Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations

Detalhes bibliográficos
Autor(a) principal: Clain, Stéphane
Data de Publicação: 2024
Outros Autores: Lopes, Diogo, Pereira, Rui M. S., Pereira, Paulo A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/87450
Resumo: An arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes for linear non-constant coefficients problem in both the conservative and non-conservative scalar equations. Extensions to non-linear scalar problems and systems are then implemented while preserving the optimal orders. Numerical simulations are carried out to provide evidence about the convergence order and the stability of the method.
id RCAP_4d4ba2bee0c373bdc2aece5d2e861d2d
oai_identifier_str oai:repositorium.sdum.uminho.pt:1822/87450
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equationsVery high-orderFinite differenceArbitrary geometriesROD polynomialImmersed boundaryCiências Naturais::MatemáticasAn arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes for linear non-constant coefficients problem in both the conservative and non-conservative scalar equations. Extensions to non-linear scalar problems and systems are then implemented while preserving the optimal orders. Numerical simulations are carried out to provide evidence about the convergence order and the stability of the method.R.M.S. Pereira acknowledges the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 – Programa Operational Fatores de Competitividade, and the National Funds through FCT – Fundação para a Ciência e a Tecnologia, project no. UID/FIS/04650/2019. P. A. Pereira acknowledges the financial support by Portuguese Funds through the Foundation for Science and Technology (FCT) in the framework of the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM. S. Clain acknowledges the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 – Programa Operational Fatores de Competitividade, and the National Funds through FCT – Fundação para a Ciência e a Tecnologia, project Nº UIDB/00324/2020.ElsevierUniversidade do MinhoClain, StéphaneLopes, DiogoPereira, Rui M. S.Pereira, Paulo A.2024-022024-02-01T00:00:00Z2025-11-28T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87450engClain, S., Lopes, D., Pereira, R. M. S., & Pereira, P. A. (2024, February). Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations. Journal of Computational Physics. Elsevier BV. http://doi.org/10.1016/j.jcp.2023.1126670021-99911090-271610.1016/j.jcp.2023.112667https://www.sciencedirect.com/science/article/pii/S0021999123007623info: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:RCAAP2024-05-11T05:30:12Zoai:repositorium.sdum.uminho.pt:1822/87450Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T05:30:12Repositório 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 Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
title Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
spellingShingle Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
Clain, Stéphane
Very high-order
Finite difference
Arbitrary geometries
ROD polynomial
Immersed boundary
Ciências Naturais::Matemáticas
title_short Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
title_full Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
title_fullStr Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
title_full_unstemmed Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
title_sort Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations
author Clain, Stéphane
author_facet Clain, Stéphane
Lopes, Diogo
Pereira, Rui M. S.
Pereira, Paulo A.
author_role author
author2 Lopes, Diogo
Pereira, Rui M. S.
Pereira, Paulo A.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Clain, Stéphane
Lopes, Diogo
Pereira, Rui M. S.
Pereira, Paulo A.
dc.subject.por.fl_str_mv Very high-order
Finite difference
Arbitrary geometries
ROD polynomial
Immersed boundary
Ciências Naturais::Matemáticas
topic Very high-order
Finite difference
Arbitrary geometries
ROD polynomial
Immersed boundary
Ciências Naturais::Matemáticas
description An arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes for linear non-constant coefficients problem in both the conservative and non-conservative scalar equations. Extensions to non-linear scalar problems and systems are then implemented while preserving the optimal orders. Numerical simulations are carried out to provide evidence about the convergence order and the stability of the method.
publishDate 2024
dc.date.none.fl_str_mv 2024-02
2024-02-01T00:00:00Z
2025-11-28T00:00:00Z
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 https://hdl.handle.net/1822/87450
url https://hdl.handle.net/1822/87450
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Clain, S., Lopes, D., Pereira, R. M. S., & Pereira, P. A. (2024, February). Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations. Journal of Computational Physics. Elsevier BV. http://doi.org/10.1016/j.jcp.2023.112667
0021-9991
1090-2716
10.1016/j.jcp.2023.112667
https://www.sciencedirect.com/science/article/pii/S0021999123007623
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)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv mluisa.alvim@gmail.com
_version_ 1817544642269282304

Registros relacionados