Verification vs validation in CFD: what a mesh-independence study does (and doesn't) prove

Verification asks whether a CFD model's equations were solved accurately; validation asks whether those equations describe the real flow. A mesh-independence study, reported with the grid convergence index (GCI), is verification: it shows that the error from the mesh is small. It cannot show that the turbulence model, the boundary conditions or the physics are right. That takes a comparison with measurements or a trusted correlation, and a good CFD report keeps the two apart.

Every CFD result has two kinds of error. Numerical error comes from turning smooth equations into millions of small cells and iterating until they balance: cells too coarse, iterations stopped too soon. Modelling error comes from the equations themselves: a turbulence model that is an approximation, an inlet profile that is a guess, a wall roughness nobody measured.

The two are easy to blur, because both end with a percentage. They answer different questions, and a small number on one says nothing about the other.

Solve the same case on three meshes, each finer than the last by a fixed ratio (we use 1.3 in each direction). If the result converges as the cells shrink, the change between the two finest meshes, scaled by how fast the result is converging and by a safety factor, is the grid convergence index. Celik et al. (2008) set the procedure out step by step, and it is what most journals ask for.

r    ≈ 1.3, mesh to mesh
p    apparent order, capped at 2
eₐ   |φ₁ − φ₂| / φ₁
GCI  1.25 · eₐ / (rᵖ − 1)

Here φ₁ is the result on the fine mesh and φ₂ on the medium one; the apparent order p comes from all three results.

When the three results go up and down instead of converging in one direction, the GCI formula breaks. A common fallback (Stern et al., 2001) is to take 1.25 times half the spread of the three results as the band.

The refinement ratio from medium to fine is (1.21 / 0.54)^⅓ ≈ 1.31. The relative change between those two meshes is 0.035 / 12.205 ≈ 0.29 %. With the order capped at 2, rᵖ − 1 ≈ 0.71, and the GCI is 1.25 × 0.29 % / 0.71 ≈ 0.5 %.

There is a catch, and it is the useful part. The medium and fine runs never quite reached their residual targets: the separated flow downstream of the bend kept moving, and their pressure drop still swung by up to 1.7 % over the last 200 iterations. That swing is larger than the differences between the meshes, so a 0.5 % band would claim more than the runs can support. We report half the swing instead.

Our second test was a straight pipe, 72 diameters long, at a Reynolds number of about 13,300. Its three meshes gave 19.94, 20.07 and 19.97 Pa, within 0.63 % of each other. The developed friction factor carried a GCI of ± 0.6 %. As verification goes, that is a clean result.

Refining the mesh would never have found that gap, because the mesh did not cause it. It comes from the turbulence model at this fairly low Reynolds number. Only a comparison with something outside the model, a correlation or a measurement, shows it. That is the whole difference between the two words in one example.

UncheckedConverged, checked

• Converged residuals, or a clear statement that the run was stopped early and why.
• Wall layers fine enough for the wall model used (y+ ≈ 1 for a resolved boundary layer).
• A mesh-independence result with its band, if the decision depends on a few per cent.
• A validation case for the same kind of flow, against a correlation or measurements, with the gap stated.
• Each of these labelled for what it is: a verified number is not called validated.

Coreframe sells the mesh-independence study as its own package, called Verified: your duct or pipe case on three meshes, the GCI and a one-line verdict in the report. See how our mesh independence study works, or start with CFD for ducts and pipes.