Is planarAvg suitable for structured multi-block extrusion meshes in nekRS?

[OH-68]

Hi everyone,

I am using nekRS v24.0.4 for a case that is periodic in the streamwise (z) direction.

Goal

I would like to compute a z-direction average so that the resulting fields become invariant in z, while preserving the cross-sectional (x,y) profiles.

In other words:
The final field should be independent of z.
Every z-slice should exhibit the same (x,y) profile.
This is not a domain-wide scalar average, but a directional average along z only.

Fields of Interest
In my setup, velocity-related quantities are stored as scalars, for example:

s0 = u ,s1 = v, s2 = w
s6 = u², s7 = v² , s8 = w²

I would like to apply the same z-averaging operator to these fields.

Mesh Characteristics
The mesh was generated in ICEM and has the following properties: Structured mesh
O-grid topology in the cross-section (rod-bundle type geometry)
Uniform extrusion in the z direction
Multi-block structured mesh (not generated with genbox, and not a single tensor-product block)
So although the mesh is structured and extruded in z, it is not a single lexicographically ordered tensor-product block.

Current Question
Previously, I was advised to use planarAvg() for this purpose.
However, from the documentation and examples, it seems that planarAvg() assumes a lexicographically ordered tensor-product mesh.

My question is:

1. Is planarAvg() still the recommended approach for a structured multi-block extrusion mesh like this?
2. If not, what is the recommended way in nekRS to perform averaging along a periodic direction?

• A custom UDF implementation?
• A built-in utility?
• External post-processing?

3. In a parallel MPI setting, what is the most robust way to define and average corresponding “(x,y) columns” across the periodic z direction?
4. Are there any recommended examples or workflows for this type of directional averaging?

Any guidance would be greatly appreciated.

Thank you. :)

[yslan]

In order to compute the z-average, $< u >(x,y) := \int_{z_0}^{z_1} u(x,y,z) dz$, the code needs to know how to gather all mesh points along the z fiber. That's why planarAvg requires lexicographical ordering.

If possible, you can first get the 2D mesh, then use Nek5000's n2to3 tool to do the extrusion.
This way, the X and Y dimensions are prolongated, and the mesh is still lexicographical ordered between XY and Z (shown as the following) and planarAvg can still get vertices index along z. This also assumes the face 5 and face 6 are in z direction.

do ez = 1,nelz
do e2d = 1, nelxy
  eg = (ez-1) * nelxy + e2d
enddo
enddo

c NUMBER_OF_ELEMENT_X = nelxy
c NUMBER_OF_ELEMENT_Y = 1
c NUMBER_OF_ELEMENT_Z = nelz

I'm not sure whether ICEM does extrusion in this way. If so, you can directly use planarAvg.

Alternatively, if you only need $< u >(x_i,y_i)$ at certain points $(x_i,y_i)$, you can manually interpolate the solutions at points $(x_i,y_i,z_j)$ and manually do averaging $< u >(x_i,y_i) = \sum_j w_j u(x_i, y_i, z_j)$ under given discretization. See pointInterpolation_t in hemi or gabls examples.

It is still possible to figure out the vertices index because we do have grid connectivity.
However, it will be much easier to mesh in the correct way at the first place.

[OH-68]

Thank you very much for the explanation and the example.
Much appreciated! :)