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Article: A higher-order macroscopic model for pedestrian flows

TitleA higher-order macroscopic model for pedestrian flows
Authors
KeywordsLinear stability analysis
Obstruction
Path choice
Pedestrian crowd dynamics
Traffic instability
Unstructured meshes
Issue Date2010
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physa
Citation
Physica A: Statistical Mechanics And Its Applications, 2010, v. 389 n. 21, p. 4623-4635 How to Cite?
Abstract
This paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional LighthillWhithamRichards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as "stop-and-go waves" observed in empirical pedestrian flows. © 2010 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/124242
ISSN
2013 Impact Factor: 1.722
2013 SCImago Journal Rankings: 0.733
ISI Accession Number ID
Funding AgencyGrant Number
National Natural Science Foundation of China70629001
10771134
National Basic Research Program of China2006CB705500
Research Grants Council of the Hong Kong Special Administrative Region of ChinaHKU7184/10E
University of Hong Kong10207394
Funding Information:

The work described in this paper was jointly supported by grants from the National Natural Science Foundation of China (70629001, 10771134), the National Basic Research Program of China (2006CB705500), the Research Grants Council of the Hong Kong Special Administrative Region of China (Project No.: HKU7184/10E), and the University of Hong Kong (10207394).

References

 

Author Affiliations
  1. The University of Hong Kong
  2. University of Science and Technology of China
  3. Shanghai University
DC FieldValueLanguage
dc.contributor.authorJiang, YQen_HK
dc.contributor.authorZhang, Pen_HK
dc.contributor.authorWong, SCen_HK
dc.contributor.authorLiu, RXen_HK
dc.date.accessioned2010-10-31T10:23:02Z-
dc.date.available2010-10-31T10:23:02Z-
dc.date.issued2010en_HK
dc.identifier.citationPhysica A: Statistical Mechanics And Its Applications, 2010, v. 389 n. 21, p. 4623-4635en_HK
dc.identifier.issn0378-4371en_HK
dc.identifier.urihttp://hdl.handle.net/10722/124242-
dc.description.abstractThis paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional LighthillWhithamRichards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as "stop-and-go waves" observed in empirical pedestrian flows. © 2010 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/physaen_HK
dc.relation.ispartofPhysica A: Statistical Mechanics and its Applicationsen_HK
dc.subjectLinear stability analysisen_HK
dc.subjectObstructionen_HK
dc.subjectPath choiceen_HK
dc.subjectPedestrian crowd dynamicsen_HK
dc.subjectTraffic instabilityen_HK
dc.subjectUnstructured meshesen_HK
dc.titleA higher-order macroscopic model for pedestrian flowsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0378-4371&volume=389&spage=4623&epage=4635&date=2010&atitle=A+higher-order+macroscopic+model+for+pedestrian+flowsen_HK
dc.identifier.emailWong, SC:hhecwsc@hku.hken_HK
dc.identifier.authorityWong, SC=rp00191en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.physa.2010.05.003en_HK
dc.identifier.scopuseid_2-s2.0-77956172545en_HK
dc.identifier.hkuros178938en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77956172545&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume389en_HK
dc.identifier.issue21en_HK
dc.identifier.spage4623en_HK
dc.identifier.epage4635en_HK
dc.identifier.isiWOS:000282241600019-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridJiang, YQ=35275312000en_HK
dc.identifier.scopusauthoridZhang, P=7404158930en_HK
dc.identifier.scopusauthoridWong, SC=24323361400en_HK
dc.identifier.scopusauthoridLiu, RX=7404551751en_HK
dc.identifier.citeulike7246303-

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