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Gradient computation

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Gradient Calculation

From Green-Gauss theorem:

$\int\limits_V {\nabla \phi dV = } \oint\limits_A {\phi dA}$

Written in discrete form:

$\left( {\nabla \phi } \right)_0 = {1 \over V}\sum\limits_f {\bar \phi _f A_f }$

Value at Face

There are many ways of estimating value of $\phi$ at face.

Weighted interpolation: $\phi _f = w\phi _1 + \left( {1 - w} \right)\phi _0$
Arithmatic Average: $\phi _f = 0.5 \left( \phi _1 + \phi _0 \right)$

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