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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.
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Submitted on : Wednesday, July 31, 2013 - 2:30:40 PM
Last modification on : Thursday, August 4, 2022 - 4:52:47 PM
Long-term archiving on: : Friday, November 1, 2013 - 4:12:19 AM


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  • HAL Id : hal-00849587, version 1


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



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