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Volume 6, Issue 4
Front Tracking Algorithm for the Lighthill-Whitham-Richards Traffic Flow Model with a Piecewise Quadratic, Continuous, Non-Smooth, and Non-Concave Fundamental Diagram

W. Chen, S. C. Wong, C.-W. Shu & P. Zhang

Int. J. Numer. Anal. Mod., 6 (2009), pp. 562-585.

Published online: 2009-06

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  • Abstract

We use a front tracking algorithm to explicitly construct entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a flow-density relationship that is piecewise quadratic, continuous, non-smooth, and non-concave. The solution is exact if the initial condition is piecewise linear and the boundary conditions are piecewise constant. The algorithm serves as a fast and accurate solution tool for the prediction of spatio-temporal traffic conditions and as a diagnostic tool for testing the performance of numerical schemes. Numerical examples are used to illustrate the effectiveness and efficiency of the proposed method relative to numerical solutions that are obtained using a fifth-order weighted essentially non-oscillatory scheme.

  • Keywords

LWR model, traffic flow, piecewise quadratic fundamental diagram, front tracking algorithm, WENO scheme.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-562, author = {Chen , W.Wong , S. C.Shu , C.-W. and Zhang , P.}, title = {Front Tracking Algorithm for the Lighthill-Whitham-Richards Traffic Flow Model with a Piecewise Quadratic, Continuous, Non-Smooth, and Non-Concave Fundamental Diagram}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {562--585}, abstract = {

We use a front tracking algorithm to explicitly construct entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a flow-density relationship that is piecewise quadratic, continuous, non-smooth, and non-concave. The solution is exact if the initial condition is piecewise linear and the boundary conditions are piecewise constant. The algorithm serves as a fast and accurate solution tool for the prediction of spatio-temporal traffic conditions and as a diagnostic tool for testing the performance of numerical schemes. Numerical examples are used to illustrate the effectiveness and efficiency of the proposed method relative to numerical solutions that are obtained using a fifth-order weighted essentially non-oscillatory scheme.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/784.html} }
TY - JOUR T1 - Front Tracking Algorithm for the Lighthill-Whitham-Richards Traffic Flow Model with a Piecewise Quadratic, Continuous, Non-Smooth, and Non-Concave Fundamental Diagram AU - Chen , W. AU - Wong , S. C. AU - Shu , C.-W. AU - Zhang , P. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 562 EP - 585 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/784.html KW - LWR model, traffic flow, piecewise quadratic fundamental diagram, front tracking algorithm, WENO scheme. AB -

We use a front tracking algorithm to explicitly construct entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a flow-density relationship that is piecewise quadratic, continuous, non-smooth, and non-concave. The solution is exact if the initial condition is piecewise linear and the boundary conditions are piecewise constant. The algorithm serves as a fast and accurate solution tool for the prediction of spatio-temporal traffic conditions and as a diagnostic tool for testing the performance of numerical schemes. Numerical examples are used to illustrate the effectiveness and efficiency of the proposed method relative to numerical solutions that are obtained using a fifth-order weighted essentially non-oscillatory scheme.

W. Chen, S. C. Wong, C.-W. Shu & P. Zhang. (1970). Front Tracking Algorithm for the Lighthill-Whitham-Richards Traffic Flow Model with a Piecewise Quadratic, Continuous, Non-Smooth, and Non-Concave Fundamental Diagram. International Journal of Numerical Analysis and Modeling. 6 (4). 562-585. doi:
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