Meshless solution of axisymmetric convection–diffusion equation: A comparison between two alternative RBIE implementations

The radial basis integral equation (RBIE) method was derived using two different approaches to solve the steady-state axisymmetric convection–diffusion equation. In the first approach (Approach 1), the integral representation of the governing equation was derived using the Laplace fundamental solution in the axisymmetric coordinates. In the second approach (Approach 2), the Laplace fundamental solution in two-dimensional Cartesian coordinates was used at the expense of an additional pseudo-source term in the domain integrals. The domain integrals were dealt with using the cell integration technique. The Approach 1 was found to produce results that were more accurate than the Approach 2. However, the CPU time requirement was higher in the Approach 1 than in the Approach 2.