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.
Mots clés : crowd motion model, contact dynamics, convex analysis, differential inclusion, prox-regularity
@article{M2AN_2011__45_1_145_0,
author = {Maury, Bertrand and Venel, Juliette},
title = {A discrete contact model for crowd motion},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {145--168},
publisher = {EDP-Sciences},
volume = {45},
number = {1},
year = {2011},
doi = {10.1051/m2an/2010035},
mrnumber = {2781134},
zbl = {1271.34020},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010035/}
}
TY - JOUR AU - Maury, Bertrand AU - Venel, Juliette TI - A discrete contact model for crowd motion JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 145 EP - 168 VL - 45 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010035/ DO - 10.1051/m2an/2010035 LA - en ID - M2AN_2011__45_1_145_0 ER -
%0 Journal Article %A Maury, Bertrand %A Venel, Juliette %T A discrete contact model for crowd motion %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 145-168 %V 45 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010035/ %R 10.1051/m2an/2010035 %G en %F M2AN_2011__45_1_145_0
Maury, Bertrand; Venel, Juliette. A discrete contact model for crowd motion. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 1, pp. 145-168. doi : 10.1051/m2an/2010035. http://www.numdam.org/articles/10.1051/m2an/2010035/
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