Geodesic
A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem
Christophe Chalons1 ; Maria Laura Delle Monache2 ; Paola Goatin3
1Université de Versailles Saint-Quentin-en-Yvelines, France
2Inria Grenoble Rhône - Alpes, France and Rutgers University, Camden, USA
3Inria Sophia Antipolis – Méditerranée, France
Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 553-570

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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.
DOI : 10.4171/ifb/392
Classification : 35-XX, 90-XX
Mots-clés : Scalar conservation laws with local moving constraints, traffic flow modeling, PDE-ODE coupling, conservative finite volume schemes

Christophe Chalons  1   ; Maria Laura Delle Monache  2   ; 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 
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, Tome 19 (2017) no. 4, pp. 553-570. doi: 10.4171/ifb/392
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     title = {A conservative scheme for non-classical solutions to a strongly coupled {PDE-ODE} problem},
     journal = {Interfaces and free boundaries},
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     year = {2017},
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     number = {4},
     doi = {10.4171/ifb/392},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/392/}
}
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