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

Author

Listed:
  • 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)
    University of Warwick)

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.

Suggested Citation

  • Elisabetta Carlini & Adriano Festa & Francisco J. Silva & Marie-Therese Wolfram, 2017. "A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow," Dynamic Games and Applications, Springer, vol. 7(4), pages 683-705, December.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0202-6
    DOI: 10.1007/s13235-016-0202-6
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    References listed on IDEAS

    as
    1. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
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    6. N/A, 2011. "The UK economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 217(1), pages 3-3, July.
    7. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
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    Cited by:

    1. Albi, G. & Herty, M. & Pareschi, L., 2019. "Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 460-477.

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