Skip to Main content Skip to Navigation
Reports

Numerical study of macroscopic pedestrian flow models

Monika Twarogowska 1 Paola Goatin 1 Régis Duvigneau 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We analyze numerically macroscopic models of crowd dynamics: 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 function standing for minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-element method to solve the problems and present error analysis in case of 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. In particular, we analyze the effect on the total evacuation time of the level of compression, the desired speed and the presence of obstacles.
Document type :
Reports
Complete list of metadata

Cited literature [50 references]  Display  Hide  Download

https://hal.inria.fr/hal-00849587
Contributor : Monika Twarogowska <>
Submitted on : Wednesday, July 31, 2013 - 2:30:40 PM
Last modification on : Monday, October 12, 2020 - 2:28:02 PM
Long-term archiving on: : Friday, November 1, 2013 - 4:12:19 AM

File

RR-8340.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00849587, version 1

Citation

Monika Twarogowska, Paola Goatin, Régis Duvigneau. Numerical study of macroscopic pedestrian flow models. [Research Report] RR-8340, INRIA. 2013. ⟨hal-00849587⟩

Share

Metrics

Record views

815

Files downloads

811