COMPUTATIONAL CONFORMAL MAPPING FOR SURFACE GRID GENERATION

摘要

The paper describes the development and application of a new approach for formulating an elliptic generation system on parametrically defined surfaces. The present derivation of the surface equations proceeds in two steps: First, conformal mapping of smooth surfaces onto rectangular regions is utilized to derive a first-order system of partial differential equations analogous to Beltrami's system for quasi-conformal mapping of planar regions. Second, a general elliptic generation system for three-dimensional surfaces, including forcing functions, is formulated based on Beltrami's system and quasi-conformal mapping. The resulting elliptic system is solved using an iterative method on arbitrary surfaces represented analytically by rational B-splines. The overall effect of this approach is a reliable and versatile elliptic method for generating and improving surface grids. Examples will be presented to demonstrate the application of the method in constructing practical grids. (C) 1996 Academic Press, Inc. [References: 21]