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Nonlinear hyperbolic partial differential equations govern continuum traffic flow models. Higher-order traffic flow models consisting of continuum equations and velocity dynamics were introduced to address the limitations of the Lighthill, Whitham, and Richards (LWR) model. However, these models are ineffective in incorporating road heterogeneity. This paper integrates an extended AW-Rascle higher-order model with the source terms in the continuum equation to predict the traffic states in heterogeneous road conditions. The system of the equations was solved numerically with the central dispersion (CD) method incorporated into the standard McCormack scheme. Smoothing is applied to take care of the numerical oscillation of the higher-order model. Different combinations of initial conditions with source terms showed that the proposed model with the numerical methods could produce a stable solution and eliminate oscillation of the McCormack scheme.
Maiti et al. (Tue,) studied this question.