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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
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: |
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| 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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