Relation between the Fourier transform, POD and VOD
Abstract
This paper presents a comparison of a decomposition of unsteady vector fields, based on the principle of Shannon-Kotelnik theorem and singular decomposition methods. The article points out the relation between the discrete Fourier transform based on Kotelnik series and methods of singular Orthogonal Decomposition. It is used with success in the image processing and modal decomposition of the vortex structures and assessing their stability in a fluid flow. The Fourier transform method has the advantage that it is not necessary to solve the problem of the eigenvalues of relatively large orders of the matrices. Both methods are equally effective for qualitative analysis.
- Publication:
-
38th Meeting of Departments of Fluid Mechanics and Thermodynamics
- Pub Date:
- June 2019
- DOI:
- 10.1063/1.5114764
- Bibcode:
- 2019AIPC.2118c0036P