مطالعه روش‌های پایدارسازی و اصلاح مدل رتبه‎کاسته چرخش اقیانوسی شبه‌‌ژئوستروفیک تک لایه بر پایه روش تجزیه مود دینامیکی

نوع مقاله : مقاله پژوهشی

نویسندگان

آزمایشگاه پژوهشی توربولانس و دینامیک سیالات محاسباتی، گروه مهندسی مکانیک، دانشگاه قـم، قم، ایران

چکیده

از آنجا که روش‌های تحلیلی دارای دقت کم و دامنه کاربرد محدودی می‌باشد، لذا محققین به استفاده از روش‌های عددی روی آوردند. این دسته از روش‌ها به دلیل محدودیت سخت‌افزارهای کامپیوتری به ویژه برای مسائل ناپایا، همواره از سرعت و عملکرد خوبی برخوردار نیستند. از جمله راهکارهای موجود، استفاده از مدل‌‌های رتبه‌کاسته بوده که با کاستن از پیچیدگی‌های سیستم، سرعت آن افزوده می‌شود. در صورتی که سیستم دینامیکی غیرخطی و دارای پیچیدگی‎های خاص باشد حساسیت به چگونگی محاسبه ساختارهای غالب در دینامیک آن بیشتر شده و نیاز است مودهای آن از روش‌هایی با ویژگی منطبق با فیزیک مسئله محاسبه شوند. مدل‌های رتبه‌کاسته حاصل از تصویر‌سازی معادلات حاکم بر میدان جریان در فضای مودال، ممکن است به دلیل خطاهای ذاتی سیستم دینامیکی دقت بالایی در پیش‌بینی تغییرات زمانی میدان جریان نداشته باشند. به منظور بهبود پیش‌بینی زمانی مدل رتبه‎کاسته یک ترم اصلاح به معادله سیستم دینامیکی افزوده می‌شود. ویژگی مهم مدل رتبه‌کاسته جایگزین با رفع مشکل دقت آن، سرعت بالای محاسبات آن می‌باشد. بر این اساس، برای عدد رینولدز 450 و عدد راسبی 0/0036، داده‎های حل عددی مستقیم در یک بازه زمانی 450 دقیقه تولید شده‎اند. در حالی که با بهره‎گیری از مدل رتبه‌کاسته جایگزین، پیش‎بینی دینامیک میدان جریان در حدود 21 دقیقه زمان برده که اختلاف زمان محاسباتی قابل توجهی را نشان می‌دهد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

‌‌Studying Stabilization Methods for Calibrating a Reduced-Order Model of Single-Layer Quasi-Geostrophic Ocean Circulation Based on Dynamic Mode Decomposition

نویسندگان [English]

  • Mohammad Kazem Moayyedi
  • Zohreh Khakzari
CFD and Turbulence Research Lab., Department of Mechanical Engineering, University of Qom, Qom, Iran
چکیده [English]

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.

کلیدواژه‌ها [English]

  • Reduce Order Model
  • Dynamic Mode Decomposition
  • Quasiـgeostrophic Flow
  • Stabilization Method
  • Geophysical Flow

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نشریه مهندسی مکانیک امیرکبیر
دوره 57، شماره 7
مهر 1404
صفحه 939-962

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