Geodesic
Non classical solution of a conservation law arising in vehicular traffic modelling
Mathieu Fabre1 ; Sylvain Faure2 ; Mathieu Laurière3 ; Bertrand Maury4 ; Charlotte Perrin5
1 EPFL SB MATHICSE MNS (Bât. MA), station 8, CH 1015 Lausanne (Switzerland)
2 Laboratoire de Mathématiques d’Orsay, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
3 NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai (China)
4 LMO, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France & DMA, École Normale Supérieure, Paris
5 Institut für Mathematik, RWTH Aachen University
ESAIM. Proceedings, Tome 55 (2016), pp. 131-147.

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We are interested in this paper in the modelling and numerical simulation of some phenomena that are observed in the context of car dynamics, in particular the appearance of persistent jams upstream critical points with no real cause of flux limitation. We shall consider the case of a stable jam on a freeway upstream an accident that took place on the opposite lane. This situation is not properly handled by most models, either micro-or macroscopic ones, since it corresponds to a phenomenon that does not have a counterpart in gas dynamics, for which only entropy solution are usually considered as physically feasible. The approach we propose consists in accounting for the very behaviour of agents in the neighbourhood of the discontinuity, and makes it possible to numerically recover in a robust way steady traffic jams.
DOI : 10.1051/proc/201655131

Mathieu Fabre 1 ; Sylvain Faure 2 ; Mathieu Laurière 3 ; Bertrand Maury 4 ; Charlotte Perrin 5

1 EPFL SB MATHICSE MNS (Bât. MA), station 8, CH 1015 Lausanne (Switzerland)
2 Laboratoire de Mathématiques d’Orsay, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
3 NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai (China)
4 LMO, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France & DMA, École Normale Supérieure, Paris
5 Institut für Mathematik, RWTH Aachen University 
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     title = {Non classical solution of a conservation law arising in vehicular traffic modelling},
     journal = {ESAIM. Proceedings},
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Mathieu Fabre; Sylvain Faure; Mathieu Laurière; Bertrand Maury; Charlotte Perrin. Non classical solution of a conservation law arising in vehicular traffic modelling. ESAIM. Proceedings, Tome 55 (2016), pp. 131-147. doi : 10.1051/proc/201655131. http://geodesic.mathdoc.fr/articles/10.1051/proc/201655131/

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