Transfinite mappings and their application to grid generation

摘要

The two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain. Mesh generators or grid generators are preprocessors whicd decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils. A number of such techiques have been developed over the past decade to alleviate the frustation and reduce the time involved in the tedious manual subdividing of a complex-shaped region or 3-D structure into finite elements. Our purpose here is to describe how the techniques of bivariate and trivariate ”blending function” interpolation, which were originally developed for and applied to geometric problems of computer-aided design of sculptured surface and 3-D solids, can be adapted and applied to the geometric problems of grid generation. In contrast to other techniques which require the numerical solution of complex partial differential equations (and, hence, a great deal of computing), the transfinite methods proposed herein are computationally inexpensive.