Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation
Abstract A fourth-order compact finite difference scheme of the two-dimensional convection–diffusion equation is proposed to solve groundwater pollution problems. A suitable scheme is constructed to simulate the law of movement of pollutants in the medium, which is spatially fourth-order accurate an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1652-5 |
| _version_ | 1818510742680240128 |
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| author | Lingyu Li Ziwen Jiang Zhe Yin |
| author_facet | Lingyu Li Ziwen Jiang Zhe Yin |
| author_sort | Lingyu Li |
| collection | DOAJ |
| description | Abstract A fourth-order compact finite difference scheme of the two-dimensional convection–diffusion equation is proposed to solve groundwater pollution problems. A suitable scheme is constructed to simulate the law of movement of pollutants in the medium, which is spatially fourth-order accurate and temporally second-order accurate. The matrix form and solving methods for the linear system of equations are discussed. The theoretical analysis of unconditionally stable character of the scheme is verified by the Fourier amplification factor method. Numerical experiments are given to demonstrate the efficiency and accuracy of the scheme proposed, and these show excellent agreement with the exact solution. |
| first_indexed | 2024-12-10T23:24:12Z |
| format | Article |
| id | doaj.art-a0021ab42947406a883a11a8dbfa93dc |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T23:24:12Z |
| publishDate | 2018-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a0021ab42947406a883a11a8dbfa93dc2022-12-22T01:29:37ZengSpringerOpenAdvances in Difference Equations1687-18472018-07-012018112410.1186/s13662-018-1652-5Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equationLingyu Li0Ziwen Jiang1Zhe Yin2College of Mathematics and Statistics, Shandong Normal UniversityCollege of Mathematics and Statistics, Shandong Normal UniversityCollege of Mathematics and Statistics, Shandong Normal UniversityAbstract A fourth-order compact finite difference scheme of the two-dimensional convection–diffusion equation is proposed to solve groundwater pollution problems. A suitable scheme is constructed to simulate the law of movement of pollutants in the medium, which is spatially fourth-order accurate and temporally second-order accurate. The matrix form and solving methods for the linear system of equations are discussed. The theoretical analysis of unconditionally stable character of the scheme is verified by the Fourier amplification factor method. Numerical experiments are given to demonstrate the efficiency and accuracy of the scheme proposed, and these show excellent agreement with the exact solution.http://link.springer.com/article/10.1186/s13662-018-1652-5Convection–diffusion equationCompact finite difference methodFourth-order accuracyNumerical experiments |
| spellingShingle | Lingyu Li Ziwen Jiang Zhe Yin Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation Advances in Difference Equations Convection–diffusion equation Compact finite difference method Fourth-order accuracy Numerical experiments |
| title | Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation |
| title_full | Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation |
| title_fullStr | Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation |
| title_full_unstemmed | Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation |
| title_short | Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation |
| title_sort | fourth order compact finite difference method for solving two dimensional convection diffusion equation |
| topic | Convection–diffusion equation Compact finite difference method Fourth-order accuracy Numerical experiments |
| url | http://link.springer.com/article/10.1186/s13662-018-1652-5 |
| work_keys_str_mv | AT lingyuli fourthordercompactfinitedifferencemethodforsolvingtwodimensionalconvectiondiffusionequation AT ziwenjiang fourthordercompactfinitedifferencemethodforsolvingtwodimensionalconvectiondiffusionequation AT zheyin fourthordercompactfinitedifferencemethodforsolvingtwodimensionalconvectiondiffusionequation |