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Calculating surface integral on Cartesian grid

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Asif Shahriar Nafi
Asif Shahriar Nafi on 13 Nov 2020
I am trying to calculate surface integral for the following problem (see figure). I have the vertex coordinates x,y,z as well as face center coordinates xm,ym,zm. If I have all the interpolated values that are needed for this calculation, then how should I approximate the surface integral for the angled surface shown above (v is velocity vector and u, v, w values are saved in xm,ym,zm coordinates)? Could you kindly describe a little? Another question, which interpolation scheme would be best for this kind of problem? If my question is not clear please let me know.

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Bjorn Gustavsson
Bjorn Gustavsson on 13 Nov 2020
Is that integral:
or
it will make a bit of a difference...

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Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 16 Nov 2020
For the sake of simplicity I'd just calculate the area of the grid-cells, multiply the velocity-vectors with those areas and add the products together. That should give you some area-averaged velocity.
HTH

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