基于Laplace方程的球面正交曲线格网生成方法

发布时间：2018-01-18 15:26

  本文关键词：基于Laplace方程的球面正交曲线格网生成方法　出处：《地理与地理信息科学》2016年01期 　论文类型：期刊论文

  更多相关文章： Laplace方程 球极投影 正交曲线格网 Neumann正交化

【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。
[Abstract]:In order to overcome the pole problem caused by the global oceanic and atmospheric numerical model based on the traditional longitude and latitude grid, the global grid coding is convenient and the information query is taken into account at the same time. In this paper, the grid projected by the spherical center of a cube is transformed into a two-dimensional plane region by the spherical pole projection, and then the orthogonal curve grid is generated by solving the Laplace equation numerically. Then a new orthogonal curvilinear grid on the sphere is obtained by using the spherical polar inverse projection. By comparing with the results of the two methods of generating spherical grid by isobaric spherical center projection, the length of the two sides of the grid is obtained. The area, orthogonality and other indexes of the unit are analyzed statistically, and the quality of the generated grid is evaluated. The results show that the size of the grid elements generated by the isobaric projection method is more uniform, but the orthogonality is not ideal. The orthogonal curvilinear grid generated by the Laplace equation method is slightly superior to the conformal transformation method and can be used as the basic grid for the large-scale numerical simulation of the global ocean and atmosphere using the finite difference method and the finite volume method.
【作者单位】： 南京师范大学虚拟地理环境教育部重点实验室;南京师范大学大规模复杂系统数值模拟江苏省重点实验室;江苏省地理信息资源开发与利用协同创新中心;
【基金】：国家自然科学基金资助项目(41306078)
【分类号】：P208
【正文快照】： 0引言随着全球气候逐渐变暖,极端天气现象发生的频率呈升高趋势,需对全球气候变化进行及时预测,以便采取可能的措施减小恶劣天气产生的危害。而这些预测在很大程度上依赖于全球大气模式、海洋模式的发展,因此需要构建一个理想的全球大气、海洋数值模型都适用的网格,以便进一步，

本文编号：1441453