Nearly Orthogonal Two-Dimensional Grid Generation with Aspect Ratio Control

Abstract

An improved method for nearly orthogonal grid generation is presented in this study. The generating system is based on solution of a system of partial differential equations with finite difference discretization. To prevent grid lines from collapsing onto each other, the grid cell aspect ratio is controlled by functions that limit excessive ratios. Bounding all the aspect ratios is essential for high-quality numerical approximations using such grid-based methods as finite elements, finite differences, or finite volumes. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides and moving boundaries is used. The proposed method is applied to various test problems from the literature. This method is shown to provide a good balance between controlling grid orthogonality and cell aspect ratio.