Special Session 100: 

Instabilities in kinetic traffic models

Gabriella Puppo
University of Insubria
Italy
Co-Author(s):    
Abstract:
I will describe the onset of unstable modes, such as stop and go waves, from the point of view of kinetic models for traffic flow. Stop and go waves can be viewed as non equilibrium phenomena which arise in the congested phase of traffic. These modes propagate backwards with respect to the microscopic velocities of individual vehicles, and they are signalled by the presence of a non positive diffusion coefficient in the Chapman-Enskog expansion around equilibrium states. I will also discuss the numerical issues linked to the capture of these waves, and the construction of asymptotic preserving schemes to capture the macroscopic equation describing traffic at equilibrium. Some numerical tests will illustrate the onset and development of unstable waves.