Reduced-order modeling based on POD of a parabolized Navier-Stokes equation model I: Forward model

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Title:	Reduced-order modeling based on POD of a parabolized Navier-Stokes equation model I: Forward model
Authors:	吳劍鋒;Du, J.;Navon, I.M.;Steward, J.L.;Alekseev, A.K.;Luo, Z.
Contributors:	地球科學學院大氣科學學系
Keywords:	correlation coefficient;H1 norm POD calibration;high Reynolds number;optimal dissipation coefficient;parabolized Navier-Stokes (PNS);proper orthogonal decomposition (POD)
Date:	2012-05-30
Issue Date:	2026-04-21 13:35:41 (UTC+8)
Publisher:	John Wiley and Sons Ltd;Chichester, UK: John Wiley & Sons, Ltd
Abstract:	摘要： SUMMARYA proper orthogonal decomposition (POD)‐based reduced‐order model of the parabolized Navier–Stokes (PNS) equations is derived in this article. A space‐marching finite difference method with time relaxation is used to obtain the solution of this problem, from which snapshots are obtained to generate the POD basis functions used to construct the reduced‐order model. In order to improve the accuracy and the stability of the reduced‐order model in the presence of a high Reynolds number, we applied a Sobolev H1 norm calibration to the POD construction process. Finally, some numerical tests with a high‐fidelity model as well as the POD reduced‐order model were carried out to demonstrate the efficiency and the accuracy of the reduced‐order model for solving the PNS equations compared with the full PNS model. Different inflow conditions and different selections of snapshots were experimented to test the POD reduction technique. The efficiency of the H1 norm POD calibration is illustrated for the PNS model with increasingly higher Reynolds numbers, along with the optimal dissipation coefficient derivation, yielding the best root mean square error and correlation coefficient between the full and reduced‐order PNS models. Copyright © 2011 John Wiley & Sons, Ltd. 其他題名： Int. J. Numer. Meth. Fluids 出版者： Chichester, UK: John Wiley & Sons, Ltd 出版日期： 2012-05-30 出處： International Journal for Numerical Methods in Fluids, 2012-05, Vol.69 (3), p.710-730 資源來源： Wiley Online Library 版權： Copyright © 2011 John Wiley & Sons, Ltd. 識別號： ISSN: 0271-2091 識別號： EISSN: 1097-0363 識別號： DOI: 10.1002/fld.2606
Appears in Collections:	[Department of Atmospheric Sciences] journal & Dissertation

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