Galerkin Method Applicable for Finite-Volume?
 

I am developing a CFD model of a continuous reactor. The model is three-dimensional, cell centered, finite-volume formulation in rectangular domain using Cartesian co-ordinates. The SIMPLE method is being used with staggered grids. I would like to use the multi-grid method to solve the pressure correction equations. I have a few questions about my approach. Is it acceptable to use the Galerkin (A1=R2A2P1) method to generate course grid coefficient matrices from fine grid coefficient matrices or is it better to re-discretize the equations? Is it valid to represent one transfer matrix (R) as the transpose of another (PT) or should R and P be developed separately? Are there compatibility restrictions on R and P matrices that are developed separately? Is it acceptable to use a weighted average restriction matrix R, along with a tri-linear interpolation matrix P? Thanks you for your help Scott