Well-balanced central schemes for the One-dimensional shallow water equations
This thesis presents and contrasts two unique Unstaggered Central Scheme (UCS)’s for hyperbolic systems, specifically Shallow Water Equations (SWE): an Unstaggered Central Scheme with the Subraction Method (UCS-Sub) and an Unstaggered Central Weighted Essentially Non-Oscillatory Scheme with the Subt...
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| Format: | masterThesis |
| Published: |
2023
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| Online Access: | http://hdl.handle.net/10725/15795 https://doi.org/10.26756/th.2023.658 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
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| _version_ | 1864513471739068416 |
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| author | Malaeb, Elissa |
| author_facet | Malaeb, Elissa |
| author_role | author |
| dc.creator.none.fl_str_mv | Malaeb, Elissa |
| dc.date.none.fl_str_mv | 2023 2023-11-24 2024-06-24T08:07:02Z 2024-06-24T08:07:02Z |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/15795 https://doi.org/10.26756/th.2023.658 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 | Lebanese American University--Dissertations Dissertations, Academic Fluid dynamics--Mathematical models Differential equations, Hyperbolic--Numerical solutions Wave equation--Numerical solutions |
| dc.title.none.fl_str_mv | Well-balanced central schemes for the One-dimensional shallow water equations |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | This thesis presents and contrasts two unique Unstaggered Central Scheme (UCS)’s for hyperbolic systems, specifically Shallow Water Equations (SWE): an Unstaggered Central Scheme with the Subraction Method (UCS-Sub) and an Unstaggered Central Weighted Essentially Non-Oscillatory Scheme with the Subtraction Method (UCWENO-Sub). Both schemes are made to protect the hyperbolic systems’ well-balanced (WB) characteristic, which keeps Steady state (SS) solutions immobile. This is made possible by implementing the subtraction method (SM), which effectively removes spurious numerical oscillations. Unstaggered schemes do not require the computationally costly step of solving Riemann problems at cell interfaces, which is a requirement of standard staggered systems. This results in notable efficiency gains. We perform an extensive comparison between UCS-Sub and UCWENO-Sub on several benchmark tasks to assess their respective performances. The outcomes show that both techniques are useful for approximating solutions to hyperbolic systems; while UCWENO-Sub gives priority to higher-order accuracy, they both strike a balance between simplicity, efficiency, and accuracy. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_631bb4a89c3ef129a3dd5fda46a159e1 |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/15795 |
| publishDate | 2023 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | Well-balanced central schemes for the One-dimensional shallow water equationsMalaeb, ElissaLebanese American University--DissertationsDissertations, AcademicFluid dynamics--Mathematical modelsDifferential equations, Hyperbolic--Numerical solutionsWave equation--Numerical solutionsThis thesis presents and contrasts two unique Unstaggered Central Scheme (UCS)’s for hyperbolic systems, specifically Shallow Water Equations (SWE): an Unstaggered Central Scheme with the Subraction Method (UCS-Sub) and an Unstaggered Central Weighted Essentially Non-Oscillatory Scheme with the Subtraction Method (UCWENO-Sub). Both schemes are made to protect the hyperbolic systems’ well-balanced (WB) characteristic, which keeps Steady state (SS) solutions immobile. This is made possible by implementing the subtraction method (SM), which effectively removes spurious numerical oscillations. Unstaggered schemes do not require the computationally costly step of solving Riemann problems at cell interfaces, which is a requirement of standard staggered systems. This results in notable efficiency gains. We perform an extensive comparison between UCS-Sub and UCWENO-Sub on several benchmark tasks to assess their respective performances. The outcomes show that both techniques are useful for approximating solutions to hyperbolic systems; while UCWENO-Sub gives priority to higher-order accuracy, they both strike a balance between simplicity, efficiency, and accuracy.1 online resource (xv, 62 leaves) : ill.Bibliography: leaves 58-62.Lebanese American University2024-06-24T08:07:02Z2024-06-24T08:07:02Z20232023-11-24Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/15795https://doi.org/10.26756/th.2023.658http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/157952024-06-24T08:07:02Z |
| spellingShingle | Well-balanced central schemes for the One-dimensional shallow water equations Malaeb, Elissa Lebanese American University--Dissertations Dissertations, Academic Fluid dynamics--Mathematical models Differential equations, Hyperbolic--Numerical solutions Wave equation--Numerical solutions |
| status_str | publishedVersion |
| title | Well-balanced central schemes for the One-dimensional shallow water equations |
| title_full | Well-balanced central schemes for the One-dimensional shallow water equations |
| title_fullStr | Well-balanced central schemes for the One-dimensional shallow water equations |
| title_full_unstemmed | Well-balanced central schemes for the One-dimensional shallow water equations |
| title_short | Well-balanced central schemes for the One-dimensional shallow water equations |
| title_sort | Well-balanced central schemes for the One-dimensional shallow water equations |
| topic | Lebanese American University--Dissertations Dissertations, Academic Fluid dynamics--Mathematical models Differential equations, Hyperbolic--Numerical solutions Wave equation--Numerical solutions |
| url | http://hdl.handle.net/10725/15795 https://doi.org/10.26756/th.2023.658 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |