Grid Generation

Abstract

Exact solutions of boundary value problems for simple regions, such as a circle, square or annulus, can be determined with relative ease even in cases where the boundary conditions are rather complicated. Although Greens functions for such simple regions are known, the solution of a boundary value problem for regions with complex structures often becomes more difficult, even for a simple problem, such as the Dirichlet problem. One approach to solving these difficult problems is to conformally transform a given region into the simplest form. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. Grid generation methods using conformal mappings are presented for problems dealing with a cascade of blades, and inlet flow configurations.