Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations

Abstract

Insight into the accuracy of steady shock-capturing CFD methods is obtained through analysis of a simple problem involving steady transonic flow in a quasi-1D diverging duct. It is proved that the discrete solution error on either side of the shock is where is the order of accuracy of the conservative finite volume discretisation. Furthermore, it is shown that provided that then the error in approximating is . This result is in contrast to the general belief that shocks in 2D and 3D Euler calculations lead to first order errors, which motivates much of the research into grid adaptation methods.