Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes
In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not...
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| Format: | Article |
| Language: | English |
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Shahid Chamran University of Ahvaz
2019-01-01
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| Series: | Journal of Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | http://jacm.scu.ac.ir/article_13518_5b73e37210ebbc234ad3cdd454b583b8.pdf |
| _version_ | 1818189048510939136 |
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| author | Mohammad Kazem Moayyedi |
| author_facet | Mohammad Kazem Moayyedi |
| author_sort | Mohammad Kazem Moayyedi |
| collection | DOAJ |
| description | In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynamical system was improved using a calibration method based on a least-square optimization process. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least- square procedure is a combination of POD method and the solution of an optimization problem. The obtained model can predict accurate time variations of flow field with high speed. For long time periods, the calibration term can be computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has recently been proposed by the authors. The results obtained from the calibrated reduced order model show close agreements to the benchmark DNS data, proving high accuracy of our model. |
| first_indexed | 2024-12-11T23:36:37Z |
| format | Article |
| id | doaj.art-339e2f5792a1447791f2d86964a70e7a |
| institution | Directory Open Access Journal |
| issn | 2383-4536 2383-4536 |
| language | English |
| last_indexed | 2024-12-11T23:36:37Z |
| publishDate | 2019-01-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-339e2f5792a1447791f2d86964a70e7a2022-12-22T00:45:51ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362019-01-015111210.22055/jacm.2018.24099.117113518Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier ModesMohammad Kazem Moayyedi0Department of Mechanical Eng., School of Engineering, University of Qom, IranIn this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynamical system was improved using a calibration method based on a least-square optimization process. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least- square procedure is a combination of POD method and the solution of an optimization problem. The obtained model can predict accurate time variations of flow field with high speed. For long time periods, the calibration term can be computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has recently been proposed by the authors. The results obtained from the calibrated reduced order model show close agreements to the benchmark DNS data, proving high accuracy of our model.http://jacm.scu.ac.ir/article_13518_5b73e37210ebbc234ad3cdd454b583b8.pdfProper orthogonal decompositionGalerkin projectionReduced order modelCalibration strategyIncompressible flowFourier modes |
| spellingShingle | Mohammad Kazem Moayyedi Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes Journal of Applied and Computational Mechanics Proper orthogonal decomposition Galerkin projection Reduced order model Calibration strategy Incompressible flow Fourier modes |
| title | Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes |
| title_full | Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes |
| title_fullStr | Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes |
| title_full_unstemmed | Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes |
| title_short | Extension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes |
| title_sort | extension ability of reduced order model of unsteady incompressible flows using a combination of pod and fourier modes |
| topic | Proper orthogonal decomposition Galerkin projection Reduced order model Calibration strategy Incompressible flow Fourier modes |
| url | http://jacm.scu.ac.ir/article_13518_5b73e37210ebbc234ad3cdd454b583b8.pdf |
| work_keys_str_mv | AT mohammadkazemmoayyedi extensionabilityofreducedordermodelofunsteadyincompressibleflowsusingacombinationofpodandfouriermodes |