The Cubic-Spline Transform Method: Basic Definitions and Tests in a 1D Single Domain
The Cubic-Spline Transform Method: Basic Definitions and Tests in a 1D Single Domain
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三次样条变换方法：一维单域中的基本定义和测试
DOI：
10.1175/1520-0493(2002)130
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发表时间：
2002
影响因子：
3.2
通讯作者：
K. Ooyama
中科院分区：
文献类型：
--
作者：
K. Ooyama
摘要本文的目的是描述一种数值方法的技术细节，该方法将有限域中空间变量的三次样条表示与非线性气象方程时间积分的谱变换方法的逻辑相结合。开发该方法的原因在于将其应用于大气的双向交互嵌套模型。与网格点表示法相比，三次样条表示法允许直接评估模型方程中的导数，并导致平流波和传播波的短波频散大大减少。与傅里叶谱表示相比，三次b样条作为基函数提供了简单而精确的方法来实现域界面以及自然边界所需的各种边界条件。一个锐利的（六阶）低通滤波器内置于三次样条变换中，有效地消除了广告干扰。
Abstract The purpose of the paper is to describe the technical details of a numerical method that combines the cubic-spline representation of spatial variables in a finite domain with the logistics of the spectral transform method for the time integration of nonlinear meteorological equations. The reason for developing the method lies in its application to two-way interacting nested models of the atmosphere. When compared with the gridpoint representation, the cubic-spline representation allows direct evaluation of derivatives in the model equations, and leads to a substantial reduction of shortwave dispersion of advecting and propagating waves. When compared with the Fourier spectral representation, the cubic B-splines as basis functions provide simple but exact means of implementing a variety of boundary conditions that are needed at the domain interfaces, as well as at natural boundaries. A sharp (sixth order) low-pass filter, which is built into the cubic-spline transform, effectively eliminates adver...