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bigphil November 24, 2011 09:18

Is there a corrected Gauss gradient scheme?

I have been looking at the accuracy of the Gauss linear gradient scheme for a simple case compared with the analytical solution, and it is exactly correct for a perfectly orthogonal mesh. But it is inaccurate if the grid is non-orthogonal.

Is there any corrected version of the Gauss linear gradient scheme where the non-orthogonality is corrected for explicitly?

I have also tried leastSquares but it seems to give strange gradients in the boundary cells. extendedLeastSquares seems to work the best but I am not entirely sure how it works.


bigphil November 27, 2011 09:54


I found that you can specify explicit correction like this (as described here):

  grad(U)  Gauss skewCorrected linear;

This certainly reduces the error on non-orthogonal grids, for my test cases anyway.

However, leastSquares gives me much better results on non-orthogonal grids. I was getting strange incorrect gradients in the boundary cells using leastSquares but this was solved by commenting and uncommenting a few lines in OpenFOAM-1.6-ext/src/finiteVolume/finiteVolume/gradSchemes/leastSquaresGrad/leastSquaresVectors.C.
I commented the following lines (lines 140 to 151):

        // Original version: closest distance to boundary                                                                                                   
        //vectorField pd =                                                                                                                                   
        //    mesh_.Sf().boundaryField()[patchi]                                                                                                           
        //  /(                                                                                                                                               
        //    mesh_.magSf().boundaryField()[patchi]                                                                                                         
        //    *mesh_.deltaCoeffs().boundaryField()[patchi]                                                                                                   
        //    );                                                                                                                                             

        //if (!mesh_.orthogonal())                                                                                                                           
        //  {                                                                                                                                               
        //    pd -= mesh_.correctionVectors().boundaryField()[patchi]                                                                                       
        //      /mesh_.deltaCoeffs().boundaryField()[patchi];                                                                                               
        //  }

and uncommented this line (line 155):

        // Better version of d-vectors: Zeljko Tukovic, 25/Apr/2010                                                                                         
        // Experimental: review fixed gradient condition.  HJ, 30/Sep/2010                                                                                   
        vectorField pd =;


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