I have problems in dealing with the singularity on the axis in a full 3D Navier Stokes compressible code in cylindircal coordinates. For the time being I was using staggered grids to avoid the problem, but it seems to me that something is wrong and I got difficulty to reach steady state solutions ( which I found with the axisymmetric code ) Any suggestions, indications or papers ? I also found in most of my simulations, when I am looking for unstable non axisymmetric modes, a mode 2 is firstly excited, although it doesn't grow up but keeps quite moderate. I guess it 's the result of a bad axis treatment. Many thanks

"Numerical Treatment of Polar Coordinate Singularities" by Kamran Mohseni and Tim Colonious, "Journal of Computational Physics 157, 787-795 (2000)"

This paper deals especially with singularities for compressible flows. I hope this would be helpful.

-chandra