Originally Posted by mkraposhin (Post 446745)

You must refer to Ferziger and Peric "Computational Fluid Dynamics" where they presented generalization for the Reynolds Transport Theorem for the moving control volume

Another good article:
"Dynamic Mesh Handling in OpenFOAM" by H. Jasak, try to google it

Originally Posted by cctv (Post 446754)

Thank you for your reply. I have ever read the article "Dynamic Mesh Handling in OpenFOAM" by H. Jasak, but I do not think he explained the reason to use fvc::makeRelative(phi, U) and fvc::makeAbsolute(phi, U) in details, In additon, do you know what would the function 'meshphi(U)' return ? Thank you very much.

Originally Posted by mkraposhin (Post 446768)

for any extensive property B and intensive property b we can write:

DB/Dt=D/Dt(int (rho*beta)dV) + int (rho*beta*(Ua-Ub))*dS

Ua - absolute velocity
Ub - velocity of the control volume boundary element
Ur=Ua-Ub - relative
D/Dt - material derivative
int (*) dV - integral over volume
int (*) dS - integral over surface

In OpenFOAM fvc::makeRelative(phi,U) estimates relative flux Ur=Ua-Ub
fvc::makeAbsolute(phi,U) estimates total flux Ua = Ur + Ub
Function fvc::meshPhi(U) returns flux of the control volume boundary Ub

This functions are used to convert from/to relative fluxes to absolute when control volume is moving, see Ferziger and Peric