Non-oscillatory central schemes for the Saint-Venant system
The research aims to develop a well-balanced numerical method for solving the shallow water equations, which account for the balance laws and the source term related to the seabed slope. The proposed method combines a Runge-Kutta scheme for accurate time integration and the natural continuous extens...
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| Format: | Article |
| Language: | English |
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Amirkabir University of Technology
2025-02-01
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| Series: | AUT Journal of Mathematics and Computing |
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| Online Access: | https://ajmc.aut.ac.ir/article_5516_d393a688621463b8a5defc5cd88efbcd.pdf |
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| _version_ | 1823858274242396160 |
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| author | Rooholah Abedian |
| author_facet | Rooholah Abedian |
| author_sort | Rooholah Abedian |
| collection | DOAJ |
| description | The research aims to develop a well-balanced numerical method for solving the shallow water equations, which account for the balance laws and the source term related to the seabed slope. The proposed method combines a Runge-Kutta scheme for accurate time integration and the natural continuous extension method for spatial discretization. To achieve high-order spatial accuracy, the method employs central non-staggered (CNS) reconstructions of the conservative variables and the water surface elevation. This is achieved through two key steps. The initial step involves determining the specific values of the flux derivative and the bed slope source term at individual points. The subsequent step entails integrating the source term spatially. Both of these steps are designed to preserve the C-property, which ensures the exact preservation of the quiescent flow solution. The method is verified using a variety of standard one-dimensional test cases, including smooth and discontinuous solutions, to demonstrate its accuracy and resolution properties. |
| format | Article |
| id | doaj-art-7bd42cf6b6324f20b22d431a9cc8e479 |
| institution | Kabale University |
| issn | 2783-2449 2783-2287 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj-art-7bd42cf6b6324f20b22d431a9cc8e4792025-02-11T12:37:04ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872025-02-01629710810.22060/ajmc.2024.22987.12125516Non-oscillatory central schemes for the Saint-Venant systemRooholah Abedian0School of Engineering Science, College of Engineering, University of Tehran, IranThe research aims to develop a well-balanced numerical method for solving the shallow water equations, which account for the balance laws and the source term related to the seabed slope. The proposed method combines a Runge-Kutta scheme for accurate time integration and the natural continuous extension method for spatial discretization. To achieve high-order spatial accuracy, the method employs central non-staggered (CNS) reconstructions of the conservative variables and the water surface elevation. This is achieved through two key steps. The initial step involves determining the specific values of the flux derivative and the bed slope source term at individual points. The subsequent step entails integrating the source term spatially. Both of these steps are designed to preserve the C-property, which ensures the exact preservation of the quiescent flow solution. The method is verified using a variety of standard one-dimensional test cases, including smooth and discontinuous solutions, to demonstrate its accuracy and resolution properties.https://ajmc.aut.ac.ir/article_5516_d393a688621463b8a5defc5cd88efbcd.pdfcentral schemesshallow water equationssource termsc-property |
| spellingShingle | Rooholah Abedian Non-oscillatory central schemes for the Saint-Venant system AUT Journal of Mathematics and Computing central schemes shallow water equations source terms c-property |
| title | Non-oscillatory central schemes for the Saint-Venant system |
| title_full | Non-oscillatory central schemes for the Saint-Venant system |
| title_fullStr | Non-oscillatory central schemes for the Saint-Venant system |
| title_full_unstemmed | Non-oscillatory central schemes for the Saint-Venant system |
| title_short | Non-oscillatory central schemes for the Saint-Venant system |
| title_sort | non oscillatory central schemes for the saint venant system |
| topic | central schemes shallow water equations source terms c-property |
| url | https://ajmc.aut.ac.ir/article_5516_d393a688621463b8a5defc5cd88efbcd.pdf |
| work_keys_str_mv | AT rooholahabedian nonoscillatorycentralschemesforthesaintvenantsystem |