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

2015/11/09 by Di Francesco, M., Fagioli, S., Rosini, M. D.
#35L65 #90B20 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.02700

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 BV estimates on the discrete particle velocity. We complement out result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.

Related

• Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows
• A deterministic particle approximation for non-linear conservation laws
• On a degenerate second order traffic model: existence of discrete evolutions, deterministic many-particle limit and first order approximation
• A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model
• Well-posedness results for the Generalized Aw-Rascle-Zhang model