Numerical Simulation of a Mathematical Traffic Flow Model Based on a Nonlinear Velocity-density Function

A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards (LWR) model appended with a closure nonlinear velocity-density relationship yielding a quasilinear first order (hyperbolic) partial differential equation as an initial boundary value problem (IBVP) was considered. The traffic model IBVP by finite difference method which leads to a first order explicit upwind difference scheme was discretized. Computer programs for the implementation of the numerical scheme and perform numerical experiments in order to verify some qualitative traffic flow behaviour for various traffic parameters were developed.