Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models (Communications in Computational Physics, 2023)
Non-equilibrium hyperbolic traffic models can be derived as continuumapproximations of car-following models and in many cases the resulting continuummodels are non-conservative. This leads to numerical difficulties, which seem to havediscouraged further development of complex behavioral continuum models, which isa significant research need.In this paper, we develop a robust numerical scheme that solves hyperbolic trafficflow models based on their non-conservative form. We develop a fifth-order alternative weighted essentially non-oscillatory (A-WENO) finite-difference scheme basedon the path-conservative central-upwind (PCCU) method for several non-equilibriumtraffic flow models. In order to treat the non-conservative product terms, we use apath-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 thisscheme 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 ona number of challenging numerical examples. Both schemes produce quite accurate results though the resolution achieved by the fifth-order A-WENO scheme is higher. Theproposed scheme in this paper sets the stage for developing more robust and complexcontinuum traffic flow models with respect to human psychological factors.
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.