On The Study And Numerical Simulation Of The Two-Car Dynamics Traffic Flow Model

Traffic problem is an important one of the people's livelihood. City traffic problem is a world difficult problem. We must take some steps and measures to reduce the city traffic congestion. We could solve the problem from the "hardware" and the "software" aspects. The "hardware" is a long and arduous task. It's hoped to get the actual effort on "software" with short time and under certain conditions. The "software" can specially model traffic flow phenomenon scientifically and rationally, and one can make good use of numerical methods to simulate it. One can choose the models with good fitting purpose and feasibility, and puts the chosen models into the practical traffic flow.This paper mainly researches the usage of high order difference scheme on the traffic flow modeling. The selected traffic flow model is two-car dynamics model which was developed by some researchers, such as Peng Guanghan. This model takes into consideration of the influence of two front cars'information for following vehicle, which overcomes the existing problem during some dynamics models that the character speed of the vehicle flow is greater than macroscopic speed.Firstly, the characters of the two-car dynamics traffic flow model were analyzed. Its hyperbolicity was proved so that difference schemes for hyperbolic equations could be utilized. Next, on the basis of the actual case, the "look-ahead" effect and the delay time algorithm were introduced. Because the existing scheme for traffic flow problems is first order accuracy which has big dissipation and low accuracy, higher order difference scheme, i.e., MHM scheme was used to numerically simulate the old traffic flow model and the new one. The numerical results were analyzed and compared which illustrated the feasibility and effectiveness of the new traffic flow model.