A new continuum model for traffic flow and numerical tests

A new continuum traffic flow model is developed in this paper based on an improved car-following model. In this new continuum model, the speed gradient replaces the density gradient in the equation of motion, and this replacement guarantees the property that the characteristic speeds are always less than or equal to the macroscopic flow speed. This new model also overcomes the backward travel problem that exists in many high-order continuum models. Shock waves, rarefaction waves, stop-and-go waves, and local cluster effects can be obtained from this new model and are consistent with the diverse nonlinear dynamical phenomena observed in the freeway traffic.