y+ First Cell Height Calculator for CFD Near-Wall Mesh Setup

Estimate first cell height for CFD near-wall mesh setup from target y+, flow conditions, and wall-treatment assumptions.

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Determining the correct first cell height is essential for resolving the boundary layer and ensuring accurate wall shear stress and heat transfer predictions. Use this calculator to estimate the required cell height for your target $y^+$, or to verify the $y^+$ of an existing mesh. After setting up your near-wall mesh, you can use our Inlet Turbulence Boundary Conditions Calculator to estimate turbulence variables, and review our CFD setup prompts for AI workflows to ensure your simulation settings are complete.

Governing Formula

y=y+μρuτy = \frac{y^+ \mu}{\rho u_\tau}
y+=yρuτμy^+ = \frac{y \rho u_\tau}{\mu}
dimensionless

Desired y+ value for your mesh.

m/s
m

For complex geometries, use the longest dimension in the flow direction.

kg/m³
Pa·s

First Cell Height

-
Awaiting Input

Use this as a quick diagnostic / starting point. Verify against your solver setup, mesh, timestep, model assumptions, and operating conditions.

Want to understand the math?

Read the theory behind y+ and First Cell Height →

Target y+ Guidance

  • y+ ≈ 1 (Viscous Sublayer Resolution): Often recommended for wall-resolved approaches, low-Re turbulence models, or enhanced wall treatments. Essential when boundary layer effects like heat transfer or separation prediction are critical.
  • y+ ≈ 30–300 (Log-Law Region): Often recommended for wall-function approaches where the solver uses empirical functions to bridge the viscous sublayer.
  • Avoid the Buffer Layer (y+ ≈ 5 to 30): Neither wall-resolved nor wall-function assumptions hold well here. Check your specific solver documentation, as modern hybrid wall treatments can handle this region better than older codes.
  • Solver Dependence:The correct target depends heavily on your specific CFD solver's guidance, chosen turbulence model, and validation requirements.

Worked Example

Scenario: External Aerodynamics

You are simulating a car (Length = 4.5m) traveling at 30 m/s in air. You want to use a k-ω SST model with wall functions, which typically requires y+ > 30.

Example Inputs:
  • Target y+ = 50
  • Velocity = 30 m/s
  • Characteristic Length = 4.5 m
  • Fluid = Air (Density = 1.225 kg/m³, Viscosity = 1.81×10⁻⁵ Pa·s)

Interpretation: The calculator recommends a first cell height of approximately 0.001 m (1 mm). You should configure the first prism layer thickness in your mesher to 1 mm to achieve the desired y+ = 50.

Assumptions & limitations

Limitations

  • Empirical Correlation: Uses a turbulent flat-plate empirical correlation: Cf = 0.0592 × Re^(-1/5).
  • Flow Regime: Assumes a fully developed turbulent boundary layer on smooth walls with incompressible Newtonian flow. It does not apply to internal pipe flows (which use Haaland or Blasius correlations).
  • Complex Flow: May underpredict or overpredict for highly separated flows, strong pressure gradients, or complex geometries. Does not account for compressibility, heat-transfer corrections, or wall roughness.
  • Verification: A mesh generated from this estimate is only a starting point. Final y+ must be verified in the CFD solver post-processing.

Related Resources

Mesh & y+ Prompts →Turbulence Model Prompts →CFD Setup Prompts for AI Workflows →Inlet Turbulence Calculator →View all Engineering Calculators →View all Downloads →Support this project →