H. Ozoe et K. Toh, A TECHNIQUE TO CIRCUMVENT A SINGULARITY AT A RADIAL CENTER WITH APPLICATION FOR A 3-DIMENSIONAL CYLINDRICAL SYSTEM, Numerical heat transfer. Part B, Fundamentals, 33(3), 1998, pp. 355-365
A technique was invented to circumvent computational singularity at a
radial center of cylindrical and spherical coordinate systems. The ide
a is as follows. The radial velocity at a center is given by the avera
ge of adjacent circumferential directional velocity components located
at +/-0.5 pi rad. Sample computations are presented for natural conve
ction in a vertical cylinder with two different thermal boundary condi
tions. Those velocity profiles through a cylinder center are smoothly
represented.