Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams

Florent Berthelin (1, 2) , Thierry Goudon (1, 2) , Bastien Polizzi (3) , Magali Ribot (4)

1 COFFEE - COmplex Flows For Energy and Environment
2 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
3 IMFT - Institut de mécanique des fluides de Toulouse
4 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic arguments. Hence, we are interested in the simulation of approached models that contain stiff terms and large speeds of propagation. We design schemes intended to apply with relaxed stability conditions.

Mots clés: Glimm scheme; Asymptotic problems; Implicit explicit numerical scheme; Traffic modeling; Pressure modeling

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Adaptation et Systèmes auto-organisés [nlin.AO]

Florent Berthelin, Thierry Goudon, Bastien Polizzi, Magali Ribot. Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams. Networks and Heterogeneous Media, 2017, 12 (4). ⟨hal-01413613⟩