Front tracking algorithm for the Lighthill-Whiteham-Richards traffic flow model with a piecewise quadratic, continuous, non-smooth, and non-concave fundamental diagram
Wenqin Chen 1, S.C. Wong 1, Chi-Wang Shu 2, Peng Zhang 31 Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China.
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
3 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China.
Received by the editors February 29, 2008 and, in revised form, February 4, 2009.
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.
AMS subject classifications: 35R35, 49J40, 60G40
Key words: LWR model, traffic flow, piecewise quadratic fundamental diagram, front tracking algorithm, WENO scheme.
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