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,w...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 secondorder 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.展开更多
基金NSFC grants 12171226 and 12111530004the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘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 secondorder 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.
