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Mathematics > Dynamical Systems

arXiv:1807.07461 (math)
[Submitted on 19 Jul 2018 (v1), last revised 19 Mar 2021 (this version, v2)]

Title:Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road

Authors:Gabriella Bretti, Emiliano Cristiani, Corrado Lattanzio, Amelio Maurizi, Benedetto Piccoli
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Abstract:In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limiting the car flux. The first algorithm, based on the Wave Front Tracking method, is suitable for theoretical investigations and convergence results. The second one, based on the Godunov scheme, is used for numerical simulations. The case of multiple bottlenecks is also investigated.
Comments: Updated to the Final Published Version
Subjects: Dynamical Systems (math.DS); Optimization and Control (math.OC)
Cite as: arXiv:1807.07461 [math.DS]
  (or arXiv:1807.07461v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1807.07461
Journal reference: Math. Eng 1 (2019), no. 1, 55-83 (published online 14 September 2018)
Related DOI: https://doi.org/10.3934/Mine.2018.1.55

Submission history

From: Corrado Lattanzio [view email]
[v1] Thu, 19 Jul 2018 14:24:42 UTC (1,174 KB)
[v2] Fri, 19 Mar 2021 09:33:36 UTC (3,147 KB)
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