Journal article 735 views 532 downloads
Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
D. Xiao,
F. Fang,
A.G. Buchan,
C.C. Pain,
I.M. Navon,
J. Du,
G. Hu,
Dunhui Xiao 
Journal of Computational Physics, Volume: 263, Pages: 1 - 18
Swansea University Author:
Dunhui Xiao
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DOI (Published version): 10.1016/j.jcp.2014.01.011
Abstract
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...
| Published in: | Journal of Computational Physics |
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| ISSN: | 0021-9991 |
| Published: |
2014
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa46460 |
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| Abstract: |
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. |
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| Keywords: |
Non-linear model reduction, Empirical interpolation method, Petrov–Galerkin, Proper orthogonal decomposition, Navier–Stokes |
| College: |
Faculty of Science and Engineering |
| Start Page: |
1 |
| End Page: |
18 |