守恒律中非局部点约束的解的定性行为及数值近似研究及人群动态在瓶颈处的建模
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
AI总结：
本文研究了人群交通模型的数值行为，验证了约束有限体积方法的收敛性，并通过模拟验证了模型在瓶颈处再现典型现象的能力，如Faster Is Slower效应和 Braess悖论。
摘要：
本文研究了在[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]中提出的行人交通模型的数值行为。我们证明了基于约束有限体积方法的方案的收敛性，并通过上述参考文献中获得的显式解进行验证。然后，我们进行了专门的模拟，以定性验证所考虑模型在瓶颈处的表现，证明其能够再现典型现象，如Faster Is Slower效应和Braess悖论。
英文摘要：
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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