This is one of the best questions that anybody has posed in a while. As you've seen, it is sometimes not simple to declare convergence. Something that may help get the residuals down more, is to switch to double precision, and tweaking relaxation parameters may also help. Also, you need to consider the differencing scheme that you are using, and how accurate your initial flow field was. Something that sometimes helps is to get 0.0001 convergence on first order upwind differencing first, and then switch to higher order to see what it does. With external flows, where the initial flow field is normally a very good solution everywhere except near the body, it may also be difficult to get the requisite 0.001 convergence. For other flows 0.001 may not even be good enough. Take a very good look at how your surface integral changes with more iterations, sometimes if you really zoom in (in terms of y-axis scale), you can readily identify a damped oscillation, which is a good indication that you are "straddling" a converged answer. As last resort (or maybe that should be first?), work on your grid quality. If you have a number of skew or very high aspect ratio cells, perhaps away from your surface of interest, it may not affect your surface integral, but could affect the residuals.
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