Сomputing drag, lift, and wall shear stress on Embedded Boundary surfaces

[IvanBut]

Hi,

I've been using IAMR with AMReX Embedded Boundaries for external-flow benchmarks — currently flow past a circular cylinder — and I'm trying to figure out the right way to compute surface forces and wall quantities on EB geometries.

What I'm after: drag and lift forces (broken down into pressure and viscous contributions), wall shear stress τw, and the standard aerodynamic coefficients Cd and Cl.

Digging through the source code, I can see that the EB infrastructure exposes volume fractions, face area fractions (apx, apy, apz), EB boundary area fractions (bndryarea), boundary normals (bndrynorm), and boundary centroids (bndrycent) — so the raw ingredients for surface integration seem to be there. What I haven't found is any documented example of how these are actually combined to integrate forces over an EB surface.

One thing I'm particularly uncertain about: computing the pressure contribution seems relatively straightforward once you have bndryarea and bndrynorm, but the viscous part requires reconstructing velocity gradients directly at the EB face, which doesn't align with the grid — so I'm not sure what the recommended approach is there.

So a few questions:

1. Is there a standard AMReX/IAMR workflow for computing drag and lift on EB bodies, or is everyone essentially rolling their own?
2. Are there any helper utilities for integrating pressure and viscous stresses over an EB surface, or is that always custom code?
3. Is wall shear stress something that falls out of existing EB data structures, or does it typically require a separate post-processing step with gradient reconstruction at the EB face?
4. Do any of the AMReX-based codes — PeleC, PeleLM, or others — have working examples of Cd, Cl, or τw evaluation on EB geometries? Even a rough reference implementation would be hugely helpful.
5. Is there a go-to validation case where these quantities are benchmarked against reference data?

For the cylinder case at moderate Reynolds numbers, I'd like to reproduce the standard benchmark quantities: mean drag coefficient Cd_mean, RMS lift coefficient Cl_rms, and Strouhal number — along with the τw distribution along the surface.

Any pointers to docs, examples, or just how people normally approach this would be really appreciated.

Thanks!

[WeiqunZhang]

In incflo, there is a ComputeDrag function. https://github.com/AMReX-Fluids/incflo/blob/3a8eb80682bd744665414e7e4461b1f981637735/src/derive/incflo_derive.cpp#L468 I don't know whether it's useful or not. The code was commented out, I think, because it was first written before we supported GPU and it was never ported to GPU.

[nataraj2]

A relatively easy way that has been done in the past (pre-GPU times) is -

1. Write (ie. append) into text files the data over the EB inside the routine wherever the quantities of interest are computed (each MPI rank writes its own text file, and usually these are small files as only data for the EB surface is written out).

2. While doing 1

   • make sure the data is written out only once during the time step (ie. not to write the data out for multiple RK stages. Pass the RKstage into the routine as an argument to be used in a if loop).
   • better to use refinement criteria so as to enclose all the EB within the finest level, so that the data writing need to be done only for the finest level (ie. file appending should be inside a if(RK stage==2 and finest_level) (for eg.). If the EB is allowed to cut across levels, this becomes difficult. ie. There can be multiple levels of refinement, but all the EB cells should be within the finest level.

3. The data to be written out is usually (a) x,y,z of the EB cell or EB face centroids, (b) EB surface area, (c) normal components of the EB surface, (d) pressure in the EB cell (for lift coefficient) assuming dpdn=0 on the EB surface (that works well), and (e) the components of stress/gradients on the EB face (for drag). Append these into the text file in-situ. ie. wherever these get computed.

4. Then read all the text files in Python, and use the x,y,z coordinates data to avoid duplicates due to any overlap. Then, what remains is all the unique points on the EB surface with all needed data. Of course, it will not be in any particular order, which is alright. And, all quantities like lift, drag, and coefficients can be computed.

5. Just fyi - Plots in this paper (Figs. 9, 14, 17, 19, 20) were done using this approach.

Hope that helps. Let us know of any issues.

[ivanbooth6-sketch]

Thanks, this is very helpful.

One follow-up question:

Does IAMR (or any AMReX-based code such as incflo, PeleC, or PeleLM) provide any form of wall modeling / wall functions for Embedded Boundary geometries?

By wall functions I mean the usual near-wall modeling approaches used when the boundary layer is not fully resolved (e.g. log-law based wall stress evaluation, LES wall models, or similar).

From what I can see, the drag and wall shear stress evaluation discussed above appears to rely on directly resolved velocity gradients at the EB surface.

Is that currently the recommended approach in AMReX applications, or are there existing wall-function / wall-model capabilities that can be used with EB geometries?

Thanks again.

[nataraj2]

1. Not aware of any WMLES kind of approach in any of the codes, but it will be good to raise an issue in the respective codebase GitHub repos to be sure.

2. This approach in the comments above - Сomputing drag, lift, and wall shear stress on Embedded Boundary surfaces #5461 (comment)
   can be used irrespective of whether wall modeling is used or not. All that is required is to write the necessary data over the EB into text files (every rank writes into its own file) wherever the calculation of the quantities of interest are performed. And then, all these files can be read into Python and integration can be performed to obtain the Cl, Cd etc.