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

Andreianov, Boris; Donadello, Carlotta; Razafison, Ulrich; Rosini, Massimiliano D.

doi:10.1051/m2an/2015078

Andreianov, Boris ^1,² ; Donadello, Carlotta ¹ ; Razafison, Ulrich ¹ ; Rosini, Massimiliano D.³

¹ Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 25030 16 route de Gray, 25030 Besançon cedex, France.
² LMPT CNRS UMR 7350, 37200 Tours, France.
³ Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Skłodowskiej 5, 20-031 Lublin, Poland.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1269-1287.

Résumé

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.

Reçu le : 2015-03-31
Accepté le : 2015-10-11

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/m2an/2015078

Classification : 35L65, 90B20, 65M12, 76M12
Mots-clés : Finite volume scheme, scalar conservation law, non-local point constraint, crowd dynamics, capacity drop, Braess’ paradox, Faster Is Slower

Affiliations des auteurs :

Andreianov, Boris ^{1, 2} ; Donadello, Carlotta ¹ ; Razafison, Ulrich ¹ ; Rosini, Massimiliano D. ³

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     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},
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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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