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Where is the grad computed in SIMPLE source code?

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Old   September 15, 2019, 06:07
Default Where is the grad computed in SIMPLE source code?
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zizhou huang
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I have been trying to figure out how SIMPLE algorithm is implemented, but here: https://openfoamwiki.net/index.php/O...hm_in_OpenFOAM
it never mentions how the gradient of scalars is computed on an irregular mesh, and I haven't found where it is computed in source code. Is there anyone could tell me where is the function of grad computation? Thank you so much!
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Old   September 16, 2019, 12:19
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The explicit calculation of gradients in OpenFOAM usually involve invoking Gauss theorem:

\int_{V}\nabla\phi\approx\frac{\sum_{f}\mathbf{S}_{f}\phi_{f}}{V}

where \mathbf{S}_{f} is the surface normal facing outwards, and \mathbf{S}_{f}\phi_{f} represents the outer product of \mathbf{S}_{f} with the tensor \phi_{f} (for example, a rank 0 tensor, i.e. an scalar).

This calculation is valid for arbitrary polyhedrons.

The relevant piece of code is in gaussGrad.C (https://cpp.openfoam.org/v6/gaussGrad_8C_source.html).
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