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an alternative to quadtree cartesian grids?

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Old   February 9, 2007, 20:50
Default an alternative to quadtree cartesian grids?
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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.



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