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Article: Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models

TitleEssence of conservation forms in the traveling wave solutions of higher-order traffic flow models
Authors
KeywordsPhysics
Issue Date2006
PublisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.org
Citation
Physical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2006, v. 74 n. 2 How to Cite?
AbstractThis paper shows the essence of conservation forms when applying the weak solution theory to solve the traveling wave solution of a wide cluster in the Payne-Whitham (PW) model. The consideration of the conservation form for the acceleration equation is an important ingredient in the development of higher-order traffic flow models, but it is largely ignored in the research community. To fix the idea, we define two conservation forms for the same PW model, and consequently derive two solutions with different sets of characteristic parameters of the wide cluster. The analytical results are in good agreement with those that are obtained from numerical simulations. Moreover, these two solutions are also shown to be asymptotic to those of the well-known KÃhne and Kerner-KonhaÃser models with a viscosity term. More importantly, the careful treatment of the conservation form for the acceleration equation closes the important gap in the literature. Without the conservation form, the solution obtained depends very much on the design of numerical schemes, and can be quite arbitrary and may not adequately conform to the physically relevant properties. © 2006 The American Physical Society.
Persistent Identifierhttp://hdl.handle.net/10722/44623
ISSN
2014 Impact Factor: 2.288
2015 SCImago Journal Rankings: 0.999
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorZhang, Pen_HK
dc.contributor.authorWong, SCen_HK
dc.date.accessioned2007-10-30T06:06:03Z-
dc.date.available2007-10-30T06:06:03Z-
dc.date.issued2006en_HK
dc.identifier.citationPhysical Review E - Statistical, Nonlinear, And Soft Matter Physics, 2006, v. 74 n. 2en_HK
dc.identifier.issn1539-3755en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44623-
dc.description.abstractThis paper shows the essence of conservation forms when applying the weak solution theory to solve the traveling wave solution of a wide cluster in the Payne-Whitham (PW) model. The consideration of the conservation form for the acceleration equation is an important ingredient in the development of higher-order traffic flow models, but it is largely ignored in the research community. To fix the idea, we define two conservation forms for the same PW model, and consequently derive two solutions with different sets of characteristic parameters of the wide cluster. The analytical results are in good agreement with those that are obtained from numerical simulations. Moreover, these two solutions are also shown to be asymptotic to those of the well-known KÃhne and Kerner-KonhaÃser models with a viscosity term. More importantly, the careful treatment of the conservation form for the acceleration equation closes the important gap in the literature. Without the conservation form, the solution obtained depends very much on the design of numerical schemes, and can be quite arbitrary and may not adequately conform to the physically relevant properties. © 2006 The American Physical Society.en_HK
dc.format.extent710590 bytes-
dc.format.extent2264 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAmerican Physical Society. The Journal's web site is located at http://pre.aps.orgen_HK
dc.relation.ispartofPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsen_HK
dc.rightsPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics). Copyright © American Physical Society.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectPhysicsen_HK
dc.titleEssence of conservation forms in the traveling wave solutions of higher-order traffic flow modelsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1539-3755&volume=74&issue=2&spage=026109:1&epage=10&date=2006&atitle=Essence+of+conservation+forms+in+the+traveling+wave+solutions+of+higher-order+traffic+flow+modelsen_HK
dc.identifier.emailWong, SC:hhecwsc@hku.hken_HK
dc.identifier.authorityWong, SC=rp00191en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1103/PhysRevE.74.026109en_HK
dc.identifier.scopuseid_2-s2.0-33747111035en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33747111035&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume74en_HK
dc.identifier.issue2en_HK
dc.identifier.isiWOS:000240238200012-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhang, P=7404158930en_HK
dc.identifier.scopusauthoridWong, SC=24323361400en_HK

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