Numerical Solution of a Fluid Dynamic Traffic Flow Model Associated with a Constant Rate Inflow

摘要

In this paper, a modification of a macroscopic traffic flow model has been presented. In most cases, the source terms that have been appeared in traffic flow equations, represent inflow and outflow in a single-lane highway. So, to demonstrate the effect of inflow, a constant source term has been introduced in a first-order traffic flow equation. Inserting a linear velocity-density relationship, the model is presented. In order to incorporate initial and boundary data, the model is treated as an Initial Boundary Value Problem (IBVP). We describe the derivation of a finite difference scheme of the IBVP which leads to a first order explicit upwind difference scheme. Rigorous well-posedness results and numerical investigations are presented. This paper contains the implementation of the numerical schemes by developing computer programming code and numerical simulation. Numerical schemes are implemented in order to bring out a variety of numerical results and to visualize the significant effects of constant rate inflow.