Numerical simulation of macroscopic continuum traffic models

This paper presents the derived Roe's flux difference splitting method for Payne's formulation of the macroscopic model. In recent years, this finite difference method has generated much interest and been used successfully in gas dynamics. Payne's equations are actually those of the isentropic gas having constant speed of sound and in homogeneous terms on the right hand side. Our motivation for deriving Roe's flux difference splitting algorithm for Payne's model and also highlighting the scalar equivalent of Roe's method (the Murman scheme) for the Lighthill-Whitham (LW) model stems from the reports of numerical simulation difficulties pertaining to two models. The numerical schemes were used on Payne's and LW models to simulate three traffic scenarios with satisfactory results. We were able to simulate the propagation of congested density upstream in one freeway bottleneck scenario at a finer discretization. Another scenario did not manage to obtain realistic results with Payne's model, we did.