EXTENSION OF THE SIMPLEN ALGORITHM DIFFERENCING SCHEME TO CYLINDRICAL POLAR COORDINATES

Abstract

The differencing scheme used with the SIMPLEN algorithm for the solution of convection-diffusion problems on nonstaggered grids, formulated by one of the authors in two previous papers for Cartesian coordinates, is extended to a cylindrical polar coordinate system. The scheme is shown to be equivalent to its Cartesian counterpart: The interpolation functions derived for the radial coordinate direction reduce to those for Cartesian coordinates when the cell interfaces are positioned at the geometric mean radial positions between grid points. Three case studies involving laminar, incompressible flow are presented to validate the scheme: stagnation in three-dimensional flow, flow near a rotating disk, and flow through an abrupt pipe expansion. Excellent agreement between the numerical solutions and the corresponding analytical solutions and experimental data is demonstrated.