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
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Date
2015Author
Andreianov, Boris
Donadello, Carlotta
Razafison, Ulrich
Rosini, Massimiliano Daniele
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In this paper we investigate numerically the model for pedestrian traffic proposed in [B. Andreianov, C. Donadello,
M.D. Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models
and Methods in Applied Sciences 24 (13) (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.
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