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# Compute Grid Spacing for a Given Y+

## Improve CFD Accuracy with Correct Mesh Resolution

It's important that your mesh near the wall is properly sized to ensure accurate simulation of the flowfield. This calculator computes the height of the first mesh cell off the wall required to achieve a desired Y+ using flat-plate boundary layer theory.

## Input

freestream velocity (m/s)
freestream density (kg/m3)
dynamic viscosity (kg/m s)
reference length (m)
desired y+

## Output

wall spacing (m)
Reynolds number
Note: -1 indicates an input error

## Calculate Grid Spacing on iPhone and AndroidTM

Now you can compute wall spacing while at your desk or while on the road with the Y+ Calculator for iPhone or Android. This free app is a handy tool for calculating the grid spacing at a wall to achieve a target y+ value for viscous computational fluid dynamics (CFD) computations. Simply specify the flow conditions, the desired y+ value, and compute your grid spacing. The Y+ Calculator converts between SI and Imperial units.

## The Math

These computations are based on flat-plate boundary layer theory from Frank M. White's Fluid Mechanics 5th edition, page 467.

${\mathrm{Re}}_{x}=\frac{\rho {U}_{\infty }L}{\mu }$

${C}_{f}=\frac{0.026}{{{\mathrm{Re}}_{x}}^{1/7}}$

${\tau }_{wall}=\frac{{C}_{f}\rho {{U}_{\infty }}^{2}}{2}$

${U}_{fric}=\sqrt{\frac{{\tau }_{wall}}{\rho }}$

$\Delta s=\frac{{y}^{+}\mu }{{U}_{fric}\rho }$

Note: The equations use MathML markup. Certain browsers (Chrome and Internet Explorer, for example), currently do not properly render MathML.

## Suggestions?

Let us know if you'd like to see variations on this Y+ calculator or other CFD calculators. Send your ideas by email to pointwise@pointwise.com.