A critical analysis of multi-dimensional upwinding for the Euler equations

Abstract

This paper provides a critical analysis and comparison of fluctuation splitting schemes applied to a linear scalar advection equation as well as to various simple wave decomposition models of the Euler equations. A theoretical analysis for the linear case and numerical experiments are presented. It is shown that compact-stencil fluctuation splitting schemes cannot provide second order accuracy either for nonhomogeneous scalar advection problems, or for general flows when combined with simple wave decompositions of the Euler equations.