Jacobi galerkin spectral method for cylindrical and spherical geometries

The approximation of the convection–diffusion problem based on the Galerkin method in Cartesian, cylindrical and spherical coordinates is considered with emphasis in the last two cases. In particular, cylindrical and spherical coordinates can lead to a degeneracy in the global system of equations. This difficulty is removed by incorporating the factor r   into the weight function which is introduced naturally by using Jacobi polynomials Pk(α,β) with α=0α=0 and β=1,2β=1,2. By doing this, an unified framework is obtained for handling the typical geometries required in chemical engineering. Examples are presented based on the Galerkin method for discussing the applicability of this approach.