y+ and First Cell Height Calculator

Estimate the first cell height for viscous sublayer resolution in CFD.

PublishedCalculatorengineering calculators

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

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