On Entropy Consistency of Large Time Step Schemes II. Approximate Riemann Solvers

Abstract

It is shown that for scalar conservation laws with a convex flux function any sequence of approximate solutions, constructed by large time step schemes using approximate Riemann solvers as a building block, gives the unique entropy solution in the limit of decreasing mesh size if the Courant number is less than 1. When the curvature of the flux function is nearly constant the above results may be extended to Courant numbers slightly larger than 1.