High-resolution Scheme In Application Of Traffic Flow Equations

It is an important research topic to discuss the macro traffic flow models in traffic flow simulation.As a typical representative of macro traffic flow model,LWR model and its extended models are not only simple to construct,but also can qualitatively analyze road traffic conditions,so LWR model is widely used in traffic flow simulation.The LWR model and its extended models can be mathematically written as a non-linear hyperbolic conservation law equation,so it can be solved by using the numerical solution technology of the hyperbolic conservation law equation.There are three main numerical methods for solving hyperbolic conservation laws.They are finite difference method,finite volume method and finite element method.From the perspective of finite volume method,more and more numerical methods satisfying the condition of entropy stability have been proposed,such as the high-resolution entropy stable scheme applied in this paper,which can avoid non-physical phenomena and reach a good application prospect.Aiming at the inaccuracy of low-order schemes in solving LWR model,this paper uses improved limiter and high-order CPR numerical method to solve LWR model of two-phase traffic flow.The specific work is as follows:(1)The entropy stable formula of traffic flow LWR model equation is constructed.In the numerical simulation,the interface of the element is discretized by the five-order weno-z + reconstruction,and the time direction is advanced by the strongly stable three-step and three-order runge-kutta method.A high precision,high resolution and numerical stability WENO-Z+ scheme is obtained.The newly constructed entropy stable weno-z + numerical algorithm is applied to the solution of several practical traffic flow problems.The results show that it has a good effect of capturing shock waves,and there is no non-physical oscillation in the discontinuous region.It is an ideal method to simulate the LWR model.(2)From the perspective of finite element,the high-order numerical method CPR for solving hyperbolic conservation laws equation is applied to solve the two-phase traffic flow LWR model equation.an improved CWENO limiter is added to control the oscillation at the discontinuity while maintaining the original high accuracy.Finally,Riemann problem and practical traffic flow phenomenon are combined for numerical simulation.The numerical examples show that the scheme is stable and accurate in solving the LWR model of two-phase traffic flow,and it is an ideal method to simulate the LWR model of two-phase traffic flow.