an alternative to quadtree cartesian grids?

cees

In cartesian finite volume methods every control volume normally has one adjacent volume on the east, west, north and south side. This leads to equations like:

Ap*Cp+ As*Cs + An*Cn + AW*Cw + Ae*Ce=Qc

for every cell.

In case we would like to refine the grid on certain locations it would be handy to have two neighbour cells on one side. A possible solution is using the cartesian quadtree grids where we have grids on different levels.

Is it possible to use a different approach? We could for instance use the two neighbours directly in the balance equation

This would lead to equations like:

Ap*Cp + As1*Cs1+As2*Cs2 + An*Cn + AW*Cw + Ae*Ce=Qc

if we have two cells on the south side and one cell on the other sides. Is such an approach possible? Or will this lead to numerical problems for instance with a pressure correction method?

Since I have never seen such an approach there must be a problem which is not yet obviously to me.

regards,

Cees