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You can find some good explanations using Google, as divergence is a not solely a CG / Houdini thing, but a mathematical operator extensively used in physics :-)

It is used in many fields of physics (and maths), like fluid dynamic, electromagnetic etc. Everytime there are vector fields involved.

It is important in simulating water because it should be an incompressible fluid, and therefore its "divergence of the flow " should be zero, which is an important constraint. That's different for gas, because you can compress it when pressure increase (so its volume changes accordingly).

https://en.wikipedia.org/wiki/Divergence

https://en.wikipedia.org/wiki/Incompressible_flow

https://betterexplained.com/articles/divergence/

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/divergence-grant-videos/v/divergence-intuition-part-1

hope this helps

 

Edited by StepbyStepVFX
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