A method to generate computationally efficient reduced order models

Alonso, D. and Velázquez, A. and Vega de Prada, José Manuel (2009). A method to generate computationally efficient reduced order models. "International Journal of Heat and Mass Transfer", v. 198 ; pp. 2683-2691. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2009.03.012.

Description

Title: A method to generate computationally efficient reduced order models
Author/s:
  • Alonso, D.
  • Velázquez, A.
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: International Journal of Heat and Mass Transfer
Date: July 2009
Volume: 198
Subjects:
Freetext Keywords: Reduced order model; Proper Orthogonal Decomposition; Incompressible nonisothermal flow
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A new method is presented to generate reduced order models (ROMs) in Fluid Dynamics problems. The method is based on the expansion of the flow variables on a Proper Orthogonal Decomposition (POD) basis, calculated from a limited number of snapshots, which are obtained via Computational Fluid Dynamics (CFD). Then, the POD-mode amplitudes are calculated as minimizers of a properly defined overall residual of the equations and boundary conditions. The residual can be calculated using only a limited number of points in the flow field, which can be scattered either all over the whole computational domain or over a smaller projection window. This means that the process is both computationally efficient (reconstructed flow fields require less than 1% of the time needed to compute a full CFD solution) and flexible (the projection window can avoid regions of large localized CFD errors). Also, various definitions of the residual are briefly discussed, along with the number and distribution of snapshots, the number of retained modes, and the effect of CFD errors, to conclude that the method is numerically robust. This is because the results are largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms. Thus, the method is amenable for practical engineering applications.

More information

Item ID: 6106
DC Identifier: http://oa.upm.es/6106/
OAI Identifier: oai:oa.upm.es:6106
DOI: 10.1016/j.cma.2009.03.012
Official URL: http://www.elsevier.com/locate/cma
Deposited by: Memoria de Investigacion 2
Deposited on: 21 Feb 2011 10:30
Last Modified: 20 Apr 2016 14:44
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