A difference scheme for conservation laws with a discontinuous flux: the nonconvex case

Abstract. The subject of this paper is a scalar finite difference algorithm, based on the Godunov or Engquist-Osher flux, for scalar conservation laws where the flux is spatially dependent through a possibly discontinuous coefficient, k. The discretization of k is staggered with respect to the discretization of the conserved quantity u, so that only a scalar Riemann solver is required. The main result of the paper is convergence of a subsequence to a weak solution when the flux is strictly concave and the coefficient k is positive and has bounded variation. The limit solution satisfies a set of entropy inequalities. Satisfaction of these inequalities is shown to rule out nonphysical discontinuities if the limit solution is piecewise smooth