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On the Verification of the Pedestrian Evacuation Model

Author

Listed:
  • Petr Kubera

    (Faculty of Science, Jan Evangelista Purkyně University, České Mládeže 8, 400 96 Ústí nad Labem, Czech Republic
    These authors contributed equally to this work.)

  • Jiří Felcman

    (Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 186 75 Praha, Czech Republic
    These authors contributed equally to this work.)

Abstract

In this article we deal with numerical solution of macroscopic models of pedestrian movement. From a macroscopic point of view, pedestrian movement can be described by a system of first order hyperbolic equations similar to 2D compressible inviscid flow. For the Pedestrian Flow Equations (PFEs) the density ρ and the velocity v are considered as the unknown variables. In PFEs, the social force is also taken into account, which replaces the outer volume force term used in the fluid flow formulation, e.g., the pedestrian movement is influenced by the proximity of other pedestrians. To be concrete, the desired direction μ of the pedestrian movement is density dependent and is incorporated in the source term. The system of fluid dynamics equations is thus coupled with the equation for μ . The main message of this paper is the verification of this model. Firstly, we propose two approaches for the source term discretization. Secondly, we propose two splitting schemes for the numerical solution of the coupled system. This leads us to four different numerical methods for the PFEs. The novelty of this work is the comparative study of the numerical solutions, which shows, that all proposed methods are in the good agreement.

Suggested Citation

  • Petr Kubera & Jiří Felcman, 2021. "On the Verification of the Pedestrian Evacuation Model," Mathematics, MDPI, vol. 9(13), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1525-:d:584724
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    References listed on IDEAS

    as
    1. Liu, Rong & Fu, Zhijian & Schadschneider, Andreas & Wen, Qiuping & Chen, Junmin & Liu, Shaobo, 2019. "Modeling the effect of visibility on upstairs crowd evacuation by a stochastic FFCA model with finer discretization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    2. Jiang, Yan-qun & Zhang, Peng & Wong, S.C. & Liu, Ru-xun, 2010. "A higher-order macroscopic model for pedestrian flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4623-4635.
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    Cited by:

    1. Xue Lin & Long Cheng & Shuo Zhang & Qianling Wang, 2023. "Simulating the Effects of Gate Machines on Crowd Traffic Based on the Modified Social Force Model," Mathematics, MDPI, vol. 11(3), pages 1-12, February.

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