In this paper we investigate numerically the model for pedestrian traffic proposed in [B. Andreianov, C. Donadello, M.D. Rosini, Math. Models Methods Appl. Sci. 24 (2014) 2685−2722]. We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess’ paradox.
Accepté le :
DOI : 10.1051/m2an/2015078
Mots clés : Finite volume scheme, scalar conservation law, non-local point constraint, crowd dynamics, capacity drop, Braess’ paradox, Faster Is Slower
@article{M2AN_2016__50_5_1269_0,
author = {Andreianov, Boris and Donadello, Carlotta and Razafison, Ulrich and Rosini, Massimiliano D.},
title = {Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1269--1287},
publisher = {EDP-Sciences},
volume = {50},
number = {5},
year = {2016},
doi = {10.1051/m2an/2015078},
zbl = {1370.65042},
mrnumber = {3554543},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015078/}
}
TY - JOUR AU - Andreianov, Boris AU - Donadello, Carlotta AU - Razafison, Ulrich AU - Rosini, Massimiliano D. TI - Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1269 EP - 1287 VL - 50 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015078/ DO - 10.1051/m2an/2015078 LA - en ID - M2AN_2016__50_5_1269_0 ER -
%0 Journal Article %A Andreianov, Boris %A Donadello, Carlotta %A Razafison, Ulrich %A Rosini, Massimiliano D. %T Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1269-1287 %V 50 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015078/ %R 10.1051/m2an/2015078 %G en %F M2AN_2016__50_5_1269_0
Andreianov, Boris; Donadello, Carlotta; Razafison, Ulrich; Rosini, Massimiliano D. Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1269-1287. doi : 10.1051/m2an/2015078. http://www.numdam.org/articles/10.1051/m2an/2015078/
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