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**Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor.**
*(English)*
Zbl 1146.76631

Summary: 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 which 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 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 examined the feasibility and efficiency of 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.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76V05 | Reaction effects in flows |

65K10 | Numerical optimization and variational techniques |

76M35 | Stochastic analysis applied to problems in fluid mechanics |

76N25 | Flow control and optimization for compressible fluids and gas dynamics |