ON ENTROPY CONSISTENCY OF LARGE TIME-STEP SCHEMES .2. APPROXIMATE RIEMANN SOLVERS

It is shown that for scalar conservation laws with a convex flux funct ion any sequence of approximate solutions, constructed by large time s tep schemes using approximate Riemann solvers as a building block, giv es 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 fun ction is nearly constant the above results may be extended to Courant numbers slightly larger than 1.