A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow

Elisabetta Carlini (), Adriano Festa (), Francisco J. Silva () and Marie-Therese Wolfram ()
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Elisabetta Carlini: Sapienza Università di Roma
Adriano Festa: Austrian Academy of Sciences (ÖAW)
Francisco J. Silva: Université de Limoges
Marie-Therese Wolfram: Austrian Academy of Sciences (ÖAW)

Dynamic Games and Applications, 2017, vol. 7, issue 4, No 10, 683-705

Abstract: 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.

Keywords: Crowd motion; Mean field models; Semi-Lagrangian schemes; 35Q91; 65N75; 60J20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13235-016-0202-6

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