Conformal mapping and orthogonal grid generation
David C. Ives, Robert M. Zacharias · 23rd Joint Propulsion Conference · 1987
This article presents a method for conformally mapping a general non-self-intersecting closed curve to a rectangle, with four designated points mapped to the corners of the rectangle. A similar mapping to a circle is also described. When carefully coded, these methods make conformal mapping of general contours nearly as simple as evaluating a function. A related fast Poisson solver method for the generation of a two-dimensional orthogonal grid from a conformal mapping is reviewed, as is the stacking of two-dimensional grids to construct a three-dimensional grid. These methods are fast, accurate, reliable, simple, general, and automatic. They constitute a developer's toolbox, enabling the creation of grids based on conformal mapping for a wide range of complex real-world configurations.