What Y+ Is and Why It Drives CFD Mesh Design
Y+ (y-plus) is a dimensionless measure of distance from a wall, expressed in "wall units" rather than meters. It is defined as y+ = y·u_τ/ν, where y is the physical distance from the wall to the center of the first mesh cell, u_τ is the friction velocity, and ν is the kinematic viscosity. Because turbulence models describe the near-wall boundary layer using this scaled distance rather than raw geometry, the value of y+ at the first grid point — not the cell height in millimeters — determines whether a CFD mesh can resolve the physics a turbulence model assumes. This calculator inverts that relationship: you supply the flow conditions and a target y+, and it returns the actual first-cell height you need to draw in your meshing tool.
Why near-wall resolution matters for turbulence modeling
The boundary layer next to a solid wall has three distinct regions in wall units: the viscous sublayer (y+ < 5), where flow is dominated by molecular viscosity and velocity is roughly linear in y+; a buffer layer (y+ 5-30) that blends viscous and turbulent effects; and the log-law region (y+ 30-300+), where velocity follows a logarithmic profile. Low-Reynolds-number turbulence models (most modern RANS models run without wall functions, including SST k-ω) integrate the equations directly through the viscous sublayer, so they need the first cell at y+ ≈ 1 or lower to avoid smearing the steep near-wall velocity gradient. Wall-function models instead skip the viscous sublayer analytically and expect the first cell center to land in the log-law region, so a first cell that is too close to the wall (y+ < 30) actually degrades accuracy with those models. Either way, mesh cells that land in the buffer layer are the worst case — neither a resolved solution nor a valid wall function applies there.
How the calculator derives the first-cell height
The tool uses the standard flat-plate boundary-layer approach. First it computes the Reynolds number Re_L = ρUL/μ from your freestream velocity U, characteristic length L, density ρ, and dynamic viscosity μ. It then estimates the turbulent skin-friction coefficient with the Schlichting correlation, C_f = (2·log₁₀(Re_L) − 0.65)⁻²·³, which is a widely used approximation for turbulent flow over a flat plate. From C_f it gets the wall shear stress τ_w = 0.5·C_f·ρ·U², then the friction velocity u_τ = √(τ_w/ρ). Finally, since y+ = y·u_τ/ν by definition, it solves for the first-cell height directly: y = y+ · ν/u_τ, with kinematic viscosity ν = μ/ρ. Because this is a flat-plate approximation, treat the result as a solid starting estimate for the near-wall cell height, then refine it once you have a converged solution by checking the actual y+ reported by your CFD solver.
Frequently Asked Questions
What y+ value should I target for my CFD mesh?
What's the difference between y+ = 1 and using wall functions?
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |