The High-Resolution Numerical Scheme For Solving Traffic Flow Equations

With the continuous improvement of people’s living standards,transportation problem has become an important problem in the current and future long time,and seriously restricts the sustainable development of our urban economy.The study of traffic flow theory can help people better understand the traffic system operation law,and can provide reliable and practical theoretical basis for urban traffic management.The research method of traffic flow mainly uses mathematics,physics and other theories to describe the real traffic phenomenon,that is,to establish the corresponding mathematical model,and then carry out numerical simulation and solution.This research method is an effective means to solve the traffic flow problem at present.This paper mainly studies the numerical solving methods of scalar LWR traffic flow model,multi-class LWR traffic flow model and multi-class LWR traffic flow model on an inhomogeneous highway.Specific work is as follows:(1)In this paper,a high-resolution entropy consistent scheme of the LWR model in traffic flow is proposed.Based on MUSCL-type reconstruction method,a new kind of slope limiter is constructed.The high-resolution entropy consistent scheme for solving LWR model can be obtained by adding a slope limiter to the entropy consistent scheme.Applying the newly constructed scheme to the solution of multiple practical traffic flow problems.The numerical results show that the scheme can capture shock waves well,there are no non-physical oscillations in the discontinuous region,and smooth transition in the rarefaction region.(2)Multi-class LWR traffic flow model and multi-class LWR traffic flow model on an inhomogeneous highway are generalized based on scalar LWR traffic flow model.The new slope limiter is applied to semi-discrete center upwind scheme to obtain high-resolution semi-discrete center upwind scheme.The separation,mixing and queuing dissipation of multi-vehicle LWR traffic flow models are simulated by using the newly constructed scheme.The problem of increasing(decreasing)lane number and traffic signal control in multi-class LWR traffic flow model on an inhomogeneous highway.A numerical example shows that the high-resolution semi-discrete center upwind scheme has a higher resolution.