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

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 simulation shows 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.