A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid
We develop here a new formulation of the two-layer shallow water equations with rigid-lid on variable-bottom topography. This formulation is presented as a conservative system where the function describing the geometry of the waterbed or bottom topography is embedded within the divergence of the flu...
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2025
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| Online Access: | http://hdl.handle.net/10725/16622 https://doi.org/10.1007/978-981-97-8152-2_2 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/chapter/10.1007/978-981-97-8152-2_2 |
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| _version_ | 1864513473225949184 |
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| author | Touma, Rony |
| author2 | Lteif, Ralph |
| author2_role | author |
| author_facet | Touma, Rony Lteif, Ralph |
| author_role | author |
| dc.contributor.none.fl_str_mv | Zeidan, Dia Hidalgo, Arturo Zhang, Lucy T. Da Silva, Eric Goncalves |
| dc.creator.none.fl_str_mv | Touma, Rony Lteif, Ralph |
| dc.date.none.fl_str_mv | 2025-02-21T10:46:48Z 2025-02-21T10:46:48Z 2025 2025-02-07 |
| dc.identifier.none.fl_str_mv | 9789819781522 http://hdl.handle.net/10725/16622 https://doi.org/10.1007/978-981-97-8152-2_2 Touma, R., & Lteif, R. (2025). A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid. In Computational Fluid Dynamics: Novel Numerical and Computational Approaches: Methodology and Numerics (pp. 25-57). Singapore: Springer Nature Singapore. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/chapter/10.1007/978-981-97-8152-2_2 |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Springer |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Computational fluid dynamics |
| dc.title.none.fl_str_mv | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| dc.type.none.fl_str_mv | Book / Chapter of a Book info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/bookPart |
| description | We develop here a new formulation of the two-layer shallow water equations with rigid-lid on variable-bottom topography. This formulation is presented as a conservative system where the function describing the geometry of the waterbed or bottom topography is embedded within the divergence of the flux term. The resulting system is then solved using an adaptation of the unstaggered central scheme (UCS) we previously developed. To satisfy the lake-at-rest physical constraint, we blend the surface gradient method (SGM) with our UCS scheme. The resulting UCS-SGM scheme is then validated and successfully implemented, representing an extension of the method previously presented for shallow water equations (one-layer flow) to address the complexities of two-layer rigid-lid flows while ensuring well-balanced characteristics. The performed numerical tests confirm the potential of the proposed method to handle two-layer flow problems on either smooth or non-smooth bottom topographies and also to handle steady- and unsteady-state flow problems. |
| eu_rights_str_mv | openAccess |
| format | bookPart |
| id | LAURepo_eba4dc7b653941ee815031d7f1b52e8a |
| identifier_str_mv | 9789819781522 Touma, R., & Lteif, R. (2025). A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid. In Computational Fluid Dynamics: Novel Numerical and Computational Approaches: Methodology and Numerics (pp. 25-57). Singapore: Springer Nature Singapore. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/16622 |
| publishDate | 2025 |
| publisher.none.fl_str_mv | Springer |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid LidTouma, RonyLteif, RalphComputational fluid dynamicsWe develop here a new formulation of the two-layer shallow water equations with rigid-lid on variable-bottom topography. This formulation is presented as a conservative system where the function describing the geometry of the waterbed or bottom topography is embedded within the divergence of the flux term. The resulting system is then solved using an adaptation of the unstaggered central scheme (UCS) we previously developed. To satisfy the lake-at-rest physical constraint, we blend the surface gradient method (SGM) with our UCS scheme. The resulting UCS-SGM scheme is then validated and successfully implemented, representing an extension of the method previously presented for shallow water equations (one-layer flow) to address the complexities of two-layer rigid-lid flows while ensuring well-balanced characteristics. The performed numerical tests confirm the potential of the proposed method to handle two-layer flow problems on either smooth or non-smooth bottom topographies and also to handle steady- and unsteady-state flow problems.vii, 217 pages : illustrations (chiefly color).Includes bibliographical references.SpringerZeidan, DiaHidalgo, ArturoZhang, Lucy T.Da Silva, Eric Goncalves2025-02-21T10:46:48Z2025-02-21T10:46:48Z20252025-02-07Book / Chapter of a Bookinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart9789819781522http://hdl.handle.net/10725/16622https://doi.org/10.1007/978-981-97-8152-2_2Touma, R., & Lteif, R. (2025). A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid. In Computational Fluid Dynamics: Novel Numerical and Computational Approaches: Methodology and Numerics (pp. 25-57). Singapore: Springer Nature Singapore.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://link.springer.com/chapter/10.1007/978-981-97-8152-2_2eninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/166222025-02-21T10:51:03Z |
| spellingShingle | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid Touma, Rony Computational fluid dynamics |
| status_str | publishedVersion |
| title | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| title_full | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| title_fullStr | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| title_full_unstemmed | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| title_short | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| title_sort | A Central Finite Volume Surface Gradient Method for the Two-Layer Shallow Water Equations with Rigid Lid |
| topic | Computational fluid dynamics |
| url | http://hdl.handle.net/10725/16622 https://doi.org/10.1007/978-981-97-8152-2_2 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://link.springer.com/chapter/10.1007/978-981-97-8152-2_2 |