Viscous airfoil computations using Richardson extrapolation

Abstract

An investigation of the use of Richardson extrapolation in the computation of viscous airfoil flowfields is presented. The Richardson extrapolation procedure uses a numerical solution obtained on a coarsened grid to improve the accuracy of a given solution. Computational results are presented for subsonic flow about the NACA 0012 airfoil and transonic flow about the NACA 0012 and the RAE 2822 airfoils. The cases studied exhibit a variety of flow features, including shock-induced separation and trailing-edge separation. The transonic flow conditions correspond to cases from the Viscous Transonic Airfoil Workshop. The computations were performed using ARC2D, a well-established Navier-Stokes code, with the Baldwin-hmax turbulence model. The results show that Richardson extrapolation can reduce the grid requirements for a given level of accuracy, especially in the prediction of drag, for a wide range of flow conditions. In addition, Richardson extrapolation produces estimates of truncation error.