An Extended AW–Rascle Model with Source Terms and Its Numerical Solution

This chapter delves into the enhancement of traffic flow modeling by integrating source terms into an extended AW–Rascle model, addressing the limitations of traditional continuum models. The study introduces an inhomogeneous continuum equation with a velocity dynamics equation, incorporating diffusion terms to better represent real-world traffic conditions. The MacCormack central dispersion smoothing scheme is employed to numerically solve the model, ensuring spatial accuracy and preventing numerical oscillations. The chapter presents a comprehensive analysis of different initial and source conditions, demonstrating the model's ability to predict traffic states with minimal error. Validation with empirical data from a road stretch in Chennai highlights the model's practical applicability and accuracy in capturing the complexities of mixed traffic conditions. The findings suggest that incorporating source terms into higher-order traffic flow models significantly improves the simulation of localized events, such as on-ramps, off-ramps, and traffic signals, providing a more realistic and accurate representation of traffic dynamics.