An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations
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: | https://hdl.handle.net/1822/89141 |
Resumo: | Stability condition is a more restrictive constraint that leads to unnecessary small-time steps with respect to the accuracy and results in computational time wastage. We propose a node by node adaptive time scheme to relax the stability constraint enabling a larger global time step for all the nodes. A nonlinear procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we shall tune in function of the physical data (velocity, diffusion), the characteristic size in time and space, and the local regularly of the function leading to a nonlinear procedure. The a posteriori strategy we adopt consists in, given the solution at time t(n), computing a candidate solution with the highest accurate schemes in time and space for all the nodes. Then, for the nodes that present some instabilities, both the schemes in time and space are modified and adapted in order to preserve the stability with a large time step. The updated solution is computed with node-dependent schemes both in time and space. For the sake of simplicity, only convection-diffusion problems are addressed as a prototype with a two-parameters five-points finite difference method for the spatial discretisation together with an explicit time two-parameters four-stages Runge-Kutta method. We prove that we manage to obtain an optimal time-step algorithm that produces accurate numerical approximations exempt of non-physical oscillations. |
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An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equationsOptimal time stepStabilityFinite difference methodMOODHigh-orderNon-stationary convection-diffusionScience & TechnologyStability condition is a more restrictive constraint that leads to unnecessary small-time steps with respect to the accuracy and results in computational time wastage. We propose a node by node adaptive time scheme to relax the stability constraint enabling a larger global time step for all the nodes. A nonlinear procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we shall tune in function of the physical data (velocity, diffusion), the characteristic size in time and space, and the local regularly of the function leading to a nonlinear procedure. The a posteriori strategy we adopt consists in, given the solution at time t(n), computing a candidate solution with the highest accurate schemes in time and space for all the nodes. Then, for the nodes that present some instabilities, both the schemes in time and space are modified and adapted in order to preserve the stability with a large time step. The updated solution is computed with node-dependent schemes both in time and space. For the sake of simplicity, only convection-diffusion problems are addressed as a prototype with a two-parameters five-points finite difference method for the spatial discretisation together with an explicit time two-parameters four-stages Runge-Kutta method. We prove that we manage to obtain an optimal time-step algorithm that produces accurate numerical approximations exempt of non-physical oscillations.G.J. Machado and S. Clain acknowledge the financial support by FEDER -Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 -Programa Operacional Fatores de Competitividade, and the National Funds through FCT -Fundacao para a Ciencia e a Tecnologia, project no. UID/FIS/04650/2019.M.T. Malheiro acknowledge the financial support by Portuguese Funds through FCT (Fundacao para a Ciencia e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM.M.T. Malheiro, G.J. Machado, and S. Clain acknowledge the financial support by FEDER - Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 -Programa Operacional Fatores de Competitividade, and the National Funds through FCT -Fundacao para a Ciencia e a Tecnologia, project no. POCI-01-0145-FEDER-028118.Elsevier Science LtdUniversidade do MinhoMalheiro, M. TeresaMachado, Gaspar J.Clain, Stéphane20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/89141engMalheiro, M. T., Machado, G. J., & Clain, S. (2021, December). An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations. Computers & Mathematics with Applications. Elsevier BV. http://doi.org/10.1016/j.camwa.2021.10.0220898-122110.1016/j.camwa.2021.10.022https://www.sciencedirect.com/science/article/abs/pii/S089812212100376Xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-02T01:19:16Zoai:repositorium.sdum.uminho.pt:1822/89141Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:11:43.588056Repositório 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 |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
title |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
spellingShingle |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations Malheiro, M. Teresa Optimal time step Stability Finite difference method MOOD High-order Non-stationary convection-diffusion Science & Technology |
title_short |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
title_full |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
title_fullStr |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
title_full_unstemmed |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
title_sort |
An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations |
author |
Malheiro, M. Teresa |
author_facet |
Malheiro, M. Teresa Machado, Gaspar J. Clain, Stéphane |
author_role |
author |
author2 |
Machado, Gaspar J. Clain, Stéphane |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Malheiro, M. Teresa Machado, Gaspar J. Clain, Stéphane |
dc.subject.por.fl_str_mv |
Optimal time step Stability Finite difference method MOOD High-order Non-stationary convection-diffusion Science & Technology |
topic |
Optimal time step Stability Finite difference method MOOD High-order Non-stationary convection-diffusion Science & Technology |
description |
Stability condition is a more restrictive constraint that leads to unnecessary small-time steps with respect to the accuracy and results in computational time wastage. We propose a node by node adaptive time scheme to relax the stability constraint enabling a larger global time step for all the nodes. A nonlinear procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we shall tune in function of the physical data (velocity, diffusion), the characteristic size in time and space, and the local regularly of the function leading to a nonlinear procedure. The a posteriori strategy we adopt consists in, given the solution at time t(n), computing a candidate solution with the highest accurate schemes in time and space for all the nodes. Then, for the nodes that present some instabilities, both the schemes in time and space are modified and adapted in order to preserve the stability with a large time step. The updated solution is computed with node-dependent schemes both in time and space. For the sake of simplicity, only convection-diffusion problems are addressed as a prototype with a two-parameters five-points finite difference method for the spatial discretisation together with an explicit time two-parameters four-stages Runge-Kutta method. We prove that we manage to obtain an optimal time-step algorithm that produces accurate numerical approximations exempt of non-physical oscillations. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 2021-01-01T00:00:00Z |
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 |
https://hdl.handle.net/1822/89141 |
url |
https://hdl.handle.net/1822/89141 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Malheiro, M. T., Machado, G. J., & Clain, S. (2021, December). An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations. Computers & Mathematics with Applications. Elsevier BV. http://doi.org/10.1016/j.camwa.2021.10.022 0898-1221 10.1016/j.camwa.2021.10.022 https://www.sciencedirect.com/science/article/abs/pii/S089812212100376X |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science Ltd |
publisher.none.fl_str_mv |
Elsevier Science Ltd |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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 |
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1799137767388610560 |