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 - <p style="text-align: justify;">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.</p>