wall resolution for finite volume
 

Greetings,

I've been wondering, for a cell-center based finite volume, how is the wall resolution determined?

To be more specific, consider this figure with a cell at the wall

Attachment 95431

Suppose all the values are stored at the cell center (the cross). Usually, finite volume codes will interpolate the cell-center data to nodal points when exporting solutions. Then, which grid spacings should one choose as the wall resolution? The distance from cell center to wall, , or the distance from the nodal points to wall, ?

Who even cares? If you want the distance from the cell center to the wall, then you have it. If you want the distance from the face to the wall, then you have it. Btw the distance from the face to the wall is equal to the sum of the distance from the face to the cell center plus the distance from the cell center to the wall.

Most finite volume codes export cell-centered data when it is requested as cell centered data.

Maybe explain the motivation for your question or I would feel bad since you made such a pretty picture. Without using the words wall resolution, what do you need to know about the grid?

dy_c is what most typically enters, for example, in a wall function or in the one sided differences typically used for the wall stress in such case. dy_n is your actual resolution that will affect your schemes.

As mentioned by LuckyTran, you need to specify in relation to what, otherwise it's difficult to understand without context.

To be honest, I don't think is relevant the difference in terms of magnitude order. It is different if you have to insert the value in some law but, especially close to the wall, the dy_c/2 of difference is small.

But when it comes to reporting the wall resolution, and , they will be differ by a factor of 2. This difference could be unacceptable for DNS.

I was referring to reporting the resolution, i.e., vs . They will differ by a factor of 2.

Why? In a DNS, your first node must be much lower than 1. Both evaluation would lie in the viscous sub-layer.

Cell to wall distance matters only for the wall adjacent nodes for your wall "function." If you are reporting wall adjacent y+, then that would be the cell to wall distance.

Resolution is the cell to cell distance (or node to node distance) typically in the core mesh far away from walls where again the original question doesn't even apply because you asked about cell to wall versus node to wall, resolution is node to node or cell to cell.

Neither have anything to do with how data is exporting in cell centers or nodes.

In my LES cases with a cell centered fv code I always ensured that both dy_c and dy_n were in my required range (which is typically the case, given they just differ by a factor of 2). In practice, you can't go above dy_c+ = 1 without being, somehow, underresolved.

When I reported those resolutions, I must admit, I don't remember what I used. For uniformity, I possibly used dy_n. The important thing is, however, to clarify what you are referring to.

Typically we report the y+ of the wall adjacent cell. Since the wall+ will be 1 or much much less and also since it most likely the smallest dimension in the entire mesh, it makes no sense to quote this number as a mesh resolution. One typically then gives the dy of the largest cell so that you know, okay, here is my lowest resolution, and there is (for sure) smaller cells as you approach the wall. So you give two numbers, wall y+~1 and dy+~10


The factor of 2 is not a problem because as mentioned by everyone already, you would have multiple cells inside the viscous layer. Mesh resolution is more related to # of cells you have at y+ < 5 than say, what is the exact y+ of that one cell next to the wall. If you have y+ of 1 or 2 and not multiple cells in the viscous layer then what you have is a bad mesh.