Grid Independence of Boundary Layer
 

Hello,

My question:
When I increase the mesh resolution in the BL, it has the result of reducing the mesh size of the last BL mesh, in comparison to the first mesh volume size of the core flow. Is this a problem, when there is a large step change between the last prism layer mesh, and first core mesh volume?

Model:
I'm modeling channel flow looking at the boundary layer on one wall that starts from a BL trip (modeled with surface roughness near the beginning of the channel). I am using a Reynolds stress turbulence model. I'm confused in how/the need to do a grid independence study for the boundary layer.

Grid independence methodology:
First I refined my core (outside the BL) as needed until I was happy with grid independence for the bulk flow. For these different runs of different mesh size, my boundary layer mesh was always the same-- y+=~0.85, with 20 prism layers across the BL thickness (as calculated from normal flat plate turbulent BL growth).

Now, any insight into the proper methodology to reach grid independence in the BL? Do I, as state above, just increase the number of cells in the BL, while keeping the first mesh size the same to preserve y+=~1.0?

Alternatively, I could also reduce the size of the first mesh, so now it would be even less than y+=~0.85 and it is more refined all the way across the BL.

Also since there seems to be two variables to change (first mesh size, and prism layer number), any advice to know when the BL mesh is sufficient? Since it isn't like bulk flow where you just refine it until your variables of interest aren't changing.

Any insight would be appreciated. Thanks!

If I am understanding you right, this is something I have always had an issue with...

The prism layer thickness should not be set as a percentage of the base size. This should not even be an option, much less the default behavior.

What you need to do is switch the prism layer thickness size type from "Relative to Base" to "Absolute". Then you can input an actual dimension for your prism layer, and when you change the base size for a mesh independence study it will not effect your y+ values.

Actually, I already have the prism layer thickness as absolute. But if I refine my mesh in the BL, by adding more prism layers, while keeping the thickness of the first cell near the wall constant, and the overall prism layer thickness constant, then my most internal prism layer mesh decreases in size. So now there is a larger discontinuity in mesh size between the innermost prism layer mesh, and the first mesh in the core flow. Is this a problem if there is this big step change in size going from prism layer mesh volume to core mesh volume?

And ultimately, I'm trying to figure out how to make sure my boundary layer mesh is grid independent. Thanks for the reply and looking.

I see what you are saying. This is what Star-CCM+ refers to as "Volume Change." It should be pretty robust over quite a large range. There is a field function for it. The manual suggests anything over 1e-5 is OK, but you may be able to handle even more with the high aspect ratio cells that you have in the prism layer.

Thanks, I had not know about that quantity in Star. I was able to run a report on that quantity, and I am still well above 1E-5. So I am not so much worried about that anymore.

So to get mesh independence in my BL, I can add prism layers while keeping the overall mesh thickness constant to refine my mesh in this area. That seems to make sense since it is like the bulk flow mesh refinement. But I'm still a little confused about whether I also reduce the size of the outermost prism layer thickness (i'm using this as a specification, as opposed to the stretching method). Right now it is below y+ of 1.0, which is the recomendation for low y+ models. But it seems like since I'm using a low y+ wall treatment, it calculates quantities down to the wall, so a more refined mesh in this region would be better. Can anyone confirm this? Is there a danger of having your outermost prism layer cell too thin/too close to the wall? As long as you have y+ less than 1.0 for that cell, is it just a decision on how much refinement you want in that region?

Thanks again!

Completely agree with this. I do not understand why they still have it like this.

"Volume change smaller than 1e5 is OK" is not applicable to all cases.
In some cases volume changes even as low as 10 can give completely wrong result.

Once you have your y+ criterion satisfied, you just need to make sure you have "enough" cells to completely resolve the boundary layer. Normally this means making sure that there is a gradual growth in cell size until you approach the core mesh size. Because the cell size closest to the wall for y+ <1 is already small, usually there is not a problem of the outermost cell being "too small" if the volume change is already gradual.