Well‐balanced central schemes for the Saint‐Venant systems
In this paper we present a new well‐balanced unstaggered central finite volume scheme for the numerical solution of the one‐dimensional Saint‐Venant systems on flat or variable bottom topographies. The Saint‐Venant equations also known as the shallow water equations (SWE) are useful when modeling th...
محفوظ في:
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| مؤلفون آخرون: | |
| التنسيق: | conferenceObject |
| منشور في: |
2011
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/8429 https://doi.org/10.1063/1.3636929 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://aip.scitation.org/doi/abs/10.1063/1.3636929 |
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| _version_ | 1864513484630261760 |
|---|---|
| author | Touma, R. |
| author2 | Khankan, S. |
| author2_role | author |
| author_facet | Touma, R. Khankan, S. |
| author_role | author |
| dc.creator.none.fl_str_mv | Touma, R. Khankan, S. |
| dc.date.none.fl_str_mv | 2011 2018-09-06T12:07:53Z 2018-09-06T12:07:53Z 2018-09-06 |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/8429 https://doi.org/10.1063/1.3636929 Touma, R., & Khankan, S. (2011, September). Well‐Balanced Central Schemes for the Saint‐Venant Systems. In AIP Conference Proceedings (Vol. 1389, No. 1, pp. 1664-1667). AIP. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://aip.scitation.org/doi/abs/10.1063/1.3636929 |
| dc.language.none.fl_str_mv | en |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | Well‐balanced central schemes for the Saint‐Venant systems |
| dc.type.none.fl_str_mv | Conference Paper / Proceeding info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/conferenceObject |
| description | In this paper we present a new well‐balanced unstaggered central finite volume scheme for the numerical solution of the one‐dimensional Saint‐Venant systems on flat or variable bottom topographies. The Saint‐Venant equations also known as the shallow water equations (SWE) are useful when modeling the hydrodynamics of coastal oceans and lakes and the simulation of tsunami waves and inundation floods. The Saint‐Venant system is a hyperbolic system with a nonzero geometrical source term when flows over variable bottom topographies are considered. In this work we develop a new one‐dimensional well‐balanced central scheme for the numerical solution of SWE systems: The numerical base scheme is an unstaggered extension of the 1D Nessyahu and Tadmor central scheme that evolves the numerical solution on a unique grid and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells. As is the case with general balance laws, the SWE system admits steady‐state solutions in which the nonzero divergence of the flux is exactly balanced by the source term. This balance is very difficult to maintain at the discrete level, and in general most numerical schemes for hyperbolic systems fail to preserve it, and thus generate nonphysical waves. In this work we propose a special discretization of the source term according to the discretization of the divergence of the flux by the numerical base scheme, and then adapt the surface gradient method to the case of one‐dimensional unstaggered central schemes. The resulting scheme ensures the well‐balanced constraint at the discrete level and is consistent with the SWE system. |
| eu_rights_str_mv | openAccess |
| format | conferenceObject |
| id | LAURepo_d963df2448db9e8024e54c5cb0da9c40 |
| identifier_str_mv | Touma, R., & Khankan, S. (2011, September). Well‐Balanced Central Schemes for the Saint‐Venant Systems. In AIP Conference Proceedings (Vol. 1389, No. 1, pp. 1664-1667). AIP. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/8429 |
| publishDate | 2011 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Well‐balanced central schemes for the Saint‐Venant systemsTouma, R.Khankan, S.In this paper we present a new well‐balanced unstaggered central finite volume scheme for the numerical solution of the one‐dimensional Saint‐Venant systems on flat or variable bottom topographies. The Saint‐Venant equations also known as the shallow water equations (SWE) are useful when modeling the hydrodynamics of coastal oceans and lakes and the simulation of tsunami waves and inundation floods. The Saint‐Venant system is a hyperbolic system with a nonzero geometrical source term when flows over variable bottom topographies are considered. In this work we develop a new one‐dimensional well‐balanced central scheme for the numerical solution of SWE systems: The numerical base scheme is an unstaggered extension of the 1D Nessyahu and Tadmor central scheme that evolves the numerical solution on a unique grid and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells. As is the case with general balance laws, the SWE system admits steady‐state solutions in which the nonzero divergence of the flux is exactly balanced by the source term. This balance is very difficult to maintain at the discrete level, and in general most numerical schemes for hyperbolic systems fail to preserve it, and thus generate nonphysical waves. In this work we propose a special discretization of the source term according to the discretization of the divergence of the flux by the numerical base scheme, and then adapt the surface gradient method to the case of one‐dimensional unstaggered central schemes. The resulting scheme ensures the well‐balanced constraint at the discrete level and is consistent with the SWE system.N/A2018-09-06T12:07:53Z2018-09-06T12:07:53Z20112018-09-06Conference Paper / Proceedinginfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjecthttp://hdl.handle.net/10725/8429https://doi.org/10.1063/1.3636929Touma, R., & Khankan, S. (2011, September). Well‐Balanced Central Schemes for the Saint‐Venant Systems. In AIP Conference Proceedings (Vol. 1389, No. 1, pp. 1664-1667). AIP.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://aip.scitation.org/doi/abs/10.1063/1.3636929eninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/84292021-03-19T10:43:09Z |
| spellingShingle | Well‐balanced central schemes for the Saint‐Venant systems Touma, R. |
| status_str | publishedVersion |
| title | Well‐balanced central schemes for the Saint‐Venant systems |
| title_full | Well‐balanced central schemes for the Saint‐Venant systems |
| title_fullStr | Well‐balanced central schemes for the Saint‐Venant systems |
| title_full_unstemmed | Well‐balanced central schemes for the Saint‐Venant systems |
| title_short | Well‐balanced central schemes for the Saint‐Venant systems |
| title_sort | Well‐balanced central schemes for the Saint‐Venant systems |
| url | http://hdl.handle.net/10725/8429 https://doi.org/10.1063/1.3636929 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://aip.scitation.org/doi/abs/10.1063/1.3636929 |