The nutUSpaldingWallFunction is boundary condition that provides a wall function for the turbulent viscosity (i.e. nut) based on velocity (i.e. U). Using Spalding’s law gives a continuous nut profile to the wall.

\[y^+ = u^+ + \frac{1}{E} \left[exp(\kappa u^+) - 1 - \kappa u^+\, - 0.5 (\kappa u^+)^2 - \frac{1}{6} (\kappa u^+)^3\right]\]


Property Description
\(y^+\) Wall-normal height of a cell centre in wall units
\(u^+\) Velocity at \f$y^+\f$ in wall units
\(\kappa\) von Karman constant


The condition requires entries in both the boundary and field files.

Boundary file

    type            wall;

Field file

    // Mandatory entries
    type            nutUSpaldingWallFunction;

    // Optional entries
    maxIter         <label>;
    tolerance       <scalar>;

    // Inherited entries


Property Description Type Required Default
type Type name: nutUSpaldingWallFunction word yes -
maxIter Number of Newton-Raphson iterations label no 10
tolerance Convergence tolerance scalar no 0.0001

The inherited entries are elaborated in:

  • nutWallFunctionFvPatchScalarField.H

  • Suffers from non-exact restart since correctNut() (called through turbulence->validate) returns a slightly different value every time it is called. This is since the seed for the Newton-Raphson iteration uses the current value of *this (\c =nut ).
  • This can be avoided by overriding the tolerance. This also switches on a pre-detection whether the current nut already satisfies the turbulence conditions and if so does not change it at all. This means that the nut only changes if it ‘has really changed’. This probably should be used with a tight tolerance, to make sure to kick every iteration, e.g. maxIter 100; tolerance 1e-7;

Further information


Source code:



  • Introduced in version 2.4.0