Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic - Marco Di Francesco; Simone Fagioli; Massimiliano D. Rosini (Mathematical Biosciences and Engineering)
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 our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.