A Framework for Mimetic Discretization of the Rotating Shallow-Water Equations on Arbitrary Polygonal Grids
A Framework for Mimetic Discretization of the Rotating Shallow-Water Equations on Arbitrary Polygonal Grids
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DOI：
10.1137/110850293
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
J. Thuburn;C. Cotter
中科院分区：
文献类型：
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作者：
J. Thuburn;C. Cotter
在天气和气候预报模式中，精确地模拟大气流动要求控制方程的离散化具有许多理想的性质。虽然这些属性可以在经纬度网格上相对简单地实现，但在现在正在考虑的各种准均匀球形网格上，它们更具挑战性。最近开发的计划，称为TRISK，具有这些理想的性质，具有正交对偶网格。目前的工作扩展TRiSK计划到一个更一般的框架，适用于网格，有一个非正交的对偶，如等角立方球。我们还表明，这个框架适合在更广泛的框架内的模仿离散化和离散外部演算。其中一个关键要素是某些映射算子的定义，这些算子是霍奇星星算子的离散类似物，使得能够定义相容的内积。离散科里奥利条款也包括在米梅.
Accurate simulation of atmospheric flow in weather and climate prediction models requires the discretization of the governing equations to have a number of desirable properties. Although these properties can be achieved relatively straightforwardly on a latitude-longitude grid, they are much more challenging on the various quasi-uniform spherical grids that are now under consideration. A recently developed scheme—called TRiSK—has these desirable properties on grids that have an orthogonal dual. The present work extends the TRiSK scheme into a more general framework suitable for grids that have a nonorthogonal dual, such as the equiangular cubed sphere. We also show that this framework fits within the wider framework of mimetic discretizations and discrete exterior calculus. One key ingredient is the definition of certain mapping operators that are discrete analogues of the Hodge star operator, enabling the definition of a compatible inner product. Discrete Coriolis terms are also included within the mimet...