FDA (loss of) accuracy in non-uniform grids
 

Hi all,

When faced with gridding a flattened domain (10-100 micrometres x 5mm x 5mm) I chose to use a (structured) one-way biased non-uniform grid to achieve adequate cell resolution in the area of interest while keeping within the memory capacity of the machine.

However, my concern is that the extent of the biasing may be limiting the accuracy of the solution. I've searched the literature but I cannot find any definitive answer as to how the accuracy of an FDA is compromised by moving from a (structured) uniform grid to a (structured) non-uniform grid. I get the impression the answer to this question is dependent on the particular FDA used. I have come across comments (Flow 3D website) stating that in general FDAs drop an order of accuracy on non-uniform grids. This would mean second order schemes are the minimum standard required.

Is there a threshold ratio of cell lengths of adjacent cells? Or a threshold value of maximum and minimum cell length in a given dimension/or across the entire model?

Any clarification on this matter would be greatly appreciated. Also, please feel free to suggest any salient reference articles/books.

cheers, Novak.

Re: FDA (loss of) accuracy in non-uniform grids
 

Hi Novak,

what might help for an estimate is:

@article{Darwish94, author ={Darwish, M. S. and Moukalled, F.}, title ={Normalized variable and space formulation methodology for high-resolution schemes}, journal ={Journal of Numerical Heat Transfer B}, volume ={26}, pages ={79-96}, year ={1994} }

Hope that helps. However, it does not include a recipe how to adjust the grid stretching for a certain accuracy.

Best regards Romuald