Equidistribution schemes, poisson generators, and adaptive grids

摘要

Equidistribution of a weight function over a mesh is the main concept employed in the recent development of adaptive grid schemes. This idea is reviewed in this paper, and several examples of grids produced using equidistribution are presented. The shortcomings of this approach are identified, and its usefulness is evaluated. Next, the traditional Poisson grid generators are written as nonlinear equidistribution schemes. In this form, the relationship between the numerical solution of a physical problem, the source terms in the grid generation equations, and the weight functions in equidistribution schemes are identified. Examples are given illustrating the case of providing a useful adaptive grid with this approach.