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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 Orcid Logo

Journal of Computational Physics, Volume: 263, Pages: 1 - 18

Swansea University Author: Dunhui Xiao Orcid Logo

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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...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa46460
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spelling 2020-09-28T12:26:03.5885430 v2 46460 2018-12-06 Non-linear model reduction for the Navier–Stokes equations using residual DEIM method 62c69b98cbcdc9142622d4f398fdab97 0000-0003-2461-523X Dunhui Xiao Dunhui Xiao true false 2018-12-06 AERO 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. Journal Article Journal of Computational Physics 263 1 18 0021-9991 Non-linear model reduction, Empirical interpolation method, Petrov–Galerkin, Proper orthogonal decomposition, Navier–Stokes 15 4 2014 2014-04-15 10.1016/j.jcp.2014.01.011 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2020-09-28T12:26:03.5885430 2018-12-06T14:52:30.3004731 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering D. Xiao 1 F. Fang 2 A.G. Buchan 3 C.C. Pain 4 I.M. Navon 5 J. Du 6 G. Hu 7 Dunhui Xiao 0000-0003-2461-523X 8 0046460-13122018163111.pdf deim.pdf 2018-12-13T16:31:11.4170000 Output 2286682 application/pdf Accepted Manuscript true 2018-12-13T00:00:00.0000000 true eng
title Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
spellingShingle Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
Dunhui Xiao
title_short Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
title_full Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
title_fullStr Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
title_full_unstemmed Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
title_sort Non-linear model reduction for the Navier–Stokes equations using residual DEIM method
author_id_str_mv 62c69b98cbcdc9142622d4f398fdab97
author_id_fullname_str_mv 62c69b98cbcdc9142622d4f398fdab97_***_Dunhui Xiao
author Dunhui Xiao
author2 D. Xiao
F. Fang
A.G. Buchan
C.C. Pain
I.M. Navon
J. Du
G. Hu
Dunhui Xiao
format Journal article
container_title Journal of Computational Physics
container_volume 263
container_start_page 1
publishDate 2014
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2014.01.011
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
active_str 0
description 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.
published_date 2014-04-15T03:58:03Z
_version_ 1763752944002400256
score 11.036706

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