Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform
Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform
复制标题
使用快速傅立叶变换的非均匀网格的离散正交函数展开
DOI：
10.1016/0021-9991(84)90096-2
复制
发表时间：
1984
影响因子：
4.1
通讯作者：
W. Reynolds
中科院分区：
文献类型：
--
作者：
A. Cain;J. Ferziger;W. Reynolds
通过结合使用映射函数和快速傅里叶变换，得到了非均匀间隔数据的离散正交函数展开式。结果产生无别名的微分和积分算子。该方法适用于周期性、零或零导数边界条件（或其组合）。需要截断以避免混叠和/或奇异性，但是截断误差是明确的、可定量表达的并且通常较小。这种方法被证明是在一个无限的物理域与应用程序的线性对流和扩散。由此产生的误差的数量级小于由标准的有限差分方法产生的。由象场引起的困难是一个重要的现象。微分方法以及边界条件隐含了（人工）像场。一个涡配对问题，这表明图像流可以完全改变的解决方案。新方案通过保持图像流无限远来避免这种不良影响。
Discrete orthogonal function expansions are obtained for non-uniformly spaced data by combined use of mapping functions and the fast Fourier transform. The result yields alias-free differentiation and integration operators. The method is applicable to periodic, zero, or zero derivative boundary conditions (or combinations thereof). Truncation is required to avoid aliasing and/or singularity but the truncation error is explicit, quantitatively expressible, and generally small. This approach is demonstrated in an infinite physical domain with application to linear convection and diffusion. The resulting errors are orders of magnitude smaller than those generated by standard finite-difference methods. Difficulties arising from image fields are an important phenomena. The method of differentiation, as well as the boundary conditions, imply (artificial) image fields. A vortex-pairing problem is presented which shows that image flows can totally alter the solution. The new scheme avoids this undesirable effect by keeping image flows infinitely far away.