MESH / 001

y⁺ & First Cell Height Calculator

Estimate the near-wall first-cell height required for a target y⁺. The calculator also exposes the Reynolds number, skin-friction estimate, wall shear stress and friction velocity used in the calculation.

FreeRuns in your browserSI units

CORE RELATION

y⁺ = y u_τ / ν

u_τ= √(τ_w / ρ)

ν= μ / ρ

y= y⁺ ν / u_τ

INPUTS

Flow & wall inputs

Fluid preset

Presets are approximate. For temperature-sensitive work, enter properties at your actual wall/flow condition.

Flow velocity U m/s Characteristic length L m Use the streamwise distance to the location of interest for external flow. Density ρ kg/m³ Dynamic viscosity μ Pa·s

Wall-shear estimate

Default: local turbulent flat-plate skin-friction estimate, C_f = 0.0592 / Re^0.2.

Target y⁺ Choose based on your wall treatment and turbulence model.

y⁺

HOW THE CALCULATOR WORKS

First-cell height is a wall-shear estimate, not a universal constant.

The target y⁺ is converted into a physical wall-normal distance using the friction velocity and kinematic viscosity. Because the friction velocity depends on wall shear, this calculator must estimate the skin-friction coefficient before it can estimate the first-cell height.

Reynolds number
Re = ρUL / μ

Wall shear
τ_w = ½ ρU²C_f

Friction velocity
u_τ = √(τ_w/ρ)

First cell height
y = y⁺ν/u_τ

IMPORTANT

Use this as a pre-mesh estimate.

Check the solved y+ field. The actual wall shear comes from your CFD solution, so the final y+ can differ from the pre-processing estimate.

Use local conditions when possible. Fluid properties, velocity and characteristic length should represent the wall region you care about.

Correlation choice matters. The built-in correlations are smooth-wall engineering estimates. Separated flow, strong pressure gradients, roughness, rotation, compressibility and complex geometry can change wall shear substantially.

Wall-treatment requirements are solver-specific. Always check the documentation for your turbulence model and wall treatment.

ABECATOR CFD TOOLS

Next: turn this first-cell height into a prism-layer strategy.

Prism layer count, growth rate and total thickness are the natural next decisions after choosing the first-cell height.

See the tool roadmap

FROM NUMBER TO MODEL DECISION

If the solved y+ does not match the estimate, diagnose the wall model next.

Use the calculator for the starting mesh scale, then verify the solved wall field, wall treatment and prism strategy in the actual CFD model.

Technical Case

y⁺ & First Cell Height Calculator

Flow & wall inputs

First-cell height is a wall-shear estimate, not a universal constant.

Use this as a pre-mesh estimate.

Next: turn this first-cell height into a prism-layer strategy.

If the solved y+ does not match the estimate, diagnose the wall model next.

Solved y+ misses the target

Wall-treatment mismatch

CFD model review

y+ & First Cell Height Calculator

Flow & wall inputs

First-cell height is a wall-shear estimate, not a universal constant.

Use this as a pre-mesh estimate.

Next: turn this first-cell height into a prism-layer strategy.

If the solved y+ does not match the estimate, diagnose the wall model next.

Solved y+ misses the target

Wall-treatment mismatch

CFD model review

y⁺ & First Cell Height Calculator