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

Abstract

A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards(LWR) model appended with a closure nonlinear velocity-density relationship yielding a quasilinearfirst 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 firstorder explicit upwind difference scheme was discretized. Computer programs for theimplementation of the numerical scheme and perform numerical experiments in order to verifysome qualitative traffic flow behaviour for various traffic parameters were developed.Key words: Numerical simulation; Traffic flow model; Nonlinear velocity; Density functionDOI: 10.3329/jbas.v34i1.5488Journal of Bangladesh Academy of Sciences, Vol.34, No.1, 15-22, 2010