CFD Online Discussion Forums - why is the pressure equation in OpenFoam the same for moving grids and for fixed grid

While looking at the source code of pimpleFoam in the com version of OpenFOAM (see https://develop.openfoam.com/Develop...ble/pimpleFoam) i was wondering why they use the same pressure equation. In books like the one of Ferziger we find the continuity equation in the ALE formulation for moving grids written as:

$\frac{d}{dt}\int\rho dV + \oint\rho \mathbf{n} \cdot (\mathbf{U} - \mathbf{U_g} ) dS = 0.$

For incompressible flows of coarse the first term should vanish.

For non moving grids the continuity equation looks like

$\frac{d}{dt}\int\rho dV + \oint\rho \mathbf{n} \cdot (\mathbf{U} ) dS = 0.$

So i was expecting some relative flux in the pressure equation for the moving grids. But I did not find it.

After thinking a while I realized that for moving grid we have to fulfill also the space conservation equation:

$\frac{d}{dt}\int dV = \oint \bold{n} \cdot \mathbf{U_g} dS$ .

So if we insert the above equation into the continuity equation for moving grid, the term including the grid velocity cancels out and we have the same continuity equation as for the non moving case.

Hope my reflections are right and saves someone some thinking (if they are right and if not please correct me).

Best

Michael