I have a structured 3d fine grid whose vertices are given by xf(i,j,k), yf(i,j,k), zf(i,j,k). The coarse grid is obtained by deleting every other vertex. The code is a cell centered finite volume code.
In the prolongation step, the cell average of a fine grid cell are to be interpolated from surrounding coarse grid cell averages. In the restriction step, the cell average of a coarse grid cell is to be obtained from surrounding fine grid averages.
I was wondering if someone could point me to robust methods for doing these steps in 3d. In particular, are there ways to do these steps which preserve positivity of the variables and be atleast second order accurate ?