A technique to circumvent a singularity at a radial center with application for a three-dimensional cylindrical system

A technique was invented to circumvent computational singularity at a radial center of cylindrical and spherical coordinate systems. The idea is as follows. The radial velocity at a center is given by the average of adjacent circumferential directional velocity components located at +/-0.5 pi rad. Sample computations are presented for natural convection in a vertical cylinder with two different thermal boundary conditions. Those velocity profiles through a cylinder center are smoothly represented.