English

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

Dynamical Systems 2021-03-22 v2 Optimization and Control

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.

Keywords

Cite

@article{arxiv.1807.07461,
  title  = {Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road},
  author = {Gabriella Bretti and Emiliano Cristiani and Corrado Lattanzio and Amelio Maurizi and Benedetto Piccoli},
  journal= {arXiv preprint arXiv:1807.07461},
  year   = {2021}
}

Comments

Updated to the Final Published Version

R2 v1 2026-06-23T03:07:31.925Z