Improved Numerical Method for Aw-Rascle Type Continuum Traffic Flow Models
Saeed Mohammadian (Queensland University of Technology)
FLM van Wageningen-Kessels (TU Delft - Transport and Planning, German University of Technology in Oman)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
Continuum traffic flow models are essentially nonlinear hyperbolic systems of partial differential equations. Except for limited specific cases, these systems must be solved numerically. Mathematical structure of continuum models can be different for each class of models. As a result, suitable numerical schemes for some classes may not be efficient for others. In this study, an improved numerical method is proposed for a class of second-order traffic flow models. The method is based on McCormack scheme, which is a widely-used method for non-homogeneous second-order traffic flow models, but fails to produce reasonable results for homogeneous models including Aw-Rascle type models which are the focus of this paper. It is shown that this is mainly due to spurious numerical oscillations. Smoothing methods to overcome these issues are studied and applied. Central dispersion and artificial viscosity (AV) methods are incorporated into the standard McCormack scheme and tested. To reduce numerical diffusion, a total variation diminishing Runge-Kutta time stepping scheme is applied. Results show the capability of the proposed methods, and especially the AV method, to eliminate the oscillations of the standard McCormack scheme as well as controlling numerical diffusion.