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

Gabriella Bretti, Emiliano Cristiani, Corrado Lattanzio, Amelio Maurizi, Benedetto Piccoli

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)55-83
Number of pages29
JournalMathematics In Engineering
Volume1
Issue number1
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematical Physics
  • Analysis

Keywords

  • Conservation laws
  • Discontinuous ODEs
  • Fluid dynamic models
  • LWR model

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