[K.C.]

Hello OpenFoam-community,

I have found many publications using the least-square-method to calculate the gradient of a scalarField at cell vertices (and not at cell centers).
Now I need to do this as well for my code, but can not find the Header-File or the function to do this. The User-Manual and the Programmer-Manual mention gradient at cell centers only.

Is there an already written Header-file in OpenFoam to calculate gradient at cell vertices?

Thanks a lot,
K.C.

[Tobi]

Dear K.C.,

do you mean cell vertices or face centers? Out of the box I just have the following in mind:

- calculate the gradient at face centers
- interpolate the gradients at face centers to cell vertices

[K.C.]

Hello Tobi,


thanks for your reply.


I mean the cell vertices (e.g. 8 for a cube). A cell consists of faces. A face consists of edges and the edge connects two vertices/points. So I want to calculate a pointVectorField and not a surfaceVectorField.


Furthermore I dont know how you would calculate the vector gradient on faces (except by interpolation). The surface normal Gradient can't be interpolated into a vector on vertices in my opinion. Can you explain a bit more detailed?


Greets,
K.C.

[Tobi]

Originally Posted by K.C.

A cell consists of faces. A face consists of edges and the edge connects two vertices/points.

Thanks for the clarification. I did not know that.

[quote]
... calculate the vector gradient on faces (except by interpolation).
[/code]

Out of the box, I don´t think that this is possible. However, you could check the least square schemes available in OpenFOAM to get a better feeling how they do it here (also available for point and edge limiting stuff or something like that). Maybe this is what you are searching for.

[K.C.]

- calculate the gradient at face centers

Hello Tobi,
it was your idea of calculating gradient on faces. I hoped you had an idea of calculating gradient in vector form on faces. But maybe I missunderstood you.

.... least square schemes available in OpenFOAM to get a better feeling how they do it here (also available for point and edge limiting stuff or something like that)....

What do you mean with "available"? Do you mean that least square method is already implemented for edges and points? I can not find it in my OF-version, which indeed is very old.

[Tobi]

Originally Posted by K.C.

Hello Tobi,
What do you mean with "available"? Do you mean that least square method is already implemented for edges and points? I can not find it in my OF-version, which indeed is very old.

Just see:

Unknown grad scheme linear

Valid grad schemes are :

11
(
Gauss
cellLimited
cellLimited<Venkatakrishnan>
cellLimited<cubic>
cellMDLimited
edgeCellsLeastSquares
faceLimited
faceMDLimited
fourth
leastSquares
pointCellsLeastSquares
)

Description
Gradient calculated using weighted least-squares on an arbitrary stencil.
The stencil type is provided via a template argument and any cell-based
stencil is supported:

\table
Stencil | Connections | Scheme name
centredCFCCellToCellStencil | cell-face-cell | Not Instantiated
centredCPCCellToCellStencil | cell-point-cell | pointCellsLeastSquares
centredCECCellToCellStencil | cell-edge-cell | edgeCellsLeastSquares
\endtable

The first of these is not instantiated by default as the standard
leastSquaresGrad is equivalent and more efficient.

The gradient calculation I meant was gradient calculation at cell center, interpolate to face center and interpolate to edges. However, this is not what you were searching for.