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

Christophe Chalons (1) , Maria Laura Delle Monache (2) , Paola Goatin (3)

1 LMV - Laboratoire de Mathématiques de Versailles
2 NECS - Networked Controlled Systems
3 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

We consider a strongly coupled PDE-ODE system that describes 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 a tracking algorithm for the ODE. We show numerical tests and compute numerically the order of convergence.

Mots clés: Conservative finite volume schemes; Scalar conservation laws with local moving constraints; Traffic flow modeling; PDE-ODE coupling; Conservative finite volume schemes.

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Chalons, Maria Laura Delle Monache, Paola Goatin. A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem. Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, 2017, 19 (4), pp.553-570. ⟨10.4171/IFB/392⟩. ⟨hal-01070262⟩