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 (Q2830698)
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scientific article; zbMATH DE number 6645492
| Language | Label | Description | Also known as |
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| English | 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 |
scientific article; zbMATH DE number 6645492 |
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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)
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28 October 2016
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finite volume scheme
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scalar conservation law
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non-local point constraint
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crowd dynamics
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capacity drop
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Braess' paradox
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faster is slower
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A numerical model for pedestrian traffic, originally presented in [\textit{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.
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