Well-balanced central finite volume methods for the Ripa system
We propose a new well-balanced central finite volume scheme for the Ripa system both in one and two space dimensions. The Ripa system is a nonhomogeneous hyperbolic system with a non-zero source term that is obtained from the shallow water equations system by incorporating horizontal temperature gra...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2015
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/8443 https://doi.org/10.1016/j.apnum.2015.07.001 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0168927415001002 |
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| _version_ | 1864513484941688832 |
|---|---|
| author | Touma, R. |
| author2 | Kingenberg, C. |
| author2_role | author |
| author_facet | Touma, R. Kingenberg, C. |
| author_role | author |
| dc.creator.none.fl_str_mv | Touma, R. Kingenberg, C. |
| dc.date.none.fl_str_mv | 2015 2018-09-07T12:58:55Z 2018-09-07T12:58:55Z 2018-09-07 |
| dc.identifier.none.fl_str_mv | 1873-5460 http://hdl.handle.net/10725/8443 https://doi.org/10.1016/j.apnum.2015.07.001 Touma, R., & Klingenberg, C. (2015). Well-balanced central finite volume methods for the Ripa system. Applied Numerical Mathematics, 97, 42-68. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0168927415001002 |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | Applied Numerical Mathematics |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | Well-balanced central finite volume methods for the Ripa system |
| dc.type.none.fl_str_mv | Article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We propose a new well-balanced central finite volume scheme for the Ripa system both in one and two space dimensions. The Ripa system is a nonhomogeneous hyperbolic system with a non-zero source term that is obtained from the shallow water equations system by incorporating horizontal temperature gradients. The proposed numerical scheme is a second-order accurate finite volume method that evolves a non-oscillatory numerical solution on a single grid, avoids the process of solving Riemann problems arising at the cell interfaces, and follows a well-balanced discretization that ensures the steady state requirement by discretizing the geometrical source term according to the discretization of the flux terms. Furthermore the proposed scheme mimics the surface gradient method and discretizes the water height according to the discretization of the water level. The proposed scheme is then applied and classical one and two-dimensional Ripa problems with flat or variable bottom topographies are successfully solved. The obtained numerical results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential and efficiency of the proposed method. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | LAURepo_bed4cb54d40126ee46cff3dca96ae7c3 |
| identifier_str_mv | 1873-5460 Touma, R., & Klingenberg, C. (2015). Well-balanced central finite volume methods for the Ripa system. Applied Numerical Mathematics, 97, 42-68. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/8443 |
| publishDate | 2015 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Well-balanced central finite volume methods for the Ripa systemTouma, R.Kingenberg, C.We propose a new well-balanced central finite volume scheme for the Ripa system both in one and two space dimensions. The Ripa system is a nonhomogeneous hyperbolic system with a non-zero source term that is obtained from the shallow water equations system by incorporating horizontal temperature gradients. The proposed numerical scheme is a second-order accurate finite volume method that evolves a non-oscillatory numerical solution on a single grid, avoids the process of solving Riemann problems arising at the cell interfaces, and follows a well-balanced discretization that ensures the steady state requirement by discretizing the geometrical source term according to the discretization of the flux terms. Furthermore the proposed scheme mimics the surface gradient method and discretizes the water height according to the discretization of the water level. The proposed scheme is then applied and classical one and two-dimensional Ripa problems with flat or variable bottom topographies are successfully solved. The obtained numerical results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential and efficiency of the proposed method.PublishedN/A2018-09-07T12:58:55Z2018-09-07T12:58:55Z20152018-09-07Articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1873-5460http://hdl.handle.net/10725/8443https://doi.org/10.1016/j.apnum.2015.07.001Touma, R., & Klingenberg, C. (2015). Well-balanced central finite volume methods for the Ripa system. Applied Numerical Mathematics, 97, 42-68.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://www.sciencedirect.com/science/article/pii/S0168927415001002enApplied Numerical Mathematicsinfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/84432021-03-19T10:43:18Z |
| spellingShingle | Well-balanced central finite volume methods for the Ripa system Touma, R. |
| status_str | publishedVersion |
| title | Well-balanced central finite volume methods for the Ripa system |
| title_full | Well-balanced central finite volume methods for the Ripa system |
| title_fullStr | Well-balanced central finite volume methods for the Ripa system |
| title_full_unstemmed | Well-balanced central finite volume methods for the Ripa system |
| title_short | Well-balanced central finite volume methods for the Ripa system |
| title_sort | Well-balanced central finite volume methods for the Ripa system |
| url | http://hdl.handle.net/10725/8443 https://doi.org/10.1016/j.apnum.2015.07.001 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0168927415001002 |