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

## 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.

- Authors:

- Inner Mongolia University of Science and Technology, School of Mathematics, Physics and Biological Engineering (China)
- Ningxia University, Institute of Applied Mathematics and Mechanics (China)

- Publication Date:

- OSTI Identifier:
- 22769338

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; DIFFUSION EQUATIONS; DISTRIBUTION FUNCTIONS; ITERATIVE METHODS; NUMERICAL SOLUTION

### Citation Formats

```
Cao, Fujun, Yuan, Dongfang, and Ge, Yongbin.
```*The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0412-Y.

```
Cao, Fujun, Yuan, Dongfang, & Ge, Yongbin.
```*The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers*. United States. doi:10.1007/S40314-016-0412-Y.

```
Cao, Fujun, Yuan, Dongfang, and Ge, Yongbin. Tue .
"The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers". United States. doi:10.1007/S40314-016-0412-Y.
```

```
@article{osti_22769338,
```

title = {The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers},

author = {Cao, Fujun and Yuan, Dongfang and Ge, Yongbin},

abstractNote = {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.},

doi = {10.1007/S40314-016-0412-Y},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}