CFD Online Discussion Forums - Documentation for Neumann boundary conditions in OpenFOAM

Hi,

I was looking to implement some Neumann boundary conditions.

I am taking a look at fixedGradient and https://www.openfoam.com/documentati...-gradient.html and mixed boundary conditions https://www.openfoam.com/documentati...d.html#details.

They appear to be the same (on the latter I should set the valueFraction to zero), but the documentation seems weird:
The fixedGradient will tell you that it is a Neumann condition defined as:

$\phi_f = \phi_C + \Delta \nabla \phi_{ref}$

Where $\phi_{ref}$ should be the gradient normal to the face?

Upon checking the code, the implementation seems to be on the evaluate function with:

Code:

    Field<Type>::operator=

    (

        this->patchInternalField() + gradient_/this->patch().deltaCoeffs()

    );

And deltaCoeffs() should be the inverse of the distance between face center and cell center?

On the other hand the mixed boundary is defined as:

$x_p = w x_p + (1-w) \left( x_c + \dfrac{\nabla_{\perp } x}{\Delta}\right)$

Here $\nabla_{\perp }$ is specifically stated to be the patch normal gradient and the distance term appears in the denominator.

Upon checking the code of the evaluate function I see:

Code:

    Field<Type>::operator=

    (

        valueFraction_*refValue_

      +

        (1.0 - valueFraction_)*

        (

            this->patchInternalField()

          + refGrad_/this->patch().deltaCoeffs()

        )

    );

Where the last term seems to be the same as the fixedGradient boundary.

So my question here is: Why two different documentations for something that seems to be the same ? Did I misunderstood something?