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Paper Information

Journal:   JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN)   NOVEMBER 2007 , Volume 41 , Number 4 (106); Page(s) 401 To 413.
 
Paper: 

USING OF THE POD METHOD IN EXTRACTION OF THE COHERENT STRUCTURES OF A STATISTICALLY HOMOGENOUS TURBULENT FIELD

 
 
Author(s):  SABET GHADAM F., EFTEKHAR YAZDI M.*, ESFAHANIAN V.
 
* SCIENCE AND RESEARCH BRANCH ISLAMIC AZAD UNIVERSITY, I.R. IRAN
 
Abstract: 

Capability of the Proper Orthogonal Decomposition (POD) method in extraction of the coherent structures from a spatio-temporal chaotic field is assessed in this paper. As the chaotic field, an ensemble of 40 snapshots, obtained from Direct Numerical Simulation (DNS) of the Kuramoto-Sivashinsky (KS) equation, has been used. Contrary to the usual methods, where the ergodicity of the field is needed, the ensemble members are generated directly by disturbing the initial conditions in a random fashion. The POD eigenvalues and eigenmodes are extracted, using the POD/SVD technique and an ensemble averaging process is performed on the resulting modes, which are used in reconstruction of the field. The resulted mean field is compared with the Fourier mean field as well as the original (instantaneous) field. The results strictly have shown presence of non-coherent parts in the POD reconstructed field, which can be interpreted as the POD weakness in the filtering of the random part of the field. On the other hand, the ensemble averaged POD modes had obvious superiority, in comparison with the mean Fourier modes, in tracing of the mean behavior of the field and the mean temporal gradients. As a consequence, use of the ensemble averaging in the POD modes can be suggested, at least in some spatio-temporal the fields with dominant coherent structures.

 
Keyword(s): ENSEMBLE AVERAGING, PROPER ORTHOGONAL DECOMPOSITION, COHERENT STRUCTURES, SPATIO, TEMPORAL CHAOS, SINGULAR VALUE DECOMPOSITION, GALERKIN METHOD
 
References: 
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