Entropy Schemes for One-Dimensional Convection-Diffusion Equations
In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate ent...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/3435018 |
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| author | Rongsan Chen |
| author_facet | Rongsan Chen |
| author_sort | Rongsan Chen |
| collection | DOAJ |
| description | In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy. |
| format | Article |
| id | doaj-art-8944b78cfcc8425cba62e2f7c86e7b86 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8944b78cfcc8425cba62e2f7c86e7b862025-02-03T01:03:40ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/34350183435018Entropy Schemes for One-Dimensional Convection-Diffusion EquationsRongsan Chen0School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, ChinaIn this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy.http://dx.doi.org/10.1155/2020/3435018 |
| spellingShingle | Rongsan Chen Entropy Schemes for One-Dimensional Convection-Diffusion Equations Complexity |
| title | Entropy Schemes for One-Dimensional Convection-Diffusion Equations |
| title_full | Entropy Schemes for One-Dimensional Convection-Diffusion Equations |
| title_fullStr | Entropy Schemes for One-Dimensional Convection-Diffusion Equations |
| title_full_unstemmed | Entropy Schemes for One-Dimensional Convection-Diffusion Equations |
| title_short | Entropy Schemes for One-Dimensional Convection-Diffusion Equations |
| title_sort | entropy schemes for one dimensional convection diffusion equations |
| url | http://dx.doi.org/10.1155/2020/3435018 |
| work_keys_str_mv | AT rongsanchen entropyschemesforonedimensionalconvectiondiffusionequations |