Traffic Modelling and Some Inequalities in Banach Spaces
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/26575 |
Resumo: | Modelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes. The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t. The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t. An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions. Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes. |
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Traffic Modelling and Some Inequalities in Banach SpacesHyperbolic conservation lawsTraffic flowRiemann problemLax-Friedrichs schemeLax-Wendroff schemeModelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes. The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t. The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t. An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions. Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes.Edited by Thepsavanh Kitignavong, Faculty of Natural Sciences, National University of Laos2020-01-23T16:33:01Z2020-01-232017-07-10T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10174/26575http://hdl.handle.net/10174/26575eng"Traffic Modelling and Some Inequalities in Banach Spaces", Master Thesis in Applied Mathematics, Bouasy Doungsavanh, Dissertation Period: September 2016 to May 2017, Defence on July 2017, Supervised by N. Bedjaoui, J.M.C. Correia and S. Sirisack, Diploma on July 26, 2017, at FNS, National University of Laos, Vientiane, PDR LaosFaculty of Natural Sciences, National University of Laos, Vientiane, PDR Laos60 pp.National University of Laos (NUOL)Master Thesisndjmcorreia@uevora.ptndndN/AN/ABedjaoui, NabilCorreia, JoaquimSirisack, SackmoneDoungsavanh, Bouasyinfo: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:RCAAP2024-01-03T19:21:13Zoai:dspace.uevora.pt:10174/26575Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:16:45.848337Repositório 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 |
Traffic Modelling and Some Inequalities in Banach Spaces |
title |
Traffic Modelling and Some Inequalities in Banach Spaces |
spellingShingle |
Traffic Modelling and Some Inequalities in Banach Spaces Bedjaoui, Nabil Hyperbolic conservation laws Traffic flow Riemann problem Lax-Friedrichs scheme Lax-Wendroff scheme |
title_short |
Traffic Modelling and Some Inequalities in Banach Spaces |
title_full |
Traffic Modelling and Some Inequalities in Banach Spaces |
title_fullStr |
Traffic Modelling and Some Inequalities in Banach Spaces |
title_full_unstemmed |
Traffic Modelling and Some Inequalities in Banach Spaces |
title_sort |
Traffic Modelling and Some Inequalities in Banach Spaces |
author |
Bedjaoui, Nabil |
author_facet |
Bedjaoui, Nabil Correia, Joaquim Sirisack, Sackmone Doungsavanh, Bouasy |
author_role |
author |
author2 |
Correia, Joaquim Sirisack, Sackmone Doungsavanh, Bouasy |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Bedjaoui, Nabil Correia, Joaquim Sirisack, Sackmone Doungsavanh, Bouasy |
dc.subject.por.fl_str_mv |
Hyperbolic conservation laws Traffic flow Riemann problem Lax-Friedrichs scheme Lax-Wendroff scheme |
topic |
Hyperbolic conservation laws Traffic flow Riemann problem Lax-Friedrichs scheme Lax-Wendroff scheme |
description |
Modelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes. The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t. The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t. An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions. Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-07-10T00:00:00Z 2020-01-23T16:33:01Z 2020-01-23 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/26575 http://hdl.handle.net/10174/26575 |
url |
http://hdl.handle.net/10174/26575 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Traffic Modelling and Some Inequalities in Banach Spaces", Master Thesis in Applied Mathematics, Bouasy Doungsavanh, Dissertation Period: September 2016 to May 2017, Defence on July 2017, Supervised by N. Bedjaoui, J.M.C. Correia and S. Sirisack, Diploma on July 26, 2017, at FNS, National University of Laos, Vientiane, PDR Laos Faculty of Natural Sciences, National University of Laos, Vientiane, PDR Laos 60 pp. National University of Laos (NUOL) Master Thesis nd jmcorreia@uevora.pt nd nd N/A N/A |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Edited by Thepsavanh Kitignavong, Faculty of Natural Sciences, National University of Laos |
publisher.none.fl_str_mv |
Edited by Thepsavanh Kitignavong, Faculty of Natural Sciences, National University of Laos |
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 |
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 |
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1799136649719840768 |