Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined thewind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFDhas had its most favorable impact on the aerodynamic design of the high-speed cruiseconfiguration of a transport. This success has raised expectations among aerodynamiciststhat the applicability of CFD can be extended to the full flight envelope. However, thecomplex nature of the flows and geometries involved places substantially increased demandson the solution methodology and resources required. Currently most simulations involveReynolds-Averaged Navier-Stokes (RANS) codes although Large Eddy Simulation (LES) andDetached Eddy Suimulation (DES) codes are occasionally used for component analysis ortheoretical studies. Despite simplified underlying assumptions, current RANS turbulencemodels have been spectacularly successful for analyzing attached, transonic flows. Whetheror not these same models are applicable to complex flows with smooth surface separation isan open question. A prerequisite for answering this question is absolute confidence thatthe CFD codes employed reliably solve the continuous equations involved. Too often,failure to agree with experiment is mistakenly ascribed to the turbulence model ratherthan inadequate numerics. Grid convergence in three dimensions is rarely achieved. Evenresidual convergence on a given grid is often inadequate. This paper discusses issuesinvolved in residual and especially grid convergence.