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Custom surface interpolation scheme

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Old   September 22, 2022, 15:44
Default Custom surface interpolation scheme
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Hi everyone,

I want to implement a custom surface interpolation scheme for the convective term, so that:

Code:
div(phi,T)      Gauss myCustomScheme;
For each face (both internal or boundary) I have an array of 6 coefficients representing the weights (w_k) of my custom scheme. With them, I obtain the value of T at the face as a linear combination of 6 neighbouring cell center values:

T_{f}=\sum^{N}_{k=1}w_{k}T_{k}, being: T the transport property, f the face to get the interpolated value, w the corresponding weight and k=1,2,...,6 each neighboring cell.

These 6 cells correspond to the E, W, NE, NW, SE, and SW neighbouring cells of the face f. Besides, these coefficients are time dependent, so I will have new coefficients every timestep.

I am using the code of the upwing scheme as template for my implementation, however, the upwing scheme only uses previous or following cell (E or W) instead of the 6 neighbours. I also tried the QUICK scheme as template, but I did not get any good result.

Could anyone help me on how i should modify a existing scheme to fullfil my requirements? Thank you very much in advance.
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