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Volume 33, Issue 3
Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models

Shaoshuai Chu, Alexander Kurganov, Saeed Mohammadian & Zuduo Zheng

Commun. Comput. Phys., 33 (2023), pp. 692-732.

Published online: 2023-04

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  • 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.

  • AMS Subject Headings

76M20, 76M12, 65M06, 65M08, 76A30, 35L65, 35L67

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COPYRIGHT: © Global Science Press

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@Article{CiCP-33-692, author = {Chu , ShaoshuaiKurganov , AlexanderMohammadian , Saeed and Zheng , Zuduo}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0263}, url = {http://global-sci.org/intro/article_detail/cicp/21657.html} }
TY - JOUR T1 - Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models AU - Chu , Shaoshuai AU - Kurganov , Alexander AU - Mohammadian , Saeed AU - Zheng , Zuduo JO - Communications in Computational Physics VL - 3 SP - 692 EP - 732 PY - 2023 DA - 2023/04 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0263 UR - https://global-sci.org/intro/article_detail/cicp/21657.html KW - Finite-difference A-WENO schemes, finite-volume central-upwind schemes, path-conservative central-upwind schemes, non-oscillatory schemes, continuum traffic flow model, driver behavior. AB -

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.

Shaoshuai Chu, Alexander Kurganov, Saeed Mohammadian & Zuduo Zheng. (2023). Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models. Communications in Computational Physics. 33 (3). 692-732. doi:10.4208/cicp.OA-2022-0263
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