For
F=(F1,F2,F3) in Cartesian coordinates,
∇⋅F=∂iFi=∂x∂F1+∂y∂F2+∂z∂F3.
Takes
a vector field
as input and produces
a scalar field.
Mnemonic: it gives out the amount of fluid that is going in or out of
a given
volume per
unit of time.
Therefore, if you take
a cubic
volume:
- the input has to be the 6 flows across each face, therefore 3 derivatives
- the output is the variation of the quantity of fluid, and therefore a scalar
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