Grid refinement study for Order of accuracy and GCI
 

I am trying to ascertain the numerical accuracy of my simulations in CFX by following the procedure mentioned in the editorial policy of Journal of engineering.

My simulations are 3D turbulent flow . I take the overall pressure drop from inlet to outlet as the solution variable to calculate GCI and I use a representative mesh size for each mesh which I calculate as (total volume/total number of cells)^(1/3).

I have generated results for many meshes and tried to calculate GCI for 3 meshes at any time. I have ensured that the grid refinement ratios r21 and r32 are both above 1.3 for any of the mesh set that i consider.

However, I find that for the different mesh sets that i consider:
a)either the the parameter GCI_fine*(r21^p)/GCI_course is not close to one. This parameter should be close to one for the grids to be in asymptotic range.

b)when this parameter is indeed close to one for a set of meshes, (and GCI_fine is also is small..less than 2 percent), the observed order of accuracy p that I calculate comes out to be around 4 . Now I think it is incorrect and should be less than 2 (as the formal order of accuracy of CFX is 2...please correct me if I am wring). I have tried many fine and coarse meshes.

Is the way I am calculating GCI correct? Is the value of p>2 indeed correct?
For the results to be considered accurate what is the maximum acceptable value of GCI?

Firstly well done on having a good look into mesh refinement. I reckon about half of the weird questions on this forum are from people who have not done a proper check of whether their simulation is accurate so I am glad you are doing it properly.

Yes, CFX is a second order code for much of its numerics but in my experience that rarely equates to a order of convergence of 2 due to numerical issues, non-linearities etc. So if it is converging nicely I am happy regardless of the number.

If the parameter is not in the asymptotic range then you generally have to use a much tighter mesh for convergence, or you have a model which does not converge. Turbulence models with wall functions often do this as if they refine below y+<11 the model is not valid.

Thanks Glenn for your reply. So as you said above, getting observed order of convergence > 2 is ok and I can report results as such?
Secondly regarding the turbulence models, I am using the standard k-omega model in CFX. As you know, it uses automatic wall treatment which as per CFX manual should work for any mesh refinement. I could not use the commonly recommended SST model as it simply does not converge. Do you think something could be wrong here?

And lastly, I have obtained the converged results by reducing the automatically determined time-step for steady state simulations by one order of magnitude. I have checked my set-up again and again and it seems that it is fine. I have also played with boundary conditions for turbulence but convergence seems impossible without such large reduction in time-step. I remember that you had mentioned once before that convergence is fine irrespective of the time-step used as long as we get convergence. Still, it would be great if you could also have a look at another thread of mine here:
http://www.cfd-online.com/Forums/mai...tions-cfx.html

SST is usually quite a numerically robust turbulence model. Divergence caused by the turbulence model is uncommon. This problem should be fixable.

Hi Glen,

I am a bit concerned after your reply. I am not able to get convergence with SST.
I am attaching a crosssection of my mesh that I have used for SST. n the first pic showing the mesh, the fine mesh is the fluid part and the surrounding coarse mesh is the solid part.
I am also attaching the convergence plots. The convergence criteria was rms residual of 1e-6
Do you see any obvious mistake/issue here?

It is common to have steady state convergence problems as you refine the grid. Some tips are here:

http://www.cfd-online.com/Wiki/Ansys...gence_criteria