Grid convergence
 

Hi, I am performing a grid convergence study for a steady state simulation of an impeller and volute.

For this convergence study I used
http://www.cfd.com.au/cfd_conf09/PDFs/136ALI.pdf

well, to tell the truth I do not consider that paper to be a good reference ...
they wrote about DNS while using a 2D geometry (...) furthermore, DNS is by definition a case in which your grid is fine enough to resolve all scales of the motion, so that a further refinement does not improve nothing...

In your case you wrote about an "error", but to compute an error you need to know the exact solution. What you can estimate is the "difference" from the solution obtained on the finest grid you use. That still need some care in defining the rate of convergence

You are absolutely right.

However I only used a similar method with the richardson extrapolation (which determines my extrapolated solution)

ok, so you assume the "exact" solution to be that obtained by Richardson extrapolation like in the book of Peric?
However, be sure to extrapolate from a quite refined grid

To answer your initial question, no. The solution is not grid independent. Can you tell us how you refined the grid? if it is just a random increase in distribution of nodes across the domain, you might have an issue.


Here is a link that might be useful:
http://www.grc.nasa.gov/WWW/wind/val.../spatconv.html

I refined it with the relevance button in ansys mesh since there is no structured way of doing it with an unstructured mesh, why might i have a problem?

special care is required when a non-uniform/unstuctured grid is used for grid refinement study... you should be aware to get the ratio hmax/hmin going to zero in a certain way.
Some issues are illustrated in the book of Peric

I didn't read the paper but I've experienced solutions converging in an overdamped fashion for the grid convergence process for RANS cases. And I gather it's related to the different parts (B.C.s, Euler, Viscous, RANs equ set, artificial/numberical damping) converging at different rates. In regards to DNS, you probably need to look at the different solutions and see if the physics have changed in a qualitative way. But that is just my guess since I have little experience with DNS. If the physics are changing in a qualitative way then you need to ignore the coarse solution and your mid becomes your coarse and your fine becomes your mid. I have also noticed in my studies that sometimes it takes *a lot* of grid points to get to the point where the Richardson extrapolation behaves nicely for a RANS case.

When talking about DNS solution You have only a fully resolved field, otherwise we should denote that as no-model LES (grid filtered solution without SGS model). Of course, One has a time dependent field, not a convergent to steady solution.
I still believe that using a 3D analytical solution is the better approach

Agreed, I am using RANS as well, but 5 million cells for just a volute is a lot