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 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.