A Multigrid Scheme for Three-Dimensional Body-Fitted Coordinates in Turbomachine Applications

Abstract

An efficient numerical scheme for the generation of curvilinear body-fitted coordinate systems in three dimensions is presented. The grid is obtained by the solution of a system of three elliptic partial differential equations. The method is based on the classical SOR scheme with an acceleration of convergence using the multigrid technique. The full approximation scheme has been used and is described with the overall algorithm. A number of numerical experiments are given with comparisons to illustrate the efficiency of the method. Practical applications to typical three-dimensional turbomachinery geometries are then shown.