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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 ›› 2021, Vol. 38 ›› Issue (6): 869-878.doi: 10.3969/j.issn.1005-3085.2021.06.009

• • 上一篇    下一篇

二维抛物型奇异摄动问题的移动网格方法

周   琴   

  1. 湖南涉外经济学院信息与机电工程学院，长沙 410205
  • 出版日期:2021-12-15 发布日期:2022-02-15
  • 基金资助:
    湖南省教育厅资助科研项目 (21B0826)；湖南省普通高校省级一流本科课程项目 (2019-370; 2020-741).

A Moving Mesh Method for Two Dimensional Parabolic Singularly Perturbed Problems

ZHOU Qin   

  1. School of Information, Mechanical and Electrical Engineering, Hunan International Economics University, Changsha 410205
  • Online:2021-12-15 Published:2022-02-15

PDF (PC)

103

摘要：

奇异摄动问题在力学、声学、光学、工程等领域有广泛的应用。研究了一类含源项二维抛物型奇异摄动问题，通过坐标变换和有限体积方法，构造了该问题在空间移动网格上的数值格式，给出了网格移动时的网格迭代方法和解的更新方法，提出了局部加密的自适应移动网格算法。数值实验的结果表明，与均匀网格上求解的结果相比，自适应移动网格方法能更好地体现解在局部区域的特性，具有更理想的求解精度。

关键词: 奇异摄动, 抛物型问题, 自适应移动网格, 网格迭代

Abstract:

Singular perturbation problems have been applied in various areas of mechanics, acoustics, optics, engineering and others. A class of two-dimensional parabolic singular perturbation problem with source terms is considered. The numerical scheme of the problem on spatial moving meshes is constructed by means of coordinate transformation and finite volume method. The mesh iteration method and updating method of solution on moving mesh are given, and an adaptive moving mesh algorithm with local refinement is proposed. The numerical results show that, compared with the solution on uniform mesh, the adaptive moving mesh method can reflect the local characteristics of the solution better and has better solution accuracy.

Key words: singular perturbation, parabolic problems, adaptive moving mesh, mesh iteration

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