Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations
We present in this thesis a new well-balanced unstaggered central scheme for computing the transport of pollutants in water flows. The shallow water equations are used to model the water flow, and a transport equation is used to model the propagation of the pollutant. Our proposed scheme avoids the...
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| Format: | masterThesis |
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2020
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| Online Access: | http://hdl.handle.net/10725/13475 https://doi.org/10.26756/th.2022.311 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
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| _version_ | 1864513490750799872 |
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| author | Abou Saleh, Mira |
| author_facet | Abou Saleh, Mira |
| author_role | author |
| dc.creator.none.fl_str_mv | Abou Saleh, Mira |
| dc.date.none.fl_str_mv | 2020 2020-07-28 2022-04-12T06:27:11Z 2022-04-12T06:27:11Z |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/13475 https://doi.org/10.26756/th.2022.311 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Lebanese American University |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Pollution -- Mathematical models Water -- Pollution -- Mathematical models Wave equation -- Numerical solutions Finite element method Dam failures -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| dc.title.none.fl_str_mv | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | We present in this thesis a new well-balanced unstaggered central scheme for computing the transport of pollutants in water flows. The shallow water equations are used to model the water flow, and a transport equation is used to model the propagation of the pollutant. Our proposed scheme avoids the resolution of Riemann problems arising at the cell interfaces; it is second order accurate in space and time, evolves the numerical solution on a single grid and benefits from the non-dissipativeness of the particle method. Our scheme is also well-balanced due to a special discretization of the source term with the surface gradient method. We implement the proposed scheme and solve some selected problems featuring transport of pollutant. Accurate pollutant’s location and concentration are observed and reported in the numerical test cases. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_fd2bc680301420cecb0b9c8166d86e24 |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/13475 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water EquationsAbou Saleh, MiraPollution -- Mathematical modelsWater -- Pollution -- Mathematical modelsWave equation -- Numerical solutionsFinite element methodDam failures -- Mathematical modelsLebanese American University -- DissertationsDissertations, AcademicWe present in this thesis a new well-balanced unstaggered central scheme for computing the transport of pollutants in water flows. The shallow water equations are used to model the water flow, and a transport equation is used to model the propagation of the pollutant. Our proposed scheme avoids the resolution of Riemann problems arising at the cell interfaces; it is second order accurate in space and time, evolves the numerical solution on a single grid and benefits from the non-dissipativeness of the particle method. Our scheme is also well-balanced due to a special discretization of the source term with the surface gradient method. We implement the proposed scheme and solve some selected problems featuring transport of pollutant. Accurate pollutant’s location and concentration are observed and reported in the numerical test cases.1 online resource (xi, 71 leaves) : col. ill.Bibliography: leaf 68-71.Lebanese American University2022-04-12T06:27:11Z2022-04-12T06:27:11Z20202020-07-28Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/13475https://doi.org/10.26756/th.2022.311http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/134752022-07-13T08:56:46Z |
| spellingShingle | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations Abou Saleh, Mira Pollution -- Mathematical models Water -- Pollution -- Mathematical models Wave equation -- Numerical solutions Finite element method Dam failures -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| status_str | publishedVersion |
| title | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| title_full | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| title_fullStr | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| title_full_unstemmed | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| title_short | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| title_sort | Well-Balanced Unstaggered Central Schemes for Models of Transport of Pollutant in Shallow Water Equations |
| topic | Pollution -- Mathematical models Water -- Pollution -- Mathematical models Wave equation -- Numerical solutions Finite element method Dam failures -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| url | http://hdl.handle.net/10725/13475 https://doi.org/10.26756/th.2022.311 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |