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Navier Stokes Equation for ALE Formulation

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Hello, so I came across this Navier Stokes equation for ALE as stated in the Comsol module here : https://www.comsol.jp/model/fluid-structure-interaction-361 Screenshot of the equation is attached.

The difference with the usual incompressible Navier Stokes equation is that the spatial coordinate velocity is added into it. While I understand the concept about coordinate transformation with ALE that leads to this, I wonder if someone can recommend me a reference to proof this in theoritical basis. I tried to look about it in several Comsol manuals but yet to find one.

Thank you.


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