Problèmes mathématiques de la mécanique
Modélisation du trafic autoroutier au second ordre
[Modelling of motorway traffic to second order]
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1203-1206.

In the first part of the Note, we introduce a second order traffic flow model, which we derive from simple physical considerations. We consider the related Riemann problem and solve it in any cases. In the second part, we examine what is required for the construction of proper analytical solutions to be always possible, and what the extended model implies in term of incompressibility, and conservation of physically meaningful quantities.

Nous considérons un modèle de trafic autoroutier au second ordre que nous bâtirons à partir de considérations comportementales simples. L'analyse du problème de Riemann afférent sera menée. Dans la seconde partie nous développerons la définition d'une solution obtenue à la limite, issue d'une famille de problèmes perturbés rendant le problème de Riemann toujours solvable. Nous constaterons enfin les conséquences de cette extension en terme de limite de compressibilité et de conservation de quantités comportementales.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.09.024
Lebacque, Jean Patrick 1; Louis, Xavier 1; Mammar, Salim 1; Schnetzler, Bernard 1; Haj-Salem, Habib 1

1 Paris Est, Inrets, Gretia, 94114 Arcueil, France
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Lebacque, Jean Patrick; Louis, Xavier; Mammar, Salim; Schnetzler, Bernard; Haj-Salem, Habib. Modélisation du trafic autoroutier au second ordre. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1203-1206. doi : 10.1016/j.crma.2008.09.024. http://www.numdam.org/articles/10.1016/j.crma.2008.09.024/

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