Hello everyone, I'm trying to develop a fully 3D code in cylindrical coordinates; finite difference; Do you have any suggestion about how dealing with the point on the centerline? I would prefer to avoid the de l'Hopital rule for the singularity, and I believe that maybe one can consider the centerline point in cartesian coordinate...but whatever is the strategy adopted...my question is: how do I choose the planes to which the centerline belong? ( I mean, PHISICALLY, the centeline belongs to all the meridian planes ) Many thanks

This may not be very helpful, since you already specified that you would like to use a finite difference method -- but if you have the choice, I would suggest you consider a finite volume approach. I find it easier to implement for arbitrary geometries, including yours.

ctr.stanford.edu/ResBriefs00/constantinescu.pdf

Have a look at this paper. You will find the method for dealing with singularity.

Also do a google search for

"cylindrical coordinates" + "lele" + "finite difference"

Regards

A.S.