An interface-free multi-scale multi-order model for traffic flow

In this paper we present a new multi-scale method for reproducing traffic flow which couples a first-order macroscopic model with a second-order microscopic model, avoiding any interface or boundary conditions between them. The multi-scale model is characterized by the fact that microscopic and macroscopic descriptions are not spatially separated. On the contrary, the macro-scale is always active while the micro-scale is activated only if needed by the traffic conditions. The Euler-Godunov scheme associated to the model is conservative and it is able to reproduce typical traffic phenomena like stop & go waves.