Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models
Year: 2023
Author: Shaoshuai Chu, Alexander Kurganov, Saeed Mohammadian, Zuduo Zheng
Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 692–732
Abstract
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.
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0263
Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 692–732
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 41
Keywords: Finite-difference A-WENO schemes finite-volume central-upwind schemes path-conservative central-upwind schemes non-oscillatory schemes continuum traffic flow model driver behavior.