Hasan, M., Sultana, S., Andallah, L. and Azam, T. (2015) Lax-Friedrich Scheme for the Numerical Simulation of a Traffic Flow Model Based on a Nonlinear Velocity Density Relation. American Journal of Computational Mathematics, 5, 186-194.
http://dx.doi.org/10.4236/ajcm.2015.52015

has been cited by the following article:

• TITLE: Inflow Outflow Effect and Shock Wave Analysis in a Traffic Flow Simulation

  AUTHORS: Ahsan Ali, Laek Sazzad Andallah

  KEYWORDS: Macroscopic Model, Source Term, Shock Wave, Lax Friedrichs Scheme, Godunov Method

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.6 No.2, April 27, 2016

  ABSTRACT: This paper investigates the effect of inflow, outflow and shock waves in a single lane highway traffic flow problem. A constant source term has been introduced to demonstrate the inflow and outflow. The classical Lighthill Whitham and Richards (LWR) model combined with the Greenshields model is used to obtain analytical and numerical solutions. The model is treated as an IBVP and numerical solutions are presented using Lax Friedrichs scheme. Godunov method is also used to present shock wave analysis. The numerical procedures adopted in this investigation yield results which are very much consistent with real life scenario in terms of traffic density and velocity.