Numerical study of the non-conservative NET-RAT traffic flow model by path-conservative central-upwind schemes

Behavioral non-equilibrium hyperbolic traffic models, derived from approximated car-following models with human factors, can lose their conservative form, rendering traditional flux-based numerical methods ineffective. This challenge also applies to the recently proposed behavioral continuum (non-equilibrium traffic model based on risk allostasis theory, that is, NET-RAT) model. This paper is focused on solving the Riemann problem and several other initial-value problems for the novel NET-RAT model in the non-conservative form by path-conservative central-upwind (PCCU) schemes. We design extensive numerical tests considering the unique behavioral properties of the NET-RAT model. The PCCU schemes are then applied to these tests and the obtained results demonstrate that major wave types are effectively and accurately captured. At the same time, the fifth-order scheme, which is constructed using an alternative weighted essentially non-oscillatory (A-WENO) approach, yields substantially sharper resolution than its second-order counterpart. The presented numerical study can facilitate the practical implementation of the NET-RAT model for real-world traffic.