Solving the Payne-Whitham traffic flow model as a hyperbolic system of conservation laws with relaxation

In this paper, we study the Payne-Whitham (PW) model as a hyperbolic system of conservation laws with relaxation. After studying the Riemann problem for the homogeneous version of the PW model, we introduce three first-order numerical solution methods for solving the system. In these methods, the homogeneous part of the PW model is approximated by Godunovtype difference equations, and different treatments of the source term are used. Numerical results show that solutions of the PW model with these methods are close to those of the LWR model when the PW model is stable, and that the PW model can simulate cluster effect in traffic when it is unstable. The PW model is also studied for roadways with inhomogeneities.