期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 263, 期 -, 页码 1-18出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.01.011
关键词
Non-linear model reduction; Empirical interpolation method; Petrov-Galerkin; Proper orthogonal decomposition; Navier-Stokes
资金
- UK's Natural Environment Research Council [NER/A/S/2003/00595, NE/C52101X/1, NE/C51829X/1]
- Engineering and Physical Sciences Research Council [GR/R60898, EP/I00405X/1, EP/J002011/1]
- Imperial College High Performance Computing Service
- NSF/CMG [ATM-0931198]
- China Scholarship Council
- EPSRC [EP/J002011/1]
- Div Atmospheric & Geospace Sciences
- Directorate For Geosciences [0931198] Funding Source: National Science Foundation
- Engineering and Physical Sciences Research Council [EP/I00405X/1, EP/J002011/1] Funding Source: researchfish
- Natural Environment Research Council [NE/C52101X/1, NE/J015938/1, NER/A/S/2003/00595, NE/C51829X/1] Funding Source: researchfish
- EPSRC [EP/J002011/1, EP/I00405X/1] Funding Source: UKRI
- NERC [NE/J015938/1] Funding Source: UKRI
This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov-Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions. A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier-Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy. (C) 2014 Elsevier Inc. All rights reserved.
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