On the Verification of the Pedestrian Evacuation Model

Petr Kubera and Jiří Felcman
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Petr Kubera: Faculty of Science, Jan Evangelista Purkyně University, České Mládeže 8, 400 96 Ústí nad Labem, Czech Republic
Jiří Felcman: Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 186 75 Praha, Czech Republic

Mathematics, 2021, vol. 9, issue 13, 1-23

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 ? 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 ? 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 ? . 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.

Keywords: pedestrian flow equations; Eikonal equation; finite volume method; discontinuous Galerkin method; hyperbolic equations; pedestrian evacuation problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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