nonorthogonality vs skewness
 

hi,

i was wondering whether someone could provide some insight regarding the difference between non-orthogonality and skewness in terms of corrections available in the OF fvSchemes file.

From what i had read, non-orthogonality affects only the diffusion terms and can be fixed using 'corrected' schemes in fvSchemes. What i dont understand is how the convection terms 'seem' to remain unaffected by nonorthogonality, or why there is a differentiation made between skewness and non-orthogonality when it seems an non-orthogonal mesh will probably be 'skew' as well.

Can anyone point me in the right direction for some answers or provide a brief explanation as to how skewness and non-orthogonality differ and why they affect only the diffusion and convection terms respectively, and whether these should be dealt with in the fvSchemes file or by running additional nonOrtho corrector loops in the fvSolution SIMPLE control dictionary.

I am using a modified version of SRFSimpleFoam in OF-2.1.1 to do steady-state simulations of a turbine rotor. checkMesh gives me some warnings about nonOrtho faces, but mesh skewness is OK. I am using linear interpolations for the grad and laplacian terms and upwind discretisation for the convective terms.

many thanks in advance
kind regards
Jonathan

so i have some answers for myself - i'll just share them in case someone else finds them usefull ... :)

1) Unless you are running an unsteady simulation, you dont really need to include additional nOrthoCorrector loops in your simulation setup, as the iterative nature of the p-v coupling will address it as you go along. nOrthoCorrectors is mainly useful where you need extra loops to correct for non-orthogonality in a single time step.

2) the nonortho corrections used in OF is the over-relaxed method as per HRV's thesis

3) As for the nonorthogonality vs skewness:

i) non-orthogonality is mainly related to the non-parallel of the face normal vector, while

ii)skewness is more related to the fact that distorted meshes result in the intersection of the vector between the adjacent nodes not being at the face centroid

iii) so a nonorthogonal mesh may not necessarily be skew

What i am still trying to figure out is:

i) why convective terms do not need to be corrected for as the diffusion terms are? Seems strange since both terms use a face normal vector to calculate the face fluxes and therefore should be affected by non-orthogonality ...

ii) how much non-orthogonal correction to apply i.e. is this decision purely based on the trade-off between stability (nonortho correction reducing stability as reduces the diagonal dominance of the system) and accuracy?

Many thanks for any help in advance,
regards
jon

Thank you for sharing

Hi - no problem!

Since it seems a couple people are reading this post, i will update some of the things i did not yet understand since last time:

This is because the correction applies to the gradient term only, and therefore, since diffusion only relies on the this term, the convective terms are not affected by it.

Yes, this only depends on the trade-off between stability and accuracy. Since correction reduces diagonal dominance of the coefficient matrices, it comes down to that only.

cheer and best regards
jonathan

I was wandering if somebody can give some hint on this one.

Checking geometry...
Overall domain bounding box (-50 -50.0901 -0.035) (50.29 50 0)
Mesh (non-empty, non-wedge) directions (1 1 1)
Mesh (non-empty) directions (1 1 1)
Boundary openness (-3.43443e-20 4.80201e-21 5.39969e-15) OK.
Max cell openness = 4.90788e-16 OK.
Max aspect ratio = 739.181 OK.
Minimum face area = 2.55578e-06. Maximum face area = 10.688. Face area magnitudes OK.
Min volume = 1.6488e-08. Max volume = 0.0751724. Total volume = 274.745. Cell volumes OK.
Mesh non-orthogonality Max: 79.9874 average: 11.9844
*Number of severely non-orthogonal faces: 715.
Non-orthogonality check OK.
<<Writing 715 non-orthogonal faces to set nonOrthoFaces
Face pyramids OK.
Max skewness = 1.47068 OK.
Coupled point location match (average 0) OK.

Mesh OK.


Does this high skewness affect the accuracy of my solution? I know that maximum admissible skewness is defined as 4. I just wanted to know can the skewness be the source of inaccuracy or not. And also how one can deal with the skewed cells in OpenFOAM and is there any remedy for this problem ?