Hi,

has someone made experiences with the study on grid independence using the standard k-eps model ?

I got the impression that is it not easy to converge to a grid independent solution (e.g. airfoil flow) due to the use of wall functions.

Could some shed some light on that problem ?

Regards,

Mark

Hello Mark,

Yes. It's not possible to get grid independent solutions using wall functions. y+ is a function of the mesh, which prevents from getting mesh independent solutions.

Thanks,

Thomas

If you keep your first node on the same y+ distance all the time you should be able to get grid independence. You can of course not refine your grid so that y+ becomes too low - then the wall-function formulation becomes invalid.

This is not quite right. In order to get grid independent solutions using wall functions you must integrate all equations exactly from the point you are holding at y+ = 30 (say) down to the wall. The gradients at the near wall cell are usually large and, for example, the transverse velocity components are usually integrated in the continuity equation by assuming they are constant in the direction normal to the wall. Claims of "grid independence" in a numerical sense are quite unjustified under these circumstances.

A parametric change of methods of integration within the near wall cell can lead to changes of wall shear stress of several percent but it is not a trivial task to perform. It also doesn't tell you a great deal at the end.

Parametric changes to the wall function numerics combined with grid resolution changes are easier to perform and probably more informative. For fully developed profiles, again, one would typically see differences of around 3-5% or so in wall shear stress (1% the best and 9% the worst in the table I just looked at). Of course, there is no best approach except for limited conditions but it does help estimate the error band when using wall functions particularly unknown ones in commercial codes.