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Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models

Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models
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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.

Author Details

Shaoshuai Chu

Alexander Kurganov

Saeed Mohammadian

Zuduo Zheng

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    Chu, Shaoshuai | Kurganov, Alexander | Xin, Ruixiao

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