The Research Of Low Dissipation Central-upwind Scheme For Complicated Traffic Flow Model Equations

With the improvement of national living standard,the traffic problem has become an important factor restricting the development of national economy.The study of traffic flow theory is an important part of the city's road planning and the city's transportation system,and it can also provide scientific support for the city's transportation management,and reduce unnecessary financial input.Therefore,in recent years,the research on traffic flow problems has also been an important subject for many scholars.In this article,we study on the high-resolution numerical format for multi-class Lighthill-Whitham-Richards traffic model,the multi-class Lighthill-Whitham-Richards traffic model on an inhomogeneous highway and the high-order traffic flow model of the macro traffic flow model,and mainly from the following aspects:(1)Considering the close relationship between the traffic flow model equation and the hyperbolic conservation law equation,this paper introduces in detail the fourth order center upwind format for solving the hyperbolic conservation law equation,which combines the central windward numerical flux with the fourth order CWENO reconstruction proposed by Levy.Although the fourth order central-upwind scheme can meet the requirements of high precision and high resolution in the smooth region of the solution,the accuracy of the continuous solution will decrease at the extreme points and discontinuities.Considering that most of the traffic flow phenomena in traffic flow model of the numerical results will be more the phenomenon of discontinuities and extremum.So in this paper,the fourth order center upwind scheme is improved.(2)Firstly,by defining a new slope calculation method and conducting piecewise linear reconstruction in the projection step,to obtain a central-upwind numerical flux with lower numerical dissipation.Then combined with the improved 4rd-order CWENO reconstruction by increasing the nonlinear weight corresponding to the non-smooth template and changing the global smoothing indictor,a fourth-order low dissipation central-upwind scheme was constructed for solving hyperbolic conservation law equation.Finally,numerical results show that the new scheme has not only 4-order accuracy,but also has the characteristics of high resolution.(3)The a fourth order low dissipation central-upwind scheme is extended and applied to solve the traffic light release problem,initial disturbance problem and traffic queue dissipation problem of the multi-class Lighthill-Whitham-Richards(LWR)traffic model;the problem of lane number increase(decrease)and the problem of the traffic signal transformation of the multi-class Lighthill-Whitham-Richards(LWR)traffic model on an inhomogeneous highway;the problem of stop-and-go waves and traffic jams problem of conserved high order model are simulated respectively;and the traffic flow phenomena and traffic wave caused by these traffic flow problems are analyzed in detail.By comparing numerical errors and graphs,it's shown that the new scheme has the advantages of high resolution and low dissipation,and it has universality for different traffic flow models.It is an effective method to solve the traffic flow model.