Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere
Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere
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DOI：
10.1006/jcph.2002.7075
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发表时间：
2002-07
影响因子：
4.1
通讯作者：
A. Layton
中科院分区：
文献类型：
--
作者：
A. Layton
目前，全球气象应用中常用的空间离散化方案仅限于光谱方法或低阶有限差分/有限元方法。产生高阶近似的谱变换方法需要Legendre变换，其计算复杂度为O(N3)，其中N是一维中的子区间数。因此，高阶有限元方法可能是光谱方法的可行替代方案。本文提出了一种在球坐标下求解浅水方程（SWE）的数值方法。在这个实现中，SWE在时间上用半隐式跳跃方法离散，在空间上用三次样条搭配方法在跳过的纬度？经度网格。Williamson等的数值结果。SWE测试用例D. L. Williamson， J. B. Blake， J. J. Hack， R. Jakob， P. N. Swarztrauber， J. Comput。物理学报，102,211(1992)]，以证明该方法的稳定性和准确性。结果还显示了该方法与在均匀纬度上进行空间离散化的类似方法之间的效率比较。经度网格。
Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finite-element methods. The spectral transform method, which yields high-order approximations, requires Legendre transforms, which have a computational complexity of O(N3), where N is the number of subintervals in one dimension. Thus, high-order finite-element methods may be a viable alternative to spectral methods. In this study, we present a new numerical method for solving the shallow water equations (SWE) in spherical coordinates. In this implementation, the SWE are discretized in time with the semi-implicit leapfrog method, and in space with the cubic spline collocation method on a skipped latitude?longitude grid. Numerical results for the Williamson et al. SWE test cases D. L. Williamson, J. B. Blake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, J. Comput. Phys.102, 211 (1992)] are presented to demonstrate the stability and accuracy of the method. Results are also shown for an efficiency comparison between this method and a similar method in which spatial discretization is done on a uniform latitude?longitude grid.