Flux difference splittings and limiters for the resolution of contact discontinuities

摘要

Harten, Lax, and van Leer developed a theory of approximate Riemann solutions and used it to derive numerical methods for systems of conservation laws. In the first part of this paper, we reformulate this theory so that it can be used to compare various flux difference splitting formulae. In particular we show how to compare the resolution of contact discontinuities by various methods with that of the Roe method. Since the Roe method can resolve an isolated steady contact perfectly, it is a good standard for comparison. In the second part of the paper, we show that Harten's subcell resolution method is the ultimate compressive limiter. We discuss the differences between compressive and noncompressive limiters and show why it is important to choose the limiter to suit the problem at hand.