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The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers

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Abstract

In this paper, an adaptive mesh method is proposed to generate orthogonal nonuniform mesh for 2D rectangular computational domain. The algorithm adopts the dimension split idea which redistribute the mesh on each direction sequently. This approach efficiently decreases the difficultly of algorithm and enables the adapted mesh to be orthogonal. The adaptive mesh method can redistribute the mesh based on the solution without specifying the location of the boundary layer or the grid distribution function to generate the nonuniform mesh in advance. To verify the effectiveness and robustness of the algorithm, the presented method combined with the HOC difference scheme on nonuniform grid is used to solve the 1D and 2D convection diffusion problems with boundary layers. Besides, the multigrid method is used to accelerate the iterative convergence speed. The numerical solutions of adaptive mesh is more flexible than uniform or nonuniform grids methods if the location of the boundary layers is unknown in advance.

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Acknowledgements

This work was supported by the Foundation of National Nature Science Foundation of China (11361045), and the Foundation of Science of Inner Mongolia University of Science and Technology (2014QDL004).

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Authors and Affiliations

  1. School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia, 014010, China

    Fujun Cao & Dongfang Yuan

  2. Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, Ningxia, 750021, China

    Yongbin Ge

Authors
  1. Fujun Cao
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  2. Dongfang Yuan
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  3. Yongbin Ge
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Correspondence to Fujun Cao.

Additional information

Communicated by Jorge X. Velasco.

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Cao, F., Yuan, D. & Ge, Y. The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers. Comp. Appl. Math. 37, 1581–1600 (2018). https://doi.org/10.1007/s40314-016-0412-y

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  • DOI: https://doi.org/10.1007/s40314-016-0412-y

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