A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

We present a high-resolution relaxation scheme for a multi-class Lighthill-Whitham-Richards (MCLWR) traffic flow model. This scheme is based on high-order reconstruction for spatial discretization and an implicit-explicit Runge-Kutta method for time integration. The resulting method retains the simplicity of the relaxation schemes. There is no need to involve Riemann solvers and characteristic decomposition. Even the computation of the eigenvalues is not required. This makes the scheme particularly well suited for the MCLWR model in which the analytical expressions of the eigenvalues are difficult to obtain for more than four classes of road users. The numerical results illustrate the effectiveness of the presented method.