Well-balanced central schemes for systems of shallow water equations with wet and dry states
In this paper we propose a new well-balanced unstaggered central finite volume scheme for the shallow water equations on variable bottom topographies, with wet and dry states. Based on a special piecewise linear reconstruction of the cell-centered numerical solution and a careful discretization of t...
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| المؤلف الرئيسي: | |
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| التنسيق: | article |
| منشور في: |
2016
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/8438 https://doi.org/10.1016/j.apm.2015.09.073 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0307904X15006071 |
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| _version_ | 1864513484936445952 |
|---|---|
| author | Touma, R. |
| author_facet | Touma, R. |
| author_role | author |
| dc.creator.none.fl_str_mv | Touma, R. |
| dc.date.none.fl_str_mv | 2016 2018-09-07T10:03:59Z 2018-09-07T10:03:59Z 2018-09-07 |
| dc.identifier.none.fl_str_mv | 1873-5460 http://hdl.handle.net/10725/8438 https://doi.org/10.1016/j.apm.2015.09.073 Touma, R. (2016). Well-balanced central schemes for systems of shallow water equations with wet and dry states. Applied Mathematical Modelling, 40(4), 2929-2945. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0307904X15006071 |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | Applied Mathematical Modelling |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| dc.type.none.fl_str_mv | Article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this paper we propose a new well-balanced unstaggered central finite volume scheme for the shallow water equations on variable bottom topographies, with wet and dry states. Based on a special piecewise linear reconstruction of the cell-centered numerical solution and a careful discretization of the system of partial differential equations, the proposed numerical scheme ensures both a well-balanced discretization and the positivity requirement of the water height component. More precisely, the well-balanced requirement is fulfilled by following the surface gradient method, while the positivity requirement of the computed water height component is ensured by following a new technique specially designed for the unstaggered central schemes. The developed scheme is then validated and classical shallow water equation problems on variable bottom topographies with wet and dry states are successfully solved. The reported numerical results confirm the potential and efficiency of the proposed method |
| eu_rights_str_mv | openAccess |
| format | article |
| id | LAURepo_9b44bfd6d145c7b28958f726cb39b060 |
| identifier_str_mv | 1873-5460 Touma, R. (2016). Well-balanced central schemes for systems of shallow water equations with wet and dry states. Applied Mathematical Modelling, 40(4), 2929-2945. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/8438 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Well-balanced central schemes for systems of shallow water equations with wet and dry statesTouma, R.In this paper we propose a new well-balanced unstaggered central finite volume scheme for the shallow water equations on variable bottom topographies, with wet and dry states. Based on a special piecewise linear reconstruction of the cell-centered numerical solution and a careful discretization of the system of partial differential equations, the proposed numerical scheme ensures both a well-balanced discretization and the positivity requirement of the water height component. More precisely, the well-balanced requirement is fulfilled by following the surface gradient method, while the positivity requirement of the computed water height component is ensured by following a new technique specially designed for the unstaggered central schemes. The developed scheme is then validated and classical shallow water equation problems on variable bottom topographies with wet and dry states are successfully solved. The reported numerical results confirm the potential and efficiency of the proposed methodPublishedN/A2018-09-07T10:03:59Z2018-09-07T10:03:59Z20162018-09-07Articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1873-5460http://hdl.handle.net/10725/8438https://doi.org/10.1016/j.apm.2015.09.073Touma, R. (2016). Well-balanced central schemes for systems of shallow water equations with wet and dry states. Applied Mathematical Modelling, 40(4), 2929-2945.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://www.sciencedirect.com/science/article/pii/S0307904X15006071enApplied Mathematical Modellinginfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/84382021-03-19T10:43:18Z |
| spellingShingle | Well-balanced central schemes for systems of shallow water equations with wet and dry states Touma, R. |
| status_str | publishedVersion |
| title | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| title_full | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| title_fullStr | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| title_full_unstemmed | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| title_short | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| title_sort | Well-balanced central schemes for systems of shallow water equations with wet and dry states |
| url | http://hdl.handle.net/10725/8438 https://doi.org/10.1016/j.apm.2015.09.073 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0307904X15006071 |