Three-dimensional algebraic grid generation

Abstract

One of the major approaches to numerical grid generation is the explicit algebraic expression of a physical grid as a function of a uniform grid in a rectangular computational coordinate system. The algebraic methods are based on mathematical interpolation, and the primary advantages are speed and directness. The relation between interpolation and grid generation is described. For three-dimensional grid generation, transfinite interpolation using the coordinate control processes developed in the multisurface method and two-boundary technique are advocated. Grid singularities encountered in three dimensions are discussed, and the exploration of multiple overlapping grids is proposed. Some aspects of interactive algebraic grid computation in three dimensions are discussed.