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A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

Dunhui Xiao Orcid Logo, F. Fang, C.C. Pain, I.M. Navon

Computer Methods in Applied Mechanics and Engineering, Volume: 317, Pages: 868 - 889

Swansea University Author: Dunhui Xiao Orcid Logo

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DOI (Published version): 10.1016/j.cma.2016.12.033

Abstract

A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced orde...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa46451
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spelling 2022-09-27T16:57:38.8401632 v2 46451 2018-12-06 A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications 62c69b98cbcdc9142622d4f398fdab97 0000-0003-2461-523X Dunhui Xiao Dunhui Xiao true false 2018-12-06 AERO A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 [41,42]) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.The new P-NIROM technique has been applied to parameterized Navier–Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out. Journal Article Computer Methods in Applied Mechanics and Engineering 317 868 889 0045-7825 Parameterized, Non-intrusive ROM, PDE, RBF, POD, Smolyak sparse grid 15 4 2017 2017-04-15 10.1016/j.cma.2016.12.033 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2022-09-27T16:57:38.8401632 2018-12-06T14:52:05.9924331 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 C.C. Pain 3 I.M. Navon 4 0046451-13122018164452.pdf variable-para.pdf 2018-12-13T16:44:52.8770000 Output 1484943 application/pdf Accepted Manuscript true 2018-12-13T00:00:00.0000000 true eng
title A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
spellingShingle A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
Dunhui Xiao
title_short A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
title_full A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
title_fullStr A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
title_full_unstemmed A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
title_sort A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications
author_id_str_mv 62c69b98cbcdc9142622d4f398fdab97
author_id_fullname_str_mv 62c69b98cbcdc9142622d4f398fdab97_***_Dunhui Xiao
author Dunhui Xiao
author2 Dunhui Xiao
F. Fang
C.C. Pain
I.M. Navon
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 317
container_start_page 868
publishDate 2017
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2016.12.033
college_str Faculty of Science and Engineering
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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
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description A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 [41,42]) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space.The new P-NIROM technique has been applied to parameterized Navier–Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out.
published_date 2017-04-15T03:58:02Z
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