[alexandross]

Hello everyone,

I am a new OpenFOAM user, but experienced finite volume programmer. Recently we have conducted a study that shows that the Gauss gradient used in OpenFOAM (and the cell-based Gauss gradient of Fluent) is inconsistent on unstructured meshes, i.e. with grid refinement it converges to a skewness-dependent operator that is different than the actual gradient. Furthermore, we have found, by solving a Poisson equation with an analytic solution, that use of this gradient scheme results in zeroth-order accuracy for the finite volume method as a whole. This means that no matter how fine a grid you use, the accuracy is comparable to that on a very coarse mesh. Some of these tests were conducted with OpenFOAM and Gmsh or Netgen grids. Our study can be found here:

https://hal.archives-ouvertes.fr/hal-01532882v2

(An expanded version that includes also an analysis of the least-squares gradient can be found here:

https://www.researchgate.net/publica...volume_methods

I know that this is probably surprising to many people given the popularity and long history of this scheme, and its reputation for being second-order accurate. However, the analysis is straightforward and the numerical tests are simple and easily repeatable. The problem goes away if one uses the least-squares gradient, which is always at least first-order accurate.

So, I would appreciate your feedback on this issue. Has anyone had a similar experience? Is it documented somewhere else? Since "Gauss linear" is the default scheme in OpenFOAM, and the least-squares scheme is mentioned under "Other schemes that are rarely used" in the cfd-direct users guide, it is puzzling to me how this issue has gone unnoticed so far given the popularity of OpenFOAM.

Of course, the Gauss gradient is not restricted to OpenFOAM but is used more widely in the finite volume realm (I already metioned Fluent for example) but since it is the default choice in OpenFOAM and we used the latter in our numerical tests, I think it is a good idea to post this here. This is a serious issue and it is important that awareness is raised and people switch to "leastSquares" if they use unstructured meshes.