[un-cfd]

Hello everyone
I am reading an article and in the section of the governing equations, I have this question: why in these equations, the movement speed of the mesh(v') is considered only in the coefficients of the spatial derivative, and why the temporal and spatial derivatives are not taken from this velocity??

[LuckyTran]

Because that's the advective term in the so-called convective derivative and you are using a stationary reference frame.

See the wiki for an explanation between material derivative vs convective derivative

In fact, if it modifies the temporal derivative then that is a big tell that you are in a non-inertial reference frame, this is formally known as the principle of Galilean invariance.