On The Study And Numerical Simulation Of The Jiang-Wu Traffic Flow Model

With the rapid development of China's economy and society, people's living standard is raised day by day. The fact that cars quickly enter families causes our country to the automobile society with an astonishing speed. Currently, urbanization level is relatively low, so the old traffic system has failed to meet our needs and traffic congestion phenomenon is more and more serious. Traffic problem is an important problem of the people's livelihood. It is necessary to establish a suitable traffic flow model to solve the urban traffic problem. We could make good use of numerical methods to simulate it, and to find effective measures to control traffic and to improve traffic conditions.This paper mainly researches the usage of high order CWENO difference scheme on the dynamics traffic flow model. The selected traffic flow model is Jiang-Wu model which was developed by Jiang Rui and Wu Qingsong. This model overcomes the shortcomings, such as the phenomenon that the characteristic speed is greater than macroscopic speed of the vehicle flow, of some dynamics models.The classification of the Jiang-Wu model was analyzed. Its hyperbolicity was proved so that difference schemes for hyperbolic equations could be utilized; the high order CWENO difference scheme was utilized so as to get small dissipation and high accuracy. The two kinds of difference scheme were used to numerically simulate the Jiang-Wu model; the numerical results were analyzed and compared which illustrated the feasibility and effectiveness of CWENO difference scheme. Finally, CWENO difference scheme was successfully used to the two-car dynamics model, so the general form of the dynamics traffic flow model that can use CWENO difference scheme was given.