Interfaces and Free Boundaries


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Volume 19, Issue 4, 2017, pp. 553–570
DOI: 10.4171/IFB/392

Published online: 2018-01-15

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

Christophe Chalons[1], Maria Laura Delle Monache[2] and Paola Goatin[3]

(1) Université de Versailles Saint-Quentin-en-Yvelines, France
(2) Inria Grenoble Rhône - Alpes, France and Rutgers University, Camden, USA
(3) Inria Sophia Antipolis – Méditerranée, France

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.

Keywords: Scalar conservation laws with local moving constraints, traffic flow modeling, PDE-ODE coupling, conservative finite volume schemes

Chalons Christophe, Delle Monache Maria Laura, Goatin Paola: A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem. Interfaces Free Bound. 19 (2017), 553-570. doi: 10.4171/IFB/392