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
For researchers in crowd dynamics, this provides a validated numerical scheme for a model capturing bottleneck phenomena, but the work is incremental as it extends existing methods to a known model.
This paper proves convergence of a finite volume scheme for a pedestrian crowd model with non-local flux constraints, validates it against an explicit solution, and shows the model reproduces the Faster Is Slower effect and Braess' paradox.
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.