Modelling crowd movements in domains with boundaries

Abstract This paper contributes to the macroscopic modelling of crowd movements. The presented model is ‘non-local’; i.e. it takes into account interactions among pedestrians at different distances. Particular care is given to how non-local interactions are influenced by walls, obstacles and exits....

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 84; no. 5; pp. 833 - 853
Main Authors Colombo, Rinaldo M, Rossi, Elena
Format Journal Article
LanguageEnglish
Published Oxford University Press 11.10.2019
Subjects
numerical treatment of non-local conservation laws
crowd dynamics
macroscopic pedestrian model
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Summary:Abstract This paper contributes to the macroscopic modelling of crowd movements. The presented model is ‘non-local’; i.e. it takes into account interactions among pedestrians at different distances. Particular care is given to how non-local interactions are influenced by walls, obstacles and exits. The resulting dynamics captures various well-known patterns of crowd movements, such as the clogging of exits and the spontaneous formation of queues. The careful choice of obstacles near an exit is shown to be able to reduce evacuation times. An ad hoc numerical algorithm is detailed, some of its properties discussed and the convergence of the corresponding approximate solutions is investigated.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxz017