| Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Modelling and Simulations of Fluid Flows
|
|
|---|---|---|
| Article Number | 11 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/mmnp/2021002 | |
| Published online | 03 March 2021 | |
A cellular automaton model for a pedestrian flow problem*
1
Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University,
Prague, Czech Republic.
2
Department of Informatics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University,
Prague, Czech Republic.
3
Department of Software Engineering, Faculty of Science, Jan Evengelista Purkyně University,
Ústí nad Labem, Czech Republic.
** Corresponding author: felcman@karlin.mff.cuni.cz
Received:
30
June
2020
Accepted:
25
December
2020
The evacuation phenomena in the two dimensional pedestrian flow model are simulated. The intended direction of the escape of pedestrians in panic situations is governed by the Eikonal equation of the pedestrian flow model. A new two-dimensional Cellular Automaton (CA) model is proposed for the simulation of the pedestrian flow. The solution of the Eikonal equation is used to define the probability matrix whose elements express the probability of a pedestrian moving in finite set of directions. The novelty of this paper lies in the construction of the density dependent probability matrix. The relevant evacuation scenarios are numerically solved. Predictions of the evacuation behavior of pedestrians, for various room geometries with multiple exits, are demonstrated. The mathematical model is numerically justified by comparison of CA approach with the Finite Volume Method for the space discretization and Discontinuous Galerkin Method for the implicit time discretization of pedestrian flow model.
Mathematics Subject Classification: 76N15 / 70B05
Key words: Pedestrian flow / cellular atomaton / Eikonal equation / finite volume method / fast sweeping method
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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