Publicação
A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension
| Resumo: | The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple one-dimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We propose an alternative procedure by extending the Butcher Tableau to overcome this specific difficulty and achieve fourth-, sixth- or eighth-order of accuracy schemes in space and time. To this end, a new finite volume method is designed based on specific polynomial reconstructions for the space discretization, while we use the Extended Butcher Tableau to perform the time discretization. A large set of numerical tests has been carried out to validate the proposed method. |
|---|---|
| Autores principais: | Clain, Stéphane |
| Outros Autores: | Machado, Gaspar J. |
| Assunto: | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| Ano: | 2014 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1877775536475865088 |
|---|---|
| author | Clain, Stéphane |
| author2 | Machado, Gaspar J. |
| author2_role | author |
| author_facet | Clain, Stéphane Machado, Gaspar J. |
| author_role | author |
| contributor_name_str_mv | RepositóriUM - Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Clain, Stéphane\"},{\"Person.name\":\"Machado, Gaspar J.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | RepositóriUM - Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Clain, Stéphane Machado, Gaspar J. |
| datacite.date.Accepted.fl_str_mv | 2014-01-01T00:00:00Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| datacite.titles.title.fl_str_mv | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| dc.contributor.none.fl_str_mv | RepositóriUM - Universidade do Minho |
| dc.creator.none.fl_str_mv | Clain, Stéphane Machado, Gaspar J. |
| dc.date.Accepted.fl_str_mv | 2014-01-01T00:00:00Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/30783 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| dc.title.fl_str_mv | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple one-dimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We propose an alternative procedure by extending the Butcher Tableau to overcome this specific difficulty and achieve fourth-, sixth- or eighth-order of accuracy schemes in space and time. To this end, a new finite volume method is designed based on specific polynomial reconstructions for the space discretization, while we use the Extended Butcher Tableau to perform the time discretization. A large set of numerical tests has been carried out to validate the proposed method. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | rum_dc8a11df076ab81077c94186f1d177b0 |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/30783 |
| inst_facet_str | urn:organizationAcronym:repositorium{{{_:::_}}}Universidade do Minho |
| 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:1822/30783 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Clain, Stéphane Machado, Gaspar J. |
| publishDate | 2014 |
| publisher.none.fl_str_mv | Elsevier |
| repo_facet_str | urn:repositoryAcronym:rum{{{_:::_}}}RepositóriUM - Universidade do Minho |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engElsevierporThe time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple one-dimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We propose an alternative procedure by extending the Butcher Tableau to overcome this specific difficulty and achieve fourth-, sixth- or eighth-order of accuracy schemes in space and time. To this end, a new finite volume method is designed based on specific polynomial reconstructions for the space discretization, while we use the Extended Butcher Tableau to perform the time discretization. A large set of numerical tests has been carried out to validate the proposed method.application/pdfporA very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extensionClain, StéphaneMachado, Gaspar J.HostingInstitutionOrganizationalRepositóriUM - Universidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf0898-1221DOIIsPartOf10.1016/j.camwa.2014.09.00120142014-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/30783http://purl.org/coar/access_right/c_abf2open accessFinite volumeVery high-orderConvection-diffusionPolynomial reconstructionButcher Tableauhttp://www.oecd.org/science/inno/38235147.pdfFields of Science and Technology (FOS)Ciências Naturais::Matemáticas475957 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdfhttps://repositorium.uminho.pt/bitstreams/6e0be47a-74d6-4c50-bd65-6d50853138a9/download |
| spellingShingle | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension Clain, Stéphane Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| status | SINGLETON |
| subject.fl_str_mv | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau |
| subject.other.fl_str_mv | Ciências Naturais::Matemáticas |
| title | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| title_full | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| title_fullStr | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| title_full_unstemmed | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| title_short | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| title_sort | A very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extension |
| topic | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| topic_facet | Finite volume Very high-order Convection-diffusion Polynomial reconstruction Butcher Tableau Ciências Naturais::Matemáticas |
| url | https://hdl.handle.net/1822/30783 |
| visible | 1 |
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