momentum interpolation for collocated grid

Hadian

Dear friends

I am developing a 2D implicit unsteady code using collocated grid. As you know, to avoid the Checkerboard pressure prediction, the momentum interpolation is needed. since I use the under-relaxation factor in solving momentum equation the original Rhie&Chow method can not be used directly. To have the results independent of under-relaxation and time increment a modified Rhie&Chow interpolation should be used. One of them has been explained in the following paper: Lien ,F.S.; Leschziner, M.A. "A General Non-Orthogonal Collocated Finite Volume Algorithm for Turbulent flow at all Speeds…..", Comput. Methods Appl. Mech. Engrg, 114(1994) 123-148 Now my question is about implementation of such a method. 1- In this type of momentum interpolation the Ap at cell face is needed. should I interpolate the Ap by linear interpolation or 1/Ap should be interpolated? 2- In the momentum interpolation equation there are the cell face velocity at previous iteration and previous time step. So we should store 2 velocity component at each face. So in this case the required memory will be more than what is needed for staggered grid. Is this true? Or there is a trick not to store the velocities at cell faces? 3- Should I use the cell face velocity resulted from momentum interpolation only in pressure correction or it should be used in momentum equation too?

Thanks in advance for your replies.

Regards,

Hadian