全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

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

DOI: 10.4236/ajcm.2016.62007, PP. 55-65

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

Full-Text   Cite this paper   Add to My Lib

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.

References

[1]  Daganzo, C.F. (1995) A Finite Difference Approximation of the Kinematic Wave Model of Traffic Flow. Transportation Research Part B: Methodological, 29, 261-276.
[2]  Zhang, H.M. (2001) A Finite Difference Approximation of a Non-Equilibrium Traffic Flow Model. Transportation Research Part B: Methodological, 35, 337-365.
[3]  Bretti, G., Natalini, R. and Piccoli, B. (2007) A Fluid-Dynamic Traffic Model on Road Networks. Comput Methods Eng., © CIMNE, Barcelona.
[4]  Ali, A., Andallah, L.S. and Hossain, Z. (2015) Numerical Solution of a Fluid Dynamic Traffic Flow Model Associated with a Constant Rate Inflow. American Journal of Computational and Applied Mathematics, 5, 18-26.
[5]  Bagnerini, P., Colombo, R.M. and Corli, A. (2006) On the Role of Source Terms in Continuum Traffic Flow Models. Mathematical and Computer Modelling, 44, 917-930.
http://dx.doi.org/10.1016/j.mcm.2006.02.019
[6]  Lighthill, M.J. and Whitham, G.B. (1955) On Kinematic Waves. II. A Theory of Traffic Flow on Long Crowded Roads. Proceedings of the Royal Society of London. Series A, 229, 317-345.
http://dx.doi.org/10.1098/rspa.1955.0089
[7]  Greenshields, B.D. (1935) A Study of Traffic Capacity. Highway Research Board, 14, 448-477.
[8]  Andallah, L.S., Ali, S., Gani, M.O., Pandit, M.K. and Akhter, J. (2009) A Finite Difference Scheme for a Traffic Flow Model Based on a Linear Velocity-Density Function. Jahangirnagar University Journal of Science, 33, 61-71.
[9]  Haberman, R. (1977) Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow. Prentice-Hall, Inc., Englewood Cliffs.
[10]  Le Veque, R.J. (1992) Numerical Methods for Conservation Laws. Birkhauser, Berlin.
[11]  Hoogendoorn, S.P., Luding, S., Bovy, P.H.L., Schreckberg, M. and Wolf, D.E. (2005) Traffic and Granular Flow ’03. Springer.
http://dx.doi.org/10.1007/3-540-28091-x
[12]  Trangenstein, J.A. (2007) Numerical Solution of Hyperbolic Conservation Laws. Department of Mathematics, Duke University, Durham, NC 27708-0320.
https://services.math.duke.edu/~jliu/math226/
[13]  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
[14]  Tabak, E.G. (2004) Notes for PDE I (Traffic Flow) Spring 2004 [PDF Document]. Retrieved from Lecture Notes Online Website.
http://math.nyu.edu/faculty/tabak/PDEs/

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133