On the kinetic theory of vehicular traffic flow: Chapman-Enskog expansion versus Grad's moment method

TL;DR

This paper develops a second-order continuum traffic model derived from a Boltzmann-like equation using Chapman-Enskog and Grad's methods, resulting in a Navier-Stokes-like model with physically grounded viscosity.

Contribution

It introduces a novel second-order traffic model with viscosity derived from kinetic theory, avoiding ad hoc assumptions and aligning with real traffic behavior.

Findings

Model satisfies anisotropy condition

Numerical results match real traffic patterns

Viscosity coefficient derived from first principles

Abstract

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier-Stokes equations for viscous fluids by applying two well-known methods of gas-kinetic theory, namely: the Chapman-Enskog method and the method of moments of Grad. The viscosity coefficient appearing in our macroscopic traffic model is not introduced in an ad hoc way - as in other second-order traffic flow models - but comes into play through the derivation of a first-order constitutive relation for the traffic pressure. Numerical simulations show that our Navier-Stokes-like traffic model satisfies the anisotropy condition and produces numerical results which are consistent with our daily experiences in real traffic.