Generation of orthogonal curvilinear grids on the sphere surface based on Laplace-Beltrami equations

2013 International Conferences on Geological, Geographical, Aerospace and Earth Sciences

Lu, Fuqiang^1 ; Song, Zhiyao^1,2 ; Fang, Xin^1

Key Laboratory of Virtual Geographic Environment (Ministry of Education), Nanjing Normal University, Jiangsu Province, Nanjing, 210046, China^1

AA(Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China^2

关键词: Curvilinear grids;    Grid configurations;    Laplace-Beltrami;    Numerical simulating;    Ocean dynamics;    Orthogonality;    Sphere surfaces;    Two directions;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/19/1/012012/pdf
DOI  :  10.1088/1755-1315/19/1/012012

来源: IOP

【 摘 要 】

In this paper, Laplace-Beltrami equations are used to generate orthogonal curvilinear grids on the sphere for ocean models. In addition to overcoming the pole-problem, the grid configuration has quasi-uniform cell-size on the whole sphere. Some quantities such as the grid length along two directions, the angle deviation from orthogonality, the area of the cell to evaluate the quality of the grid, which demonstrate the grid produced is fit to be a model grid on which the finite difference method or finite volume method can be implemented for numerical simulating of global atmosphere and ocean dynamics on large scale.