Proper Orthogonal Decomposition (POD) coupled with Galerkin method is applied to the one-dimensional model of a tubular reactor with an external heat recycle for energy recovery, which exhibits complex oscillatory – periodic and chaotic – solutions. Particularly, the effect of the cooling medium temperature onto system dynamics is considered. The issue of the optimal construction of the POD basis is addressed by sampling of the chaotic orbits, with the aim of constructing a global basis for a reduced order model (ROM). To demonstrate that such orbits are the most appropriate – because they incorporate the maximum amount of information about the system behavior – the information entropy of the orbit is calculated. Sampling of the chaotic solutions allows for the determination of the POD basis which, when employed in the POD/Galerkin method, delivers accurate solutions, even for values of the parameter for which the model behavior is far from chaotic, i.e. periodic orbits or fixed points.

Model reduction by empirical spectral methods via sampling of chaotic orbits

Continillo G;
2010-01-01

Abstract

Proper Orthogonal Decomposition (POD) coupled with Galerkin method is applied to the one-dimensional model of a tubular reactor with an external heat recycle for energy recovery, which exhibits complex oscillatory – periodic and chaotic – solutions. Particularly, the effect of the cooling medium temperature onto system dynamics is considered. The issue of the optimal construction of the POD basis is addressed by sampling of the chaotic orbits, with the aim of constructing a global basis for a reduced order model (ROM). To demonstrate that such orbits are the most appropriate – because they incorporate the maximum amount of information about the system behavior – the information entropy of the orbit is calculated. Sampling of the chaotic solutions allows for the determination of the POD basis which, when employed in the POD/Galerkin method, delivers accurate solutions, even for values of the parameter for which the model behavior is far from chaotic, i.e. periodic orbits or fixed points.
2010
chemical reactor modeling; proper orthogonal decomposition; reduced order modeling; bifurcation analysis
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12070/12890
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 11
social impact