555 RWTH Publication No: 811906        2020       
TITLE Second-order traffic flow models on networks
AUTHORS Simone Göttlich, Michael Herty, Salissou Moutari, Jennifer Weißen
ABSTRACT This paper deals with the Aw-Rascle-Zhang model for traffic flow on uni-directional road networks. For the conservation of the mass and the generalized momentum, we construct weak solutions for Riemann problems at the junctions. We particularly focus on a novel approximation to the homogenized pressure by introducing an additional equation for the propagation of a reference pressure. The resulting system of coupled conservation laws is then solved using an appropriate numerical scheme of Godunov type. Numerical simulations show that the proposed approximation is able to approximate the homogenized pressure sufficiently well. The difference of the new approach compared with the Lighthill- Whitham-Richards model is also illustrated.
KEYWORDS Conservation laws on networks, Aw-Rascle-Zhang model, homogenized pressure
DOI 10.1137/20M1339908
PUBLICATION SIAM Journal on Applied Mathematics, Vol. 81, Iss. 1 (2021)