Stabilized finite element computations with a two-dimensional continuum model for disorderly traffic flow

Abstract

A two-dimensional continuum model of traffic flow is proposed. The model incorporates disorderly traffic, lane indiscipline, streamwise variation of the width of the road, as well as the impact of edges of the road, on the traffic. A stabilized finite element formulation is employed to solve the governing equations. The performance of the model is demonstrated using numerical experiments. Several features that are commonly observed in high speed flow of fluids, such as oblique shocks, normal shocks, slip lines, and expansion fans, are observed in the traffic flow simulated via the proposed model. The model is utilized to predict the traffic capacity of a road with varying road width. It is found that the narrow section behaves as a throat in a converging diverging nozzle in high speed fluid flow. The proposed model explains several phenomena observed in real traffic streams.