A roe solver for a multi-class traffic flow model

The dynamics of traffic flow, where drivers are distinguished by distinct velocity classes, can be described using a nonlinear system of hyperbolic conservation laws. The equations are a generalization of the scalar Lighthill, Whitham and Richards (LWR) model. We first derive the exact solution to the corresponding Riemann problem in the case of two classes. We then motivate the use of a Roe solver and derive the Roe linearization with a corresponding entropy fix. Finally, we implement the scheme for two- and three-class flow using CLAWPACK, a publicly available package for solving hyperbolic conservation laws.