Spurious entropy production and very accurate solutions to the Euler equations

Abstract

AbstractSince it is not assumed a priorito be constant, entropy can vary along streamlines in the numerical solution of the Euler equations, depending upon its accuracy, even if the flow is isentropic. The level of this spurious entropy (or equivalently loss in total pressure) produced in the solution has become a common measure for the accuracy of the solution. It was used in a recent exercise by the AGARD Working Group 07 as one of the primary criteria to judge the most accurate solutions of the Euler equations for a variety of different test problems. Of the four possible sources of this error: mesh spacing, convective difference scheme, artificial viscosity model, and boundary conditions, the latter two are found to contribute the most. The steps taken to limit the errors coming from each of these four areas are described in detail in the context of two AGARD test cases: NACA 0012 M∞, = 0·85 α= 1 deg, and NLR 7301 M∞ = 0·721 α=-0·194 deg. An accurate shock-free supercritical solution is presented for the latter case.