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. (English) Zbl 1370.65042
A numerical model for pedestrian traffic, originally presented in [B. Andreianov et al., Math. Models Methods Appl. Sci. 24, No. 13, 2685–2722 (2014; Zbl 1307.35166)], is here evaluated and validated. The non-local constrained finite volume method is described and its convergence is shown and validated with an explicit solution obtained. Two characteristic simulation problems with collective effects in crowd dynamics: Faster is slower and the Braess’ paradox are used and qualitative highlight the bottleneck behavior numerical reproduction.
Reviewer: Vasilis Dimitriou (Chania)
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 90B20 | Traffic problems in operations research |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
Keywords:
finite volume scheme; scalar conservation law; non-local point constraint; crowd dynamics; capacity drop; Braess’ paradox; faster is slowerCitations:
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