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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (12): 17-25.doi: 10.6040/j.issn.1671-9352.0.2021.327

• • 上一篇    

基于自适应移动网格的Cahn-Hilliard方程的有限元法

卢长娜,常胜祥   

  1. 南京信息工程大学数学与统计学院, 江苏 南京 210044
  • 发布日期:2021-11-25
  • 作者简介:卢长娜(1980— ),女,博士,副教授,硕士生导师,研究方向为微分方程数值解.E-mail:luchangna@nuist.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11801280);江苏省自然科学基金资助项目(BK20180780)

Finite element method of Cahn-Hilliard equation based on adaptive moving mesh method

LU Chang-na, CHANG Sheng-xiang   

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
  • Published:2021-11-25

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摘要： 针对二维Cahn-Hilliard方程,使用自适应移动网格,建立有限元数值模型。由于Cahn-Hilliard方程在初期变换迅速,且在后期变化缓慢,使用基于移动网格偏微分方程(moving mesh partial differential equation,MMPDE)的移动网格准则能够更好地捕捉相变的过程。在移动网格上,对空间方向使用线性有限元离散,对时间方向使用五阶Radau IIA格式离散。数值结果表明在移动网格下的数值解能够很好地保持原方程固有的质量守恒与能量稳定定律,提高计算效率,验证了该方法的有效性和可行性。

关键词: 线性有限元, 自适应移动网格, Cahn-Hilliard方程, 能量稳定

Abstract: A finite element method is proposed for the two-dimensional Cahn-Hilliard equation based on the adaptive moving mesh. Since the Cahn-Hilliard equation changes rapidly in the initial stage and slowly changes in the later stage, the use of the moving mesh rule based on the moving mesh partial differential equation(MMPDE)can better capture the phase diagram. The method is discretized by using linear finite element in space and fifth-order Radau IIA scheme in time. Numerical results shows that the numerical solution can well maintain the law of conservation of mass and the law of energy stability, and improve the calculation efficiency, which verifies the effectiveness and feasibility of the method.

Key words: linear finite element, adaptive moving mesh, Cahn-Hilliard equation, energy stability

中图分类号: 

  • O242.21
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