Fluid Dynamics Model Of Traffic-flow And Numerical Simulation

The study of traffic administration is mainly in virtue of mathematical method and physics law that can describe the phenomena and characteristic of traffic, simply that is the process of mathematics modeling, numerical simulation and finding its solution. This paper mainly study the fluiddynamics of traffic-flow and numerical simulation.The first chapter introduce the study results of traffic flow in the world and bring forward the question that will study. In second chapter, several typical mathematical of fluid dynamics of traffic-flow are presented and analyzed and compared with each other. The characteristics and scope of application of these models are also discussed. In third chapter, continuum equation and momentum equations and the relation of velocity and density that educed from car-following theory are presented. It also gives momentum equation in viscous traffic-flow and the relation of velocity and density that educed from it. In forth chapter, several difference methods that are suitable for solution of quasilinear equation are presented, namely, one step Lax-Wendroff scheme, two step Lax-Wendroff scheme, Mac Cormark scheme, TVD scheme, Harten TVD scheme with two-order precision. All of them are applied to simulate the same traffic-flow question and choose the best scheme under the consideration of their results. In fifth chapter, power function traffic-flow model and Harten TVD scheme with two-order precision are applied to simulate red-green signal traffic-flow, including isolated, synchronous and synchronous changing red-green signal case. The relation of velocity and density that educed from viscous traffic-flow was applied to simulate expressway incident traffic-flow, including noninterference and interference case. Its numerical results are compared with the numerical results of power function traffic-flow model.