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Proper orthogonal decomposition (which is also known as the Karhunen-Loève decomposition) is a reduction method that is used to obtain low-dimensional dynamic models of distributed parameter systems. Roughly speaking, proper orthogonal decomposition (POD) is an optimal technique of finding a basis that spans an ensemble of data, collected from an experiment or a numerical simulation of a dynamical system, in the sense that when these basis functions are used in a Galerkin procedure, they will yield a finite-dimensional system with the smallest possible degrees of freedom. Thus, the technique is well suited to treat optimal control and parameter estimation of distributed parameter systems. In this paper, the method is applied to analyze the complex flow phenomenon in a horizontal chemical vapor deposition (CVD) reactor. In particular, we show that POD can be used to efficiently approximate solutions to the compressible viscous flows coupled with the energy and the species equations. In addition, we also examine the feasibility and efficiency of the POD method in the optimal control of the source vapors to obtain the most uniform deposition profile at the maximum growth rate. Finally, issues concerning the implementation of the method and numerical calculations are discussed.
Ly et al. (Sun,) studied this question.