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Non-intrusive reduced order modelling of the Navier–Stokes equations

Dunhui Xiao Orcid Logo, F. Fang, A.G. Buchan, C.C. Pain, I.M. Navon, A. Muggeridge

Computer Methods in Applied Mechanics and Engineering, Volume: 293, Pages: 522 - 541

Swansea University Author: Dunhui Xiao Orcid Logo

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DOI (Published version): 10.1016/j.cma.2015.05.015

Abstract

This article presents two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of these methods resides in how the reduced order models are formed, that is, how the coefficients of the POD expansions are calculat...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa46458
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spelling 2020-12-18T11:36:55.2629007 v2 46458 2018-12-06 Non-intrusive reduced order modelling of the Navier–Stokes equations 62c69b98cbcdc9142622d4f398fdab97 0000-0003-2461-523X Dunhui Xiao Dunhui Xiao true false 2018-12-06 AERO This article presents two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of these methods resides in how the reduced order models are formed, that is, how the coefficients of the POD expansions are calculated. Rather than taking a standard approach of projecting the underlying equations onto the reduced space through a Galerkin projection, here two different techniques are employed. The first method applies a second order Taylor series to calculate the POD coefficients at each time step from the POD coefficients at earlier time steps. The second method uses a Smolyak sparse grid collocation method to calculate the POD coefficients, where again the coefficients at earlier time steps are used as the inputs. The advantage of both approaches are that they are non-intrusive and so do not require modifications to a system code; they are therefore very easy to implement. They also provide accurate solutions for modelling flow problems, and this has been demonstrated by the simulation of flows past a cylinder and within a gyre. It is demonstrated that accuracy relative to the high fidelity model is maintained whilst CPU times are reduced by several orders of magnitude in comparison to high fidelity models. Journal Article Computer Methods in Applied Mechanics and Engineering 293 522 541 0045-7825 Non-intrusive model reduction, Smolyak sparse grid, Taylor series, POD, Navier–Stokes 15 8 2015 2015-08-15 10.1016/j.cma.2015.05.015 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2020-12-18T11:36:55.2629007 2018-12-06T14:52:24.3053589 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Dunhui Xiao 0000-0003-2461-523X 1 F. Fang 2 A.G. Buchan 3 C.C. Pain 4 I.M. Navon 5 A. Muggeridge 6 0046458-13122018163508.pdf smolyak.pdf 2018-12-13T16:35:08.3500000 Output 3136919 application/pdf Submitted Manuscript Under Review true 2018-12-13T00:00:00.0000000 true eng
title Non-intrusive reduced order modelling of the Navier–Stokes equations
spellingShingle Non-intrusive reduced order modelling of the Navier–Stokes equations
Dunhui Xiao
title_short Non-intrusive reduced order modelling of the Navier–Stokes equations
title_full Non-intrusive reduced order modelling of the Navier–Stokes equations
title_fullStr Non-intrusive reduced order modelling of the Navier–Stokes equations
title_full_unstemmed Non-intrusive reduced order modelling of the Navier–Stokes equations
title_sort Non-intrusive reduced order modelling of the Navier–Stokes equations
author_id_str_mv 62c69b98cbcdc9142622d4f398fdab97
author_id_fullname_str_mv 62c69b98cbcdc9142622d4f398fdab97_***_Dunhui Xiao
author Dunhui Xiao
author2 Dunhui Xiao
F. Fang
A.G. Buchan
C.C. Pain
I.M. Navon
A. Muggeridge
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 293
container_start_page 522
publishDate 2015
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2015.05.015
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 two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of these methods resides in how the reduced order models are formed, that is, how the coefficients of the POD expansions are calculated. Rather than taking a standard approach of projecting the underlying equations onto the reduced space through a Galerkin projection, here two different techniques are employed. The first method applies a second order Taylor series to calculate the POD coefficients at each time step from the POD coefficients at earlier time steps. The second method uses a Smolyak sparse grid collocation method to calculate the POD coefficients, where again the coefficients at earlier time steps are used as the inputs. The advantage of both approaches are that they are non-intrusive and so do not require modifications to a system code; they are therefore very easy to implement. They also provide accurate solutions for modelling flow problems, and this has been demonstrated by the simulation of flows past a cylinder and within a gyre. It is demonstrated that accuracy relative to the high fidelity model is maintained whilst CPU times are reduced by several orders of magnitude in comparison to high fidelity models.
published_date 2015-08-15T03:58:02Z
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score 11.013371

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