Riemann Problem for Shallow Water Equation with Vegetation
We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2018-07-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2018-0023 |
| _version_ | 1811272369499537408 |
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| author | Ion Stelian Marinescu Dorin Cruceanu Stefan-Gicu |
| author_facet | Ion Stelian Marinescu Dorin Cruceanu Stefan-Gicu |
| author_sort | Ion Stelian |
| collection | DOAJ |
| description | We investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems, it is necessary to introduce a family of paths that connects the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems. |
| first_indexed | 2024-04-12T22:39:03Z |
| format | Article |
| id | doaj.art-3a44e34cdade421a87d3ee63846a26de |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:39:03Z |
| publishDate | 2018-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-3a44e34cdade421a87d3ee63846a26de2022-12-22T03:13:47ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352018-07-0126214517310.2478/auom-2018-0023Riemann Problem for Shallow Water Equation with VegetationIon Stelian0Marinescu Dorin1Cruceanu Stefan-Gicu2Institute of Statistical Mathematics and Applied Mathematics Romanian Academy Calea 13 Septembrie, No. 13,Bucharest, RomaniaInstitute of Statistical Mathematics and Applied Mathematics Romanian Academy Calea 13 Septembrie, No. 13,Bucharest, RomaniaInstitute of Statistical Mathematics and Applied Mathematics Romanian Academy Calea 13 Septembrie, No. 13,Bucharest, RomaniaWe investigate the existence of the solution of the Riemann Problem for a simplified water ow model on a vegetated surface - system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems, it is necessary to introduce a family of paths that connects the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems.https://doi.org/10.2478/auom-2018-0023hyperbolic nonconservativ lawmeasure solutionspath connectigshock waves |
| spellingShingle | Ion Stelian Marinescu Dorin Cruceanu Stefan-Gicu Riemann Problem for Shallow Water Equation with Vegetation Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica hyperbolic nonconservativ law measure solutions path connectig shock waves |
| title | Riemann Problem for Shallow Water Equation with Vegetation |
| title_full | Riemann Problem for Shallow Water Equation with Vegetation |
| title_fullStr | Riemann Problem for Shallow Water Equation with Vegetation |
| title_full_unstemmed | Riemann Problem for Shallow Water Equation with Vegetation |
| title_short | Riemann Problem for Shallow Water Equation with Vegetation |
| title_sort | riemann problem for shallow water equation with vegetation |
| topic | hyperbolic nonconservativ law measure solutions path connectig shock waves |
| url | https://doi.org/10.2478/auom-2018-0023 |
| work_keys_str_mv | AT ionstelian riemannproblemforshallowwaterequationwithvegetation AT marinescudorin riemannproblemforshallowwaterequationwithvegetation AT cruceanustefangicu riemannproblemforshallowwaterequationwithvegetation |