A time efficient finite differences algorithm for the solution of the meridional flow in turbo compressor impellers

A finite difference method is developed for solving the non-viscous formulation of a three-dimensional compressible flow problem for turbomachinery impellers. The numerical results and the time efficiency of this method are compared to that provided by a finite element method for this problem. The finite difference method utilizes a numerical, curvilinear, and non-orthogonal coordinate transformation and the ADI scheme. The finite difference method is utilized to solve a test problem of a centrifugal compressor impeller. It is shown that the finite difference method produces results in good agreement with the experimentally determined flow fields and is as accurate as the finite element technique. However, the finite difference method only requires about half the time in order to obtain the solution for this problem as that required by the finite element method.