A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem

  • Christophe Chalons

    Université de Versailles Saint-Quentin-en-Yvelines, France
  • Maria Laura Delle Monache

    Inria Grenoble Rhône - Alpes, France and Rutgers University, Camden, USA
  • Paola Goatin

    Inria Sophia Antipolis – Méditerranée, France
A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem cover
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Abstract

We consider a strongly coupled PDE-ODE system modeling the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law describing the main traffic evolution and an ODE accounting for the trajectory of the slower vehicle that depends on the downstream traffic density. The moving constraint is operated by an inequality on the flux, which accounts for the bottleneck created on the road by the presence of the slower vehicle.We introduce a conservative scheme for the constrained hyperbolic PDE and we use a tracking algorithm for the ODE. We perform numerical tests and compute numerically the order of convergence.

Cite this article

Christophe Chalons, Maria Laura Delle Monache, Paola Goatin, A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem. Interfaces Free Bound. 19 (2017), no. 4, pp. 553–570

DOI 10.4171/IFB/392