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.