A new central-upwind scheme for solving the shallow water equations
We have conducted a study where we applied one-dimensional central-upwind methods to estimate solutions of the Saint-Venant (SV) system. Our approach carefully considers the source terms associated with bottom topography. Within the context of the SV system, there are steady-state solutions that ari...
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Amirkabir University of Technology
2025-07-01
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| Series: | AUT Journal of Mathematics and Computing |
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| Online Access: | https://ajmc.aut.ac.ir/article_5515_39ab77ec814706265372bc805215b79a.pdf |
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| author | Rooholah Abedian |
| author_facet | Rooholah Abedian |
| author_sort | Rooholah Abedian |
| collection | DOAJ |
| description | We have conducted a study where we applied one-dimensional central-upwind methods to estimate solutions of the Saint-Venant (SV) system. Our approach carefully considers the source terms associated with bottom topography. Within the context of the SV system, there are steady-state solutions that arise when the non-zero gradients of flux are exactly balanced by the corresponding source terms. Maintaining this delicate equilibrium with numerical approaches presents a challenging problem. Finding slight variations in these states proves to be extremely difficult in the field of computing. To address this, we propose an extension of semi-discrete central schemes, commonly employed in hyperbolic conservation law systems, to encompass balance laws (BL). In our approach, we specifically focus on discretizing the source term with great care and attention. To verify the superior accuracy, precise preservation of the C-property, and outstanding resolution of our approach, we perform comprehensive one-dimensional simulations on both continuous and discontinuous solutions. |
| format | Article |
| id | doaj-art-0dff80eb86fc4c249f7309fc124324a0 |
| institution | OA Journals |
| issn | 2783-2449 2783-2287 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj-art-0dff80eb86fc4c249f7309fc124324a02025-08-20T02:02:47ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872025-07-016319320310.22060/ajmc.2023.22640.11825515A new central-upwind scheme for solving the shallow water equationsRooholah Abedian0School of Engineering Science, College of Engineering, University of Tehran, IranWe have conducted a study where we applied one-dimensional central-upwind methods to estimate solutions of the Saint-Venant (SV) system. Our approach carefully considers the source terms associated with bottom topography. Within the context of the SV system, there are steady-state solutions that arise when the non-zero gradients of flux are exactly balanced by the corresponding source terms. Maintaining this delicate equilibrium with numerical approaches presents a challenging problem. Finding slight variations in these states proves to be extremely difficult in the field of computing. To address this, we propose an extension of semi-discrete central schemes, commonly employed in hyperbolic conservation law systems, to encompass balance laws (BL). In our approach, we specifically focus on discretizing the source term with great care and attention. To verify the superior accuracy, precise preservation of the C-property, and outstanding resolution of our approach, we perform comprehensive one-dimensional simulations on both continuous and discontinuous solutions.https://ajmc.aut.ac.ir/article_5515_39ab77ec814706265372bc805215b79a.pdfsaint-venant systemcentral-upwind methodsbalance lawshyperbolic conservation laws |
| spellingShingle | Rooholah Abedian A new central-upwind scheme for solving the shallow water equations AUT Journal of Mathematics and Computing saint-venant system central-upwind methods balance laws hyperbolic conservation laws |
| title | A new central-upwind scheme for solving the shallow water equations |
| title_full | A new central-upwind scheme for solving the shallow water equations |
| title_fullStr | A new central-upwind scheme for solving the shallow water equations |
| title_full_unstemmed | A new central-upwind scheme for solving the shallow water equations |
| title_short | A new central-upwind scheme for solving the shallow water equations |
| title_sort | new central upwind scheme for solving the shallow water equations |
| topic | saint-venant system central-upwind methods balance laws hyperbolic conservation laws |
| url | https://ajmc.aut.ac.ir/article_5515_39ab77ec814706265372bc805215b79a.pdf |
| work_keys_str_mv | AT rooholahabedian anewcentralupwindschemeforsolvingtheshallowwaterequations AT rooholahabedian newcentralupwindschemeforsolvingtheshallowwaterequations |