapman-Enskog多尺度展开, 平衡态分布函数

Abstract: In this paper, a 5-bit single relaxation lattice Boltzmann model with additional terms is proposed for solving the generalized Ginzburg-Landau equation. Firstly, by using Chapman-Enskog expansion and Taylor expansion, we obtain a series of partial differential equations in different time scales and several high-order moments of equilibrium distribution functions. Then we establish a lattice Boltzmann model with truncation error by applying a series of moments of equilibrium distribution functions and derive the numerical dissipation term. Moreover, we obtain the stability condition of the model by ultilizing the Hirt heuristic method. Finally, we provide some numerical examples of the generalized Ginzburg-Landau equation. Numerical results indicate that the method can be used to simulate the generalized Ginzburg-Landau equation.

Key words: generalized Ginzburg-Landau equation, lattice Boltzmann model, multi-scale Chapman-Enskog expansion, equilibrium distribution function

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