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The primitiveMesh::cellCells returns with a cross cell stencil of 6 cells (the cell in question is excluded). This computation comes from the basis of OpenFOAM: face addressing. Although it is very efficient, this kind of computation introduces errros e.g. in the gradient reconstruction of sharp fields.

Try to generate a field that has a jump in a single layer of cells, whose iso surface is a plane, and try to compute the normal field of this plane from the fraction gradient using...