Front Tracking Algorithm for the Lighthill-Whitham-Richards Traffic Flow Model with a Piecewise Quadratic, Continuous, Non-Smooth, and Non-Concave Fundamental Diagram
Year: 2009
Author: W. Chen, S. C. Wong, C.-W. Shu, P. Zhang
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-784
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 562–585
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: LWR model traffic flow piecewise quadratic fundamental diagram front tracking algorithm WENO scheme.