A systematic procedure for generating useful conformal mappings

Abstract A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite−difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly−rectangular domain for a wide variety of partical problems. The introduction of sheared co−ordinates in this computational domain then provides for solution of the problem in a nearly−orthogonal (in fact, nearly−conformal) co−ordinate system, with its boundaries corresponding to co−ordinate lines. The method is based upon the Schwarz−Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.