Table of Contents
What Is Y+?
Y+ is a dimensionless wall distance used in CFD to characterize mesh resolution in the boundary layer. It relates first cell height to the viscous length scale. Proper y+ values are essential for accurate turbulence modeling and wall shear stress prediction.
Y+ determines which boundary layer region the first cell falls in: viscous sublayer (y+ < 5), buffer layer (5 < y+ < 30), or log-law region (y+ > 30). Different turbulence models require different y+ ranges.
Y+ Formulas
τ_w = 0.5 × Cf × ρ × U², with Cf ≈ 0.058 × Re^(-0.2) for flat-plate turbulent flow.
Y+ Requirements by Model
| Model | y+ | Mesh |
|---|---|---|
| k-ω SST | ~1 | Fine wall |
| k-ε (wall fn) | 30-300 | Coarser |
| Spalart-Allmaras | ~1 | Fine wall |
| LES/DNS | < 1 | Very fine |
Frequently Asked Questions
Why does y+ matter?
Turbulence models assume specific velocity profile behavior near walls. Wrong y+ gives inaccurate wall shear stress, heat transfer, and separation predictions. Getting y+ right is one of the most important CFD mesh design aspects.
What if y+ is too high for SST?
If y+ exceeds ~5, the model cannot resolve the viscous sublayer. Either refine the mesh or use wall functions (k-epsilon). Many modern solvers have automatic wall treatment.
How does Re affect cell height?
Higher Re = thinner boundary layer = smaller viscous length scale = smaller required first cell height. Doubling Re roughly halves the cell height, significantly increasing computational cost.