Front tracking algorithm for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic, continuous, non-smooth, and non-concave fundamental diagram

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. © 2009 Institute for Scientific Computing and Information.