Riemann solver for a kinematic wave traffic model with discontinuous flux

Abstract. In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira’s mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann problems can generate zero waves that propagate with infinite speed but have zero strength. We then propose an explicit Godunov-type numerical scheme that aims to avoid the otherwise severely restrictive CFL constraint from the infinite speed of the zero wave by allowing the local Riemann problems to exchange information and incorporating the effects of the zero wave directly into the local Riemann solver. Numerical simulations and a careful convergence study are provided to demonstrate the effectiveness of our approach.