Newton-Krylov Strategy for Compressible Turbulent Flows on Unstructured Meshes

Abstract

Introduction T HE objective of this Note is to investigate the performance of Newton–Krylov methods applied to the solution of compressible high Reynolds number  ows around two-dimensional geometries. Although these methods have already been employed successfully for the computationof inviscid and viscous  ows,1i3 very few attempts have been made to apply these techniques to the simulation of turbulent  ows with partial differential equation turbulencemodels.4 In this Note, which summarizes the resultspresented in Refs. 5 and 6, we consider the one-equation Spalart–Allmaras model7 and the two-equationk–! model,8 and we examine the performance of the Newton–Krylov solver for the computation of the turbulent  ow over a NACA 0012 airfoil, an RAE 2822 airfoil, and a two-element airfoil.