Boundary layer mesh: how is the first cell height computed?

Finding the first cell height by trial and error to hit a target y+ is unnecessary. The sequence is:

1. Compute the Reynolds number from the characteristic velocity and length.
2. Estimate the skin friction coefficient from a correlation (the standard flat-plate relations in terms of Re are sufficient).
3. Obtain the wall shear stress and from it the friction velocity.
4. From the target y+, obtain the first cell centre distance.
5. In a cell-centred solver the first cell height is twice that — the factor-of-two error most often comes from here.

The result is an estimate; the actual y+ is checked after the solution and corrected once if needed. It settles in two iterations.

Layer count and growth rate

Even with the first cell right, that alone is not enough:

• The layer count must span the whole boundary layer. Typically 10–20. If the layers stop inside the layer, there is an abrupt transition to coarse cells outside and the gradient computation degrades.
• Growth rate should not exceed 1.2. Faster-growing layers spoil the volume change ratio.
• The last prism layer and the first volume cell should be of similar size. A jump here is the most common hidden mesh defect.

y+ misleads at separation

At the separation point the wall shear stress goes to zero, so y+ goes to zero with it. That does not mean the mesh is fine enough — it only shows that the local velocity has dropped. Judging resolution by y+ in a separation region is wrong; what matters there is how many cells resolve the recirculation region. See the y+ map note.

Different in natural convection

In buoyancy-driven flow the velocities are low and the correlations above do not apply. There the thermal layer thickness governs, and resolving to the wall is mandatory. See the natural convection note.

References

1. Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149
2. Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6