“阴阳网格”：球面几何中的重叠网格
The "Yin-Yang Grid": An Overset Grid in Spherical Geometry
摘要：
提出了一种新的球面几何重叠网格--阴阳网格。阴阳网格是由两个相同的网格组成，它们以互补的方式组合在一起，覆盖一个边界部分重叠的球面。每个组成格网都是经纬度格网的低纬度部分。因此，网格间距是准均匀的，度量张量是简单的和解析已知的。人们可以直接应用在球极坐标或经纬度网格中编写的数学和数值资源。两个相同的组件网格的互补组合使我们能够高效和简洁的程序。开发了基于阴阳网格有限差分格式的地球发电机和地幔对流模拟程序，并进行了测试。阴阳网格适用于大规模并行计算机。
英文摘要：
A new kind of overset grid, named Yin-Yang grid, for spherical geometry is proposed. The Yin-Yang grid is composed of two identical component grids that are combined in a complemental way to cover a spherical surface with partial overlap on their boundaries. Each component grid is a low latitude part of the latitude-longitude grid. Therefore the grid spacing is quasi-uniform and the metric tensors are simple and analytically known. One can directly apply mathematical and numerical resources that have been written in the spherical polar coordinates or latitude-longitude grid. The complemental combination of the two identical component grids enables us to make efficient and concise programs. Simulation codes for geodynamo and mantle convection simulations using finite difference scheme based on the Yin-Yang grid are developed and tested. The Yin-Yang grid is suitable for massively parallel computers.
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