Difference between faceCorrected and corrected surface normal gradient schemes
 

Hello everyone,

I am currently doing Ahmed Body 3D simulations using OpenFOAM. The mesh is completely structured and done using gmsh. Check mesh results include mesh non-orthogonality of 56 (max) and 15.5 (Average). Max aspect ratio being 71. Max skewness is 2.5.

As our objectives involve analysing boundary layer physics with DNS accuracy, maximum possible care is taken in mesh design. The grid cell size transitions are considered properly and made sure to be smoother in the complete domain.

The issue I have been stuck with is the residuals of Poisson equation ( pressure solver). The initial residual is very stiff that I could manage to have it only around order of 10^-3 until 4 pressure correction steps (ncorrectors=4). I cant afford more.

The initial non-orthogonality was 65 (max) and assuming it to be reason, I improved mesh to the aforementioned check mesh values. I changed GAMG solver to PCG, range of first and second order schemes for temporal and spatial terms, increasing the correctors in PISO, momentum predictor etc.. I found the residuals were depending on snGradscheme and laplacianScheme.

I use same surface normal gradient scheme for Laplacian and snGradscheme terms. If I use

Gauss linear corrected - simulation diverges
Gauss linear limited corrected 0.33 - stable and initial pressure residuals of 10^-4
Gauss linear limited corrected 0.5 - 0.6 - stable but initial residuals are of order 10 ^ -3
Gauss linear limited corrected 0.75 - stable but initial residuals are of order 10^-2

Irrespective of nCorrectors. the order of residuals remain the same. With magnitude slightly lower with each correction.

Gauss linear uncorrected - stable and initial residuals of order 10 ^-5
Gauss linear faceCorrected - stable and initial residuals of order 10 ^-5

With increasing nCorrectors, residuals tend to go down much better. With two correctors pressure initial residuals go down to order of 10^-5. I would not use uncorrected considering it doesn't provide non-orthogonal correction.

Here is my question,

Can some one please identify the differences between faceCorrected scheme and Corrected scheme. The description in the code files says the same for both. My programming knowledge is limited and it doesn't really help in understanding the differences from source code files. I am sorry for that. I would like to know the differences in terms of order and also if possible mathematically too. And is it good idea to use faceCorrected scheme for DNS ?

Please let me know if you need any other simulation details. Thanks in advance for your time and attention.