Lax-Friedrich Scheme for the Numerical Simulation of a Traffic Flow Model Based on a Nonlinear Velocity Density Relation

DOI: 10.4236/ajcm.2015.52015   PDF   HTML   XML   3,430 Downloads   4,107 Views   Citations

Abstract

A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich’s scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.

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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. doi: 10.4236/ajcm.2015.52015.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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