Grad’s moment method for vehicular traffic

Abstract

Based on a Boltzmann-like traffic equation and on Grad’s moment method we construct asecond-order continuum traffic flow model which is similar to the usual Navier–Stokesequations for viscous fluids. The viscosity coefficient appearing in our macroscopic trafficmodel is not introduced in an ad hoc way—as in other high-order traffic flow models—butcomes into play via an iteration method akin to a Maxwellian procedure. As in some of themost popular second-order continuum models, our Navier–Stokes-like traffic model predictsthe existence of a characteristic speed which is faster than the average velocity. However,by performing a linear stability analysis, it is possible to show that the fastercharacteristic speed does not constitute a deficiency of our second-order trafficmodel since it is related to a mode that decays quickly. Numerical simulations fordifferent traffic scenarios show that the Navier–Stokes-like traffic model producesnumerical results which are consistent with our daily experiences in real traffic.