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A semi-Lagrangian scheme for a modified version of the Hughes’ Model for Pedestrian Flow

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Carlini, Elisabetta, Festa, Adriano, Silva, Francisco J. and Wolfram, Marie-Therese (2017) A semi-Lagrangian scheme for a modified version of the Hughes’ Model for Pedestrian Flow. Dynamic Games and Applications, 7 (4). pp. 683-705. doi:10.1007/s13235-016-0202-6 ISSN 2153-0785.

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Official URL: http://dx.doi.org/10.1007/s13235-016-0202-6

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Abstract

In this paper, we present a semi-Lagrangian scheme for a regularized version of the Hughes’ model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an eikonal equation to determine the weighted distance to the exit. We consider this model in the presence of small diffusion and discuss the numerical analysis of the proposed semi-Lagrangian scheme. Furthermore, we illustrate the effect of small diffusion on the exit time with various numerical experiments.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Crowds -- Mathematical models, Pedestrians -- Mathematical models, Differential equations, Partial
Journal or Publication Title: Dynamic Games and Applications
Publisher: Birkhaeuser Science
ISSN: 2153-0785
Official Date: December 2017
Dates:
DateEvent
December 2017Published
1 September 2016Available
1 September 2016Accepted
Volume: 7
Number: 4
Page Range: pp. 683-705
DOI: 10.1007/s13235-016-0202-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 19 September 2016
Date of first compliant Open Access: 1 September 2017
Funder: Österreichische Akademie der Wissenschaften [Austrian Academy of Sciences], France. Fondation Mathématiques Jacques Hadamard [Jacques Hadamard Mathematical Foundation]

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