Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.22/18627 |
Resumo: | The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2 . First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method. |
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Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo modelCaputo fractional derivativeFractional Cattaneo equationRBF-PUFinite differenceStabilityConvergenceThe generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2 . First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.The authors are appreciative for anonymous referees for their hard work reading the paper and for their recommendations to improve the manuscript.ElsevierRepositório Científico do Instituto Politécnico do PortoNikan, O.Avazzadeh, Z.Machado, J. A. Tenreiro20212031-12-01T00:00:00Z2021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/18627eng10.1016/j.apm.2021.07.025info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T13:10:42Zoai:recipp.ipp.pt:10400.22/18627Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:38:10.843363Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
title |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
spellingShingle |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model Nikan, O. Caputo fractional derivative Fractional Cattaneo equation RBF-PU Finite difference Stability Convergence |
title_short |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
title_full |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
title_fullStr |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
title_full_unstemmed |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
title_sort |
Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model |
author |
Nikan, O. |
author_facet |
Nikan, O. Avazzadeh, Z. Machado, J. A. Tenreiro |
author_role |
author |
author2 |
Avazzadeh, Z. Machado, J. A. Tenreiro |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Nikan, O. Avazzadeh, Z. Machado, J. A. Tenreiro |
dc.subject.por.fl_str_mv |
Caputo fractional derivative Fractional Cattaneo equation RBF-PU Finite difference Stability Convergence |
topic |
Caputo fractional derivative Fractional Cattaneo equation RBF-PU Finite difference Stability Convergence |
description |
The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2 . First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 2021-01-01T00:00:00Z 2031-12-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.22/18627 |
url |
http://hdl.handle.net/10400.22/18627 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1016/j.apm.2021.07.025 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131471015837696 |