Numerical Simulation of Drift-Diffusion Traffic Flow Model

In this study, we present a numerical scheme to solve the drift-diffusion traffic flow model under the steady state. The drift-diffusion traffic flow model consists of a continuity equation and a nonlinear Poisson equation. The continuity equation describes the propagation of density along the road, and the Poisson equation describes the interaction among vehicles. The system equations cannot be solved analytically. Therefore, a numerical iterative scheme, which is a finite difference approximation of the model, is presented. A numerical example is employed to explain the model and to show the advantage of the scheme. Key-Words: Traffic Flow, Finite Difference Method, Poisson Equation, Continuity Equation, Decoupled Scheme, Scharfetter-Gummel Scheme.