Convergence of a difference scheme for conservation laws with a discontinuous flux

Convergence is established for a scalar finite difference scheme, based on the Godunov or Engquist-Osher (EO) flux, for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient. Other works in this direction have established convergence for methods employing the solution of 2 x 2 Riemann problems. The algorithm discussed here uses only scalar Riemann solvers. Satisfaction of a set of Kruzkov-type entropy inequalities is established for the limit solution, from which geometric entropy conditions follow. Assuming a piecewise constant coefficient, it is shown that these conditions imply L-1-contractiveness for piecewise C-1 solutions, thus extending a well-known theorem.