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

Florent Berthelin; Thierry Goudon; Bastien Polizzi; Magali Ribot; Florent Berthelin; Thierry Goudon; Bastien Polizzi; Magali Ribot

doi:10.3934/nhm.2017024

Networks and Heterogeneous Media

2017, Volume 12, Issue 4: 591-617. doi: 10.3934/nhm.2017024

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

1.
Université Côte d'Azur, Inria, CNRS, LJAD, Parc Valrose, 06108 Nice, France
2.
Institut de Mécanique des Fluides de Toulouse, CNRS UMR 5502, France
3.
Université d'Orléans, MAPMO, UMR CNRS 7349, France

Received: 01 December 2016 Revised: 01 August 2017
Primary: 65M08; Secondary: 35L60, 90B20, 35Q91

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicle 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.
- Traffic flows,
- unilateral constraints,
- finite volume schemes,
- asymptotic preserving schemes
Citation: Florent Berthelin, Thierry Goudon, Bastien Polizzi, Magali Ribot. Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams[J]. Networks and Heterogeneous Media, 2017, 12(4): 591-617. doi: 10.3934/nhm.2017024

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Abstract

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicle 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.

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