Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic

Marco Di Francesco; Simone Fagioli; Massimiliano D. Rosini; Marco Di Francesco; Simone Fagioli; Massimiliano D. Rosini

doi:10.3934/mbe.2017009

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 127-141. doi: 10.3934/mbe.2017009

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Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic

1.
DISIM, Università degli Studi dell'Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), Italy
2.
Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Sk lodowskiej 1, 20-031 Lublin, Poland

Received: 23 November 2015 Accepted: 15 April 2016 Published: 01 February 2017
MSC : Primary: 35L65, 90B20

We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$ estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.
- Aw-Rascle-Zhang model,
- second order models for vehicular traffics,
- many particle limit
Citation: Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini. Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 127-141. doi: 10.3934/mbe.2017009

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Abstract

We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$ estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.

References

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