zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
76M25Other numerical methods (fluid mechanics)
76V05Interacting phases (fluid mechanics)
65K10Optimization techniques (numerical methods)
76M35Stochastic analysis (fluid mechanics)
76N25Flow control and optimization (compressible fluids and gas dynamics)