Studying Stabilization and Calibration Methods of the reduced-order Model of quasi-geostrophic single-layer ocean circulation based on the dynamic mode decomposition

Document Type : Research Article

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CFD and Turbulence Research Lab., Department of Mechanical Engineering, University of Qom, Qom, Iran

Abstract

Since analytical methods have low accuracy and limited applicability, researchers have turned to numerical methods. However, due to hardware limitations, especially for unsteady problems—these methods do not always offer satisfactory speed and performance. One existing solution is the use of reduced-order models (ROMs), which increase computational speed by reducing system complexity. If the dynamical system is nonlinear and exhibits specific complexities, the sensitivity to the calculation of its dominant structures becomes more critical, requiring modes to be computed using methods aligned with the problem's physics.

ROMs obtained by projecting the governing flow-field equations onto a modal space may lack high accuracy in predicting temporal flow-field variations due to inherent dynamical system errors. To improve the temporal prediction of the reduced-order model, a correction term is added to the dynamical system equation. A key advantage of the improved ROM is its high computational speed while maintaining accuracy. Accordingly, for a Reynolds number of 450 and a Rossby number of 0.0036, direct numerical simulation (DNS) data were generated over a 450-minute time interval. In contrast, using the improved ROM, predicting the flow-field dynamics took only about 21 minutes, demonstrating a significant computational time difference.

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Amirkabir Journal of Mechanical Engineering
Volume 57, Issue 7
October 2025
Pages 939-962

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