Estimation of a diffusion coefficient at a face
 

Hello,

I would like to calculate precisely a term such as div(Gf.grad(phi)) in order to create a source term for an equation.
To achieve this, I need to know how fluent evaluate the value of the coefficient Gf at faces, knowing Gc at cell centers around the face.
I have tried to estimate Gf from surrounding cells c0 and c1 like:
Gf=(2Gc0*Gc1/(Gc0+Gc1)) but it doesn't work very well. I have also tried simple linear interpolation with bad results.

If someone has an idea or an information it would help me a lot.

Thanks

hi
according to Patankar book (p. 45) you should use harmonic mean with respect to distance between center points and interface.
for interface that palace in meddle your formula is correct but in general:
Gf = G0*G1/( G1(1-fe)+G0(fe) )
fe = (distance between G0 and interface)/( distance between G0 and G1 )

Thank you Arhn for your answer. Do you think that, in fluent, it is made like you explain?
Of course I know the very good Patankar's book. You're suggestion is good, nevertheless hard to apply in unstructured mesh, due to the fact that it is quite hard to estimate precisely fe in this case especially when grid is not orthogonal .
Have you any experience about this?

I write some MATLAB codes that use unstructured meshes like Delaunay or Voronoi and use that formulation. I since don't use FLUENT, sorry.

Ok thank you arhn.

Have a nice day

Re Hello Arhn,

I have think about your message. In a Delaunay grid, I think that you can have some triangles which are not orthogonal?
It would help my understanding if you can tell me, in this case how you estimate fe?
Indeed, in this case (non orthogonal grid) the face center, and the cells centers are not on a same line. Moreover I don't know for you but in my case I can only access to the coordinates of the centers of the face and cells. Do you make a kind of approximation?

Thank you for your help

Hi
In my code I had coordinate of cell centroids and vertexes of each triangle.
With command "polyxpoly" by using of coordinate of 4 point (2 cell centroids and 2 vertexes) I find the cross point of line between cell centroids and interface line then with respect to the point's coordinates I calculate Fe.

Thank you for all, I will try

You are welcome.