Modélisation mathématique et numérique de mouvements de foule

Abstract : We are interested in modelling crowd motion in emergency evacuation. The aim of this thesis is to propose a mathematical model and a numerical method to handle contacts, in order to deal with local interactions between people and to describe the whole dynamics of the pedestrian traffic. We propose a microscopic model for crowd motion which rests on two principles. On the one hand, each individual has a spontaneous velocity that he would like to have in the absence of other people. On the other hand, the actual velocity must take into account congestion. By specifying the link between these two velocities, the evolution problem takes the form of a first order differential inclusion. Its well-posedness is proved with the help of results concerning sweeping processes by uniformly prox-regular sets. Then we present a numerical scheme and prove its convergence. In order to compute a specific spontaneous velocity (the one directed by the shortest path avoiding the obstacles), we present an object oriented programming to simulate the evacuation of any building consisting of several floors. To conclude, we describe other choices of spontaneous velocity (for example, by including individual strategies) and we present associated numerical results. These numerical simulations allow us to recover some characteristics of pedestrian traffic.
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https://tel.archives-ouvertes.fr/tel-00346035
Contributor : Juliette Venel <>
Submitted on : Wednesday, December 10, 2008 - 8:40:39 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on : Tuesday, June 8, 2010 - 4:08:21 PM

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Juliette Venel. Modélisation mathématique et numérique de mouvements de foule. Mathématiques [math]. Université Paris Sud - Paris XI, 2008. Français. ⟨tel-00346035⟩

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