  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.
