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Article: The entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationship
Title | The entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationship | ||||||||||||
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Authors | |||||||||||||
Keywords | Discontinuous flow-density relationship Entropy solution LWR model Traffic flow WENOscheme | ||||||||||||
Issue Date | 2009 | ||||||||||||
Publisher | I N F O R M S. The Journal's web site is located at http://transci.pubs.informs.org | ||||||||||||
Citation | Transportation Science, 2009, v. 43 n. 4, p. 511-530 How to Cite? | ||||||||||||
Abstract | In this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piece- wise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives.,©2009 INFORMS. | ||||||||||||
Persistent Identifier | http://hdl.handle.net/10722/71845 | ||||||||||||
ISSN | 2023 Impact Factor: 4.4 2023 SCImago Journal Rankings: 2.475 | ||||||||||||
ISI Accession Number ID |
Funding Information: The authors thank the anonymous associate editor and two anonymous referees for their helpful suggestions and critical and constructive comments on an earlier version of the paper. The work of the second author was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU7187/05E). The research of the third author was partially supported by NSFC Grant 10671190. The research of the fourth author was partially supported by NSFC Grant 10671190 while this author was visiting the Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China. Additional support was provided by AROGrants W911NF-04-1-0291 and W911NF-08-1-0520, as well as by NSF Grants DMS-0510345 and DMS-0809086. | ||||||||||||
References |
DC Field | Value | Language |
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dc.contributor.author | Lu, Y | en_HK |
dc.contributor.author | Wong, SC | en_HK |
dc.contributor.author | Zhang, M | en_HK |
dc.contributor.author | Shu, CW | en_HK |
dc.date.accessioned | 2010-09-06T06:35:41Z | - |
dc.date.available | 2010-09-06T06:35:41Z | - |
dc.date.issued | 2009 | en_HK |
dc.identifier.citation | Transportation Science, 2009, v. 43 n. 4, p. 511-530 | en_HK |
dc.identifier.issn | 0041-1655 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/71845 | - |
dc.description.abstract | In this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piece- wise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives.,©2009 INFORMS. | en_HK |
dc.language | eng | en_HK |
dc.publisher | I N F O R M S. The Journal's web site is located at http://transci.pubs.informs.org | en_HK |
dc.relation.ispartof | Transportation Science | en_HK |
dc.subject | Discontinuous flow-density relationship | en_HK |
dc.subject | Entropy solution | en_HK |
dc.subject | LWR model | en_HK |
dc.subject | Traffic flow | en_HK |
dc.subject | WENOscheme | en_HK |
dc.title | The entropy solutions for the lighthill-whitham-richards traffic flow model with a discontinuous flow-density relationship | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0041-1655&volume=43&issue=4&spage=511&epage=530&date=2009&atitle=The+entropy+solutions+for+the+Lighthill-Whitham-Richards+traffic+flow+model+with+a+discontinuous+flow-density+relationship | en_HK |
dc.identifier.email | Wong, SC:hhecwsc@hku.hk | en_HK |
dc.identifier.authority | Wong, SC=rp00191 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1287/trsc.1090.0277 | en_HK |
dc.identifier.scopus | eid_2-s2.0-73349090579 | en_HK |
dc.identifier.hkuros | 168272 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-73349090579&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 43 | en_HK |
dc.identifier.issue | 4 | en_HK |
dc.identifier.spage | 511 | en_HK |
dc.identifier.epage | 530 | en_HK |
dc.identifier.eissn | 1526-5447 | - |
dc.identifier.isi | WOS:000271944400008 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Lu, Y=24281590400 | en_HK |
dc.identifier.scopusauthorid | Wong, SC=24323361400 | en_HK |
dc.identifier.scopusauthorid | Zhang, M=7601556898 | en_HK |
dc.identifier.scopusauthorid | Shu, CW=7202122336 | en_HK |
dc.identifier.issnl | 0041-1655 | - |