584 RWTH Publication No: 811909        2020       
TITLE From kinetic to macroscopic models and back
AUTHORS Michael Herty, G. Puppo, Giuseppe Visconti
ABSTRACT We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined modeling of the space of the microscopic speeds and of the interaction rate in the kinetic model allows to obtain weakly unstable backward propagating waves in dense traffic, without relying on non-local terms or multi--valued fundamental diagrams. A stability analysis of these waves is carried out using the Chapman-Enskog expansion. This leads to a BGK-type model derived as the mesoscopic limit of a Follow-The-Leader or Bando model, and its macroscopic limit belongs to the class of second-order Aw-Rascle and Zhang models.
DOI 10.1007/978-3-030-66560-9_2
PUBLICATION Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models pp 17–34