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A discrete contact model for crowd motion

Published online by Cambridge University Press:  24 June 2010

Bertrand Maury  and
Juliette Venel
Bertrand Maury
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud XI, 91405 Orsay Cedex, France. [email protected]
Juliette Venel
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud XI, 91405 Orsay Cedex, France. [email protected]
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Abstract

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed.

Keywords

Crowd motion modelcontact dynamicsconvex analysisdifferential inclusionprox-regularity
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 1 , January 2011 , pp. 145 - 168
Copyright
© EDP Sciences, SMAI, 2010

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