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[Solution]

In the framework of finite volume approach, the divergence theorem is used to write the standard diffusion term as a gradient summed over all the faces of the control volume. Solution 2056855 gives the main steps to write such diffusion term and explains why a secondary gradient appears for non orthogonal cell arrangement. Eventually, a simple test case is set up to assess the influence of secondary gradient for internal faces when considering the mixing of cold and hot air. For this particular case, secondary gradient shows a negligible impact on temperature field in the mixing region. Remember that global deactivation of secondary gradient should be employed with caution. It is recommended to use it as a last resort if all other convergence strategies have failed. Improving mesh quality / refinement should be considered prior to this option. Please see attached document for further details. Keywords: secondary gradient, numerics

Attachments:
1. 2056855.pdf