Establishment And Simulation Of Traffic Flow Equation Based On Lagrange Coordinate

Transportation is closely related to the life of the residents,the development of the society and the progress of the country.Traffic congestion and traffic accident frequency not only caused a lot of social and environmental problems,but also hindered the healthy development of the social economy.To solve the traffic problems,it is need to use resources of the existing traffic facilities,and also through the use of the scientific methods to study traffic flow,such as reasonable planning,layout and control of the traffic.It is necessary to combine the theory with the practice,and applied to the reality of traffic project construction management.Therefore,it is particularly important to explore the scientific traffic theory,develop the advanced traffic science and technology to guide the construction of the traffic facilities in the real life,and promote the development of the national economy.Traffic flow theory described the reality of the traffic by using the analysis method,which can reflect the real phenomena and essence of the traffic.And then put forward the effective path planning design and operation management program,raised the prevention and solving measures of the road traffic accidents.Currently,a lot of discussions on traffic flow are based on the Euler coordinates.The study used the Euler method is to observe the movement of the object in the fixed space position,and observed the changes of each particle passing through the point at different time.Therefore,the Euler method has limitations in the study of the motion of a single particle.In this paper,we use the Lagrange method.Through the observation on the physical quantity changes of a single particle with time,which can accurately describe the moving interface of the individual objects and also can track the particle trajectories.Then make an average on the motion of all particles.Through summarizing which can obtain the movement law of the whole traffic flow.Next,using the cellular automata model under the Lagrange coordinate to simulate the traffic flow.Establishing and simulating the the multi-value cellular automata model under the Lagrange coordinate system according to the actual situation,the results were analyzed.First,the fluid mechanics of the traffic flow theory are summarized,the relationship between the basic parameters and the three parameters of traffic flow are introduced in detail.Then the basic principle of traffic wave are introduced,and the traffic waves have carried on the simple analysis.Secondly,by introducing the method of Lagrange coordinate and Euler coordinate,and the transformation between these two methods.The basic traffic relation under the Lagrange coordinate is built.Making discretization of the continuity equation on the basis of LWR equations,and using the law of conservation of mass,then transforming the Euler coordinate system into the Lagrange coordinates,the traffic flow continuity equation under the Lagrange coordinate is established.The Godunov method is used to solve this hyperbolic equations.It is concluded that the Lagrange form of LWR model is equivalent to the one dimensional microscopic model.Thirdly,the evolution equation of the multi-valued cellular automata model,including the BCA model,the multi-valued cellular automata model under the Lagrange coordinate and the GBCA model are introduced.The evolution equations of the multi-valued cellular automata model under the Lagrange coordinate are discussed,and the evolution equations under the arbitrarily speed condition and the multi-lane condition are obtained.Finally,the Lagrange form of the multi-valued cellular automata model is modeled and simulated.The model uses the periodic boundary.Then defining the updating rule and position tracking method of the vehicle.The simulation mainly includes three aspects: arbitrary speed condition,multi-lane condition and signal guidance condition under the Lagrange coordinate.The running chart and basic graph of the simulation are compared and analyzed.From the underlying graph of the simulation under those three conditions,it can be seen that the relationship among the three parameters: density,flux and velocity are the same with that continuity equation in Lagrange form of traffic flow in the third chapter,also corresponding to the relationship among the parameters of the macroscopic traffic flow.The research of this paper can provide theoretical support for solving the traffic problems,the spatial and temporal distribution characteristics of road traffic flow.Apply the theory to practice,which can help develop more advanced traffic research technology,and then improve the efficiency of the traffic work,promote to unblock the roads,facilitate resident trip and drive the development of green transportation.