A finite element exterior calculus framework for the rotating shallow-water equations
A finite element exterior calculus framework for the rotating shallow-water equations
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DOI：
10.1016/j.jcp.2013.10.008
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
C. Cotter;J. Thuburn
中科院分区：
文献类型：
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作者：
C. Cotter;J. Thuburn
我们使用有限元外演算的框架描述了球面上浅水方程的离散化，这是Ringler（2010）[11]中提出的模拟有限差分框架的扩展。外部演算符号提供了一个指南，其中有限元空间应用于哪些物理变量，并统一了一些理想的属性。我们提出两种配方：一种是在单个网格上定义有限元空间的“原始”公式，另一种是在对偶网格上也使用有限元空间的“原始-对偶”公式。这两个公式都有速度和层深作为预报变量，但外部演算框架导致一个保守的诊断位涡。在这两个配方中，我们将展示如何构建离散，具有质量一致（恒定的位涡保持不变），稳定和振荡的位涡平流。
We describe discretisations of the shallow-water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler (2010) [11]. The exterior calculus notation provides a guide to which finite element spaces should be used for which physical variables, and unifies a number of desirable properties. We present two formulations: a “primal” formulation in which the finite element spaces are defined on a single mesh, and a “primal–dual” formulation in which finite element spaces on a dual mesh are also used. Both formulations have velocity and layer depth as prognostic variables, but the exterior calculus framework leads to a conserved diagnostic potential vorticity. In both formulations we show how to construct discretisations that have mass-consistent (constant potential vorticity stays constant), stable and oscillation-free potential vorticity advection.