How the y+ calculator works
y+ is the distance of the first mesh point from the wall, measured in viscous units. To find the wall distance for a target y+, the calculator estimates the wall shear stress from an empirical correlation in five steps:
Reynolds number
Re = ρ U L / μ, from the velocity, the reference length and the fluid properties.
Skin friction coefficient
Cf from the chosen flat-plate correlation, or for pipes Cf = f / 4, with the Darcy friction factor f from the Colebrook-White equation solved iteratively (64/Re when laminar).
Wall shear stress
τw = ½ Cf ρ U².
Friction velocity
uτ = √(τw / ρ).
Wall distance and first cell height
y = y+ μ / (ρ uτ). The first cell height is 2y for cell-centred solvers and y for node-based solvers.
Air properties come from the ideal gas law and Sutherland's law for viscosity, and water properties from the Kell density equation and the Vogel viscosity equation, so you only need the temperature (and the pressure for air). You can also enter any fluid's density and viscosity yourself.
Which y+ should you aim for?
The target depends on how your turbulence model treats the wall. Choose one approach and mesh for it, rather than landing in between:
| Approach | Target y+ | Typical use |
|---|---|---|
| Wall-resolved | y+ ≈ 1 (below 5) | Typical use: k-ω SST, Spalart-Allmaras and k-ε with enhanced wall treatment; heat transfer and separation |
| Wall functions | 30 < y+ < 300 | Typical use: Standard and realizable k-ε with wall functions, when near-wall detail matters less |
| Avoid | 5 < y+ < 30 | Typical use: The buffer layer, where neither approach is accurate |
y+-insensitive wall treatments, such as enhanced wall treatment in Fluent or all-y+ treatment in STAR-CCM+, blend the two, but the most reliable results still come from a mesh designed for one of them.
Cell-centred and node-based solvers
Ansys Fluent, STAR-CCM+ and OpenFOAM store their results at cell centres, so the y+ they report is measured at the centre of the first cell, half its height from the wall. To reach your target y+ there, the first cell must be twice the wall distance, which is what the calculator gives for cell-centred solvers. Node-based solvers such as Ansys CFX store results at the mesh nodes, so the first cell height equals the wall distance.
Inflation layers and growth rate
The calculator also estimates the boundary layer thickness δ, from the Blasius solution for laminar flow and the 1/5 power law for turbulent flow (the pipe radius for fully developed pipe flow), and counts the inflation layers needed to cover it at your growth rate r:
Here Δs is the first cell height. Keep the growth rate around 1.1 to 1.3 and make the last layer blend smoothly into the surrounding mesh.
Check y+ after the first solution
The calculator gives a starting point from a flat-plate or pipe correlation. Around a real body the wall shear stress varies, higher where the flow accelerates and lower near separation, so plot y+ on the walls after the first solution and adjust the inflation layers where it falls outside your target. For meshes refined at the walls to capture separated flow, see our backward-facing step CFD and our Ahmed body slant angle study. If you would rather have the mesh and simulation done for you, see our CFD analysis services.
Frequently asked questions
What is y+ in CFD?
y+ is the non-dimensional distance from a wall to the first mesh point, y+ = ρ uτ y / μ, where uτ is the friction velocity. It shows which part of the boundary layer the first cell sits in, which decides whether a wall-resolved turbulence model or wall functions are appropriate.
What y+ do I need for k-ω SST?
About 1, and below 5, so the first cell sits in the viscous sublayer. SST can tolerate higher values with automatic wall treatment, but y+ ≈ 1 gives the most reliable wall shear stress, separation and heat transfer.
What y+ should I use with wall functions?
Between about 30 and 300 for standard wall functions, so the first cell lies in the log-law region. Avoid 5 to 30, the buffer layer, where neither wall functions nor wall-resolved models are accurate.
Why is the y+ in my results different from the calculator?
The calculator estimates the wall shear stress from a flat-plate or pipe correlation. In a real geometry the shear varies from place to place, so y+ is higher where the flow accelerates and lower near separation. Use the estimate for the first mesh, then plot y+ on the walls and refine the inflation layers where needed.
Is the first cell height the same as the wall distance?
Not for cell-centred solvers. Ansys Fluent, STAR-CCM+ and OpenFOAM measure y+ at the cell centre, half the first cell height from the wall, so the first cell height is twice the wall distance. In node-based solvers such as Ansys CFX, the two are the same.