Proper Orthogonal Decomposition

For POD, the Karhunen-Loeve procedure decomposes a set of distributions or functions into an optimal, orthonormal set of eigenfunctions able to represent the distributions of interest [4-6]. These eigenfunctions can offer highly efficient representations of important variables and structures in combustion systems. Furthermore, the potential for a rednced-order model utilizing these basis functions can be evaluated from the associated eigenvalue spectrum derived from decomposition. 

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Tabib, M.V. and Joshi, J.B. (2008) Analysis of dominant flow stmctures and their flow dynamics in chemical process equipment using snapshot proper orthogonal decomposition technique. Chem. Eng. Sci., 63 (14), 3695-3715. 

Figure 15 Linking models at various scales using ROMs and deriving lower scale specifications through an inverse optimization formulation. The ROM included at each scale is a reduced representation of the model at the scale below that could range from a set of parameters such as, for example, elementary rate constants to complex models derived from proper orthogonal decomposition and perhaps even to the full lower scale model. This is symbolized by coloring the ROM box with the same color as that of the box representing the adjacent lower scale model.

It is noted that during later stages of b3rpass transition caused by con-vecting vortex in the freestream, large coherent vortices are formed inside the shear layer. Such coherent structures have been characterized by Proper orthogonal Decomposition (POD) - a method that was originally developed... 

Sengupta, T.K. and De, S (2004). Proper orthogonal decomposition of direct numerical simulation data of by-pass transition. Comput. Struct. 82, 2693-2703. 

Prof. Roger Shaw (University of California, Davis) describes new developments in the analysis of the turbulent velocity fields in vegetative canopies, using proper orthogonal decomposition (a technique for eddy identification first introduced by J. Lumley in 1967). He argues that this technique complements the previous studies based on statistical models and large eddy simulation numerical methods. 

Proper orthogonal decomposition has been used to analyze ensembles of concentration and vorticity magnitude distributions in forced reacting rectangular jets... 

A RECURSIVE PROPER ORTHOGONAL DECOMPOSITION ALGORITHM FOR FLOW CONTROL PROBLEMS... 

Sahoo, D., S. Park, D. Wee, A. M. Annaswamy, and A. F. Ghoniem. 2002. A recursive proper orthogonal decomposition algorithm for flow control problems. Adaptive Control Laboratory, MIT. Technical Report 0208. 

For microfluidic systems with strong nonlinear effects, proper orthogonal decomposition (POD)-based MOR (also called Karhunen-Loeve decomposition) is employed to locate the low-dimensional subspace for modeling. POD is... 

Proper Orthogonal Decomposition is a technique that extracts the orthogonal basis function spanning the reduced subspace using an ensemble of data from experiments or numerical simulation of the original full systems. 

Danby, S.J., Echekki, T. Proper orthogonal decomposition analysis of autoignition simulation data of nonhomogeneous hydrogen-air mixtures. Combust. Flame 144, 126-138 (2006)... 

Frouzakis, C.E., Kevrekidis, Y.G., Lee, J., Boulouchos, K., Alonso, A.A. Proper orthogonal decomposition of direct numerical simulation data data reduction and observer construction. Proc. Combus. Inst. 28, 75-81 (2(KX))... 

Sportisse, B., Djouad, R. Use of proper orthogonal decompositions for the reduction of atmospheric chemistry. J. Geophys. Res. Atmos. 112(D06303) (2007)... 

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