A Comparison of Grid Quality of Optimized Spherical Hexagonal–Pentagonal Geodesic Grids

Abstract

Construction and optimization methods of spherical hexagonal?pentagonal geodesic grids are investigated. The objective is to compare grid structures on common ground. The distinction between two types of hexagonal?pentagonal grids is made. Three conventional grid optimization methods are summarized. In addition, three new optimization methods are proposed. Six desirable conditions for an ideal grid are described, and the grid optimization methods are organized in view of such conditions. Interval uniformity, area uniformity, isotropy, and bisection of cell faces are systematically investigated for optimized grids. There are compensations of preferable grid features in each optimization method, and an optimal method cannot be decided based only on the research of grid features. It is suggested that grid optimization methods should be selected based on research of numerical schemes.