Co‐located equal‐order control‐volume finite element method for two‐dimensional axisymmetric incompressible fluid flow

The formulation of a control‐volume‐based finite element method (CVFEM) for axisymmetric, two‐dimensional, incompressible fluid flow and heat transfer in irregular‐shaped domains is presented. The calculation domain is discretized into torus‐shaped elements and control volumes. In a longitudinal cross‐sectional plane, these elements are three‐node triangles, and the control volumes are polygons obtained by joining the centroids of the three‐node triangles to the mid‐points of the sides. Two different interpolation schemes are proposed for the scalar‐dependent variables in the advection terms: a flow‐oriented upwind function, and a mass‐weighted upwind function that guarantees that the discretized advection terms contribute positively to the coefficients in the discretized equations. In the discretization of diffusion transport terms, the dependent variables are interpolated linearly. An iterative sequential variable adjustment algorithm is used to solve the discretized equations for the velocity components, pressure and other scalar‐dependent variables of interest. The capabilities of the proposed CVFEM are demonstrated by its application to four different example problems. The numerical solutions are compared with the results of independent numerical and experimental investigations. These comparisons are quite encouraging.