Is there anyone who had good convergence results for a turbulent calculation of flow over a backward facing step? I'm trying the DNS case of le and Moin (Re=5100), but until now I didn't get satisfying results. I'm especially interested in a solution with the RNG turbulence model.

For the Jovic and Driver's backstep problem, you're essentially using the Wolfstein's one-equation turbulence model in the "whole" domain if you're using the two layer model in FLUENT. The reason is that the default boundary of Reynolds number Re_y (the interafce between the two-equation model and the one equation model) is 200, and the Reynolds number for the Jovic and Driver's case is such that Re_y in most of the region is below 200. This problem doesn't occur in the case of Driver and Seegmiller's case, because the Reynolds number for the latter is much higher.

With the one equation model being used in the whole domain, the transport of epsilon is completely neglected, which may be responsible for the mediocre results you're witnessing.