Computer simulation of pedestrian crowds using a macroscopic model

• ID: 2770, RIV: 10332263
• ISSN: not specified, ISBN: 978-80-8105-729-8
• source: Applied Natural Sciences 2015
• keywords: pedestrian flow; eikonal equation; finite volume method; hyperbolic problems
• authors: Petr Kubera, Jiří Felcman
• authors from KNM: Felcman Jiří

Abstract

A macroscopic model describing the pedestrian flow consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation, we get the first order hyperbolic system of partial differential equations with a source term. We use the mathematical similarity with the shallow water equations (SWE) in the numerical solution by the finite volume method. The splitting technique is applied which leads to a combination of the finite volume method for the hyperbolic problem with the numerical solution of the system of ordinary differential equations. Additionally, the solution of the so-called eikonal equation plays an important role here. Such a solution determines the density dependent direction of pedestrian motion. The algorithm giving the time evolution of the density and velocity of pedestrians in the two-dimensional domain is described. The practical application of the algorithm for the evacuation of the 2D hall for various configurations of obstacles near to the exit is presented.