Macroscopic modeling and simulations of room evacuation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Applied Mathematical Modelling Year : 2014

Macroscopic modeling and simulations of room evacuation

Abstract

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-finite element method to solve the problems and present error analysis for the eikonal solver, gradient computation and the second order model yielding a first order convergence. We show that Hughes’ model is incapable of reproducing complex crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally, using the second order model, we study numerically the evacuation of pedestrians from a room through a narrow exit.

Dates and versions

hal-01731335 , version 1 (14-03-2018)

Identifiers

Cite

Monika Twarogowska, Paola Goatin, Régis Duvigneau. Macroscopic modeling and simulations of room evacuation. Applied Mathematical Modelling, 2014, 38 (24), pp.5781-5795. ⟨10.1016/j.apm.2014.03.027⟩. ⟨hal-01731335⟩
1236 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More