The Traffic Flow Model Based On Fluid Dynamics And Numerical Simulation

The traffic, in which the jam and environment pollutions bring a big social pressure and economic lost, has become a worldwide problem. A great issue focused by the society is how to utilize the traffic resources efficiently, how to improve the supply and demand of the traffic, and how to instruct the traffic construction and management by the scientific traffic theories. Traffic is a kind of a multi-body system, with complicated interactions, including vehicles, environment and person, etc. It has an internal relation with some subjects, such as the physics, mechanics, mathematics, information sciences, traffic engineering and so on. The development of traffic flow research, not only has a far-reaching scientific meanings, but also an important engineering application values.The object of the traffic flow theoretical research is that, according to the traffic phenomena and the measuring data, a traffic flow model, reflecting the practical traffic's general characters, is built to expose the basic rules of the traffic flow. According to the theoretical foundations and research methods, it can be classified to the macro model, the medium model and the micro model. Macro fluid dynamics model, medium air dynamics model, micro car-following model and micro cellular automation model, which have the same researching objects, can be complemented, amalgamated by each other, and develop together. The model, based on the fluid dynamics, has a unique advantage in exposing the nonlinear phenomena and the macro character of the traffic flow. This dissertation has done a further research on the macro fluid dynamics model of the traffic flow and has done the numeric simulations.A general introduction on the concepts of traffic flow physical quantities, such as flowing volume, velocity character and density character, etc, has been given firstly. Some representative mathematical models in the fluid dynamics simulating theory of the traffic flow are given, including the first order continual medium models and the high order continual medium models. However, there are certain limitations. The fluid dynamics models do not consider the driver's action, which is heavily disjointed from the car-following model, and cannot analyze the stability of the traffic flow. As a result, its applicable range is limited. It is more applicable to the situation of denseness, uniform, steady traffic flow, but not the free flow and intermission flow.The fluid dynamics traffic flow research see the traffic flow as the fluid, which is treated as the continual medium. This dissertation does not consider the continual medium hypothesis supposed by the former scholars is correct, but the concepts defined by Doctor Xiong Lieqiang, who is in the Wuhan scientific and industrial university, is more reasonable. So this dissertation adopt the traffic flow continual hypothesis proposed by Doctor Xiong Lieqiang and simply introduce the Euler method, continual equations, momentum differential equations, traffic pressures and the velocity-density model educed by the car-following theory. This dissertation used the viscid traffic flow kinetic differential equation proposed by Xiong Lieqiang and educed the relations among the traffic flow parameters, which is chosen to be the mathematical model in this dissertation.From the aspect of calculations, the deflecting differential equations in the fluid dynamics model are difficult to resolve, and the traditional eigenline method has a complicated computing process. From the aspect of controls, it is necessary to discrete the models in the 3-D space inducing a difference differential equation; Considering the calculating amounts and the demand of real time, it is necessary to discrete the models in the time. The improperness in choosing the difference scheme will make the calculation unsteady or not convergent, which will affect the application of the models in practical traffic supervision. So another work in this dissertation is to choose a difference scheme which is proper to solve the strong intermission traffic flow problems. This dissertation choose the whole compound LWLFk difference scheme and the second order essentially non-oscillatory difference ENO scheme, compared with the one-step Lax-Wendroff scheme, two-steps Lax-Wendroff scheme and the Mac Cormack scheme, to numerical simulate the instant jam problems in the traffic flow. Results show that the second order ENO scheme can not only catch the traffic flow shock more correctly, but also basically not produce the oscillation, having a good effect.Numerical simulation on the specific traffic lights problems and the accidents in the speedway of the traffic flow was done by the second order ENO scheme in final part of the dissertation. For the single traffic light in the traffic flow problems, this dissertation simulates the situation that there is not moving vehicles after the static queue at the beginning time and the situation that there are in the flow of the traffic; For the problem of the corresponding traffic lights, this dissertation simulates two situations for the up and down boundary traffic lights in the traffic flow, including the synchronizing periodically change and the asynchronous periodically change. For the speedway accident problems, this dissertation simulates two accident models, one has the interference and the other has not, whose results is needed to verified by the testing data.Due to the complexity of the traffic system, there is no complete theory system for the traffic flow right now. Researches are limited in the experience method and semi-theory method, and the method in different country is separated which does not have general meanings. There is no common theoretical system. There is no time delay to build a traffic model, which is suitable for our nation's traffic with the characters of plane, low speed, mix and the specific bicycle flow and foot passenger flow. It is obvious practical and instructive.