[t.teschner]

I am currently working on a python package that calculates the GCI value for a series of grids / solutions. That is working fine if I only have 3 solutions and 3 grids available. If I use more than 3 grids, I am over constraining my system and it is not clear which approach to take here.

The paper I am implementing in the above package can be found here: https://journaltool.asme.org/Templat...umAccuracy.pdf

From that reference, Eqs. (3a--3c) indicate that in order to calculate the apparent or observed order, we need 3 grid levels (or rather, three solutions on three different grids)

We can then calculate two GCIs (using the same order) according to Eq.(7).

If I add another solution to my dataset, say I have 4 grids now with 4 solutions, then I can calculate 2 different apparent orders. I can also now calculate 3 different GCIs. The issue is that one of these GCI values (the middle one) can be now calculated with either one of the apparent orders that we just calculated, i.e. here the system becomes over-constrained.

How do we deal with this case (or in general, when we have more than 3 grids available)? One option I have seen is to split the dataset into smaller chunks, each containing 3 entries and then to calculate the GCI for each of these subsets individually, essentially calculating the GCI twice where we have more than a single apparent order available. That, however, also means that we now have essentially two GCIs for the same grid which again is not well defined (I suppose we could just take the more conservative GCI approximation here but I am not sure if that is really the best option).

[t.teschner]

I figured it out, for someone coming across this thread in the future, the reference you want to look at is:

Eca and Hoekstra, "An evaluation of verification procedures for CFD applications" (full text available here)

They propose a least-square fitting of the apparent order. I have tried it but it is not as robust as hoped, it might be useful using the correction suggested by Oberkampf and Roy (Table 8.1, page 326). However, I had much better results just splitting the dataset into chunks of 3 and then calculating the GCI for each dataset separately. An example of that can be found here, which I leave here in case someone will find it useful for their own GCI calculation in the future.