Publicação
A well-balanced scheme for the shallow-water equations with topography or Manning friction
| Resumo: | We consider the shallow-water equations with Manning friction or topography, as well as a combination of both these source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme. |
|---|---|
| Autores principais: | Michel-Dansac, V. |
| Outros Autores: | Berthon, C.; Clain, Stéphane; Foucher, F. |
| Assunto: | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| Ano: | 2017 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1866876485063671808 |
|---|---|
| author | Michel-Dansac, V. |
| author2 | Berthon, C. Clain, Stéphane Foucher, F. |
| author2_role | author author author |
| author_facet | Michel-Dansac, V. Berthon, C. Clain, Stéphane Foucher, F. |
| author_role | author |
| contributor_name_str_mv | Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Michel-Dansac, V.\"},{\"Person.name\":\"Berthon, C.\"},{\"Person.name\":\"Clain, Stéphane\"},{\"Person.name\":\"Foucher, F.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Michel-Dansac, V. Berthon, C. Clain, Stéphane Foucher, F. |
| datacite.date.Accepted.fl_str_mv | 2017-01-01T00:00:00Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_16ec |
| datacite.subjects.subject.fl_str_mv | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| datacite.titles.title.fl_str_mv | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| dc.contributor.none.fl_str_mv | Universidade do Minho |
| dc.creator.none.fl_str_mv | Michel-Dansac, V. Berthon, C. Clain, Stéphane Foucher, F. |
| dc.date.Accepted.fl_str_mv | 2017-01-01T00:00:00Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/48543 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.cclincense.fl_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_16ec |
| dc.rights.rights.copyright.fl_str_mv | restrictedAccess |
| dc.subject.none.fl_str_mv | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| dc.title.fl_str_mv | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | We consider the shallow-water equations with Manning friction or topography, as well as a combination of both these source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme. |
| dirty | 0 |
| eu_rights_str_mv | restrictedAccess |
| format | article |
| fulltext.url.fl_str_mv | https://prod-dspace.uminho.pt/bitstreams/ced779ed-f6b3-4639-9a9f-a7438c2eff5b/download |
| id | rum_ec8536f4e34141aef10fbb35ae2a839d |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/48543 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/48543 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Michel-Dansac, V. Berthon, C. Clain, Stéphane Foucher, F. |
| publishDate | 2017 |
| publisher.none.fl_str_mv | Elsevier |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engElsevierporWe consider the shallow-water equations with Manning friction or topography, as well as a combination of both these source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme.application/pdfporA well-balanced scheme for the shallow-water equations with topography or Manning frictionMichel-Dansac, V.Berthon, C.Clain, StéphaneFoucher, F.HostingInstitutionOrganizationalUniversidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf0021-9991DOIIsPartOf10.1016/j.jcp.2017.01.00920172017-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/48543http://purl.org/coar/access_right/c_16ecrestricted accesswell-balanced schemeshallow-watermanning frictionfinite volumeShallow-water equationsGodunov-type schemesWell-balanced schemesMoving steady states2583359 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal article2017http://creativecommons.org/licenses/by/4.0/restrictedAccesshttp://purl.org/coar/access_right/c_16ecapplication/pdffulltexthttps://prod-dspace.uminho.pt/bitstreams/ced779ed-f6b3-4639-9a9f-a7438c2eff5b/download |
| spellingShingle | A well-balanced scheme for the shallow-water equations with topography or Manning friction Michel-Dansac, V. well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| status | SINGLETON |
| subject.fl_str_mv | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| title | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| title_full | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| title_fullStr | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| title_full_unstemmed | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| title_short | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| title_sort | A well-balanced scheme for the shallow-water equations with topography or Manning friction |
| topic | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| topic_facet | well-balanced scheme shallow-water manning friction finite volume Shallow-water equations Godunov-type schemes Well-balanced schemes Moving steady states |
| url | https://hdl.handle.net/1822/48543 |
| visible | 1 |