摘要
为克服基于传统经纬度格网的全球海洋及大气数值模式产生的极点问题,同时顾及全球格网编码便捷及信息查询,该文将立方体球心投影的格网经球极投影转换到二维平面区域,再应用Laplace方程数值求解生成正交曲线格网;然后采用球极逆投影,得到球面上一种新的正交曲线格网。通过与等角球心投影、保角变换两种球面格网生成方法的结果相比较,从格网两边的长度、单元的面积、正交性等指标进行统计分析,对所生成格网的质量进行评价。结果表明,等角球心投影法生成的格网单元大小较均匀,但正交性不理想;Laplace方程法生成的正交曲线格网稍优于保角变换法,可作为应用有限差分方法和有限体积方法的全球海洋及大气大尺度数值模拟的基础格网。
In order to overcome the pole-problem induced by grid-based methods on traditional longitude-latitude grid for global atmosphere and ocean circulation models,a new kind of orthogonal curvilinear grids based on the gnomonic cube grids on the sphere was presented.Firstly,the gnomonic cube grids was on a two-dimensional plane by stereographic projection,then Laplace equations are solved to generate quasi-orthogonal curvilinear grids on the projection plane.Finally,the grids are transformed back to the sphere surface by the inverse of stereographic projection.The produced grid configuration has quasi-uniform cell-size on the whole sphere surface except the neighbourhood of eight major corner vertices.Moreover,another two methods which include equi-angular gnomonic projection and conformal mapping were also introduced to generate spherical grids.The resulting comparisons between three methods would be presented at last.Some quantities such as the grid length along two directions,the angle deviation from orthogonality and the area of the cell were used to evaluate the quality of the grids generated by three methods.The results show that the equi-angular gnomonic projection produces grids of the most uniform size,but are non-orthogonal,while elliptic-smoothing combined with stereographic projection method produces quasi-orthogonal curvilinear grids that are much like that of conformal mapping method.The small grid cells in the neighbourhood of eight corner vertices could be improved by stretching method,or this small defect could be circumvented by implicit time integration method,which demonstrate the kind of grid newly produced is fit to be a model grid on which the finite difference method or finite volume method can be implemented for numerical simulation of global atmosphere or ocean dynamics on large scale.
出处
《地理与地理信息科学》
CSCD
北大核心
2016年第1期18-23,共6页
Geography and Geo-Information Science
基金
国家自然科学基金资助项目(41306078)
关键词
LAPLACE方程
球极投影
正交曲线格网
Neumann正交化
Laplace equations
stereographic projection
orthogonal curvilinear grids
Neumann orthogonal boundary condition
