Riemann solver for a kinematic wave traffic model with discontinuous flux
We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the flux function over a small distance epsilon   0. For certain initial data, the Riemann problem can give rise to zero waves that propagate with infinite speed but have zero strength. We propose a Godunov-type numerical scheme that avoids the otherwise severely restrictive CFL constraint that would arise from waves with infinite speed by exchanging information between local Riemann problems and thereby incorporating the effects of zero waves directly into the Riemann solver. Numerical simulations are provided to illustrate the behavior of zero waves and their impact on the solution. The effectiveness of our approach is demonstrated through a careful convergence study and comparisons to computations using a third-order WENO scheme. (C) 2013 Elsevier Inc. All rights reserved.
discontinuous flux traffic flow lighthill-whitham-richards model hyperbolic conservation law zero waves finite volume scheme