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-   -   gradient at boundary(FVM) ? (https://www.cfd-online.com/Forums/main/5721-gradient-boundary-fvm.html)

 Yim February 10, 2003 01:26

gradient at boundary(FVM) ?

Hello all.

I study FVM with unstructured grid(tetrahedron). In some references, normal gradient at cell face is (d@/dn)=(@N-@P)*G +{(grad@)f .n-G*(grad@)f .d(PN)} [.:inner product,n:face normal vector,d(PN):vector between P&N, G:geometrical factor]

At interior cell face, (grad @)f,gradient@ at cell face,is interpolated from the two adjacent cell gradients or vertex gradients(the average of the surrounding cell gradients). however, I don't know how can define gradient at boundary face. Is it also the average of the surrounding cell gradients(half of above case)? I think it's not correct.. Any referenses would be helpful !!!!

thank you !!

 Praveen February 17, 2003 04:06

Re: gradient at boundary(FVM) ?

One way is to use the least squares (also called Energy) method which basically fits a polynomial to the local function data. Differentiating the polynomial gives you the gradient. See the VKI lecture notes of Barth. You can get these from his website.

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