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

TL;DR

This paper extends the AW-Rascle traffic flow model by incorporating source terms to better simulate heterogeneous road conditions and introduces a numerical solution that stabilizes the system and reduces oscillations.

Contribution

The paper develops an extended AW-Rascle model with source terms and proposes a numerical scheme that improves stability and accuracy in heterogeneous traffic scenarios.

Findings

The model successfully predicts traffic states on heterogeneous roads.

The numerical method reduces oscillations and stabilizes solutions.

The approach is effective across various initial conditions.

Abstract

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.