@Article{CiCP-33-3,
author = {Shaoshuai, Chu and Kurganov, Alexander and Saeed, Mohammadian and Zuduo, Zheng},
title = {Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {3},
pages = {692--732},
abstract = {<p style="text-align: justify;">Non-equilibrium hyperbolic traffic models can be derived as continuum
approximations of car-following models and in many cases the resulting continuum
models are non-conservative. This leads to numerical difficulties, which seem to have
discouraged further development of complex behavioral continuum models, which is
a significant research need.<br/>In this paper, we develop a robust numerical scheme that solves hyperbolic traffic
flow models based on their non-conservative form. We develop a fifth-order alternative weighted essentially non-oscillatory (A-WENO) finite-difference scheme based
on the path-conservative central-upwind (PCCU) method for several non-equilibrium
traffic flow models. In order to treat the non-conservative product terms, we use a
path-conservative technique. To this end, we first apply the recently proposed second-order finite-volume PCCU scheme to the traffic flow models, and then extend this
scheme to the fifth-order of accuracy via the finite-difference A-WENO framework.
The designed schemes are applied to three different traffic flow models and tested on
a number of challenging numerical examples. Both schemes produce quite accurate results though the resolution achieved by the fifth-order A-WENO scheme is higher. The
proposed scheme in this paper sets the stage for developing more robust and complex
continuum traffic flow models with respect to human psychological factors.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0263},
url = {https://global-sci.com/article/79430/fifth-order-a-weno-path-conservative-central-upwind-scheme-for-behavioral-non-equilibrium-traffic-models}
}