توسعة مدل رتبه‌کاسته پارامتری و وابسته به زمان برای مسائل نفوذ و نفوذ-جابجایی بر مبنای روش تجزیه متعامد بهینه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 بخش مهندسی مکانیک، دانشگاه قم

2 گروه مهندسی مکانیک، دانشگاه قم

چکیده

مدلسازی و شبیه‌سازی عددی به عنوان یک ابزار مناسب جهت تحلیل رفتار دینامیکی سیستم‌های مهندسی به‌شمار‌می‎رود. استفاده از این روش‌ها، به ویژه برای مسائل ناپایا، معمولا نیازمند صرف زمان زیادی است. به همین دلیل، توسعه روش‌هایی با سرعت بالاتر و افزایش راندمان محاسباتی همواره به عنوان یک موضوع مهم مورد توجه پژوهشگران بوده‌است. روش کاهش مرتبه روشی است که در سالیان اخیر برای کاهش زمان محاسبات به طور گسترده‌ای مورد استفاده قرار گرفته‌است. در این روش، با کاستن از قیود سیستم، بدون تغییر در ویژگی‌های ذاتی مسئله، سرعت محاسبات به طرز چشم‎گیری افزایش می‌یابد. در این پژوهش، با بهره‌گیری از مفاهیم پایه‌ای سیستم‌های دینامیکی، دو مسئله نفوذ حرارتی و نفوذ-جابجایی به صورت مستقل مورد بررسی قرار گرفته و با استفاده از روش تجزیه متعامد بهینه، الگوی رتبه کاسته برای معادلات حاکم بر این پدیده‌ها ایجاد شده‌است. بر همین اساس، برای هر یک از مسائل، مبتنی بر تصویرسازی معادله حاکم در فضای برداری مودهای میدان، با استفاده از مودهای پرانرژی‌تر، مدل رتبه کاسته با توجه به ویژگی پایه‌های متعامد به دست می‌آید. مدل به‌دست‌آمده به منظور شبیه‌سازی تغییرات زمانی فرآیند، به درستی می‌تواند جایگزین معادلة اصلی شده و با دقت بسیار مناسبی رفتار سیستم موردنظر را پیش‌بینی کند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Development of parametric and time dependent reduced order model for diffusion and convection-diffusion problems based on proper orthogonal decomposition method

نویسندگان [English]

  • Mohammad Kazem Moayyedi 1
  • Farshad Sabaghzadeghan 2
1 Department of Mechanical Engineering, University of Qom
2 Department of Mechanical Eng. Univ. Qom
چکیده [English]

Simulation and numerical analysis of physical phenomena, especially for unstable problems, due to dependency of the numerical algorithms on the computer hardware to the increasing of the number of computational nodes, is the most important feature of their solutions. For this reason, increases the number of computations then increased computational costs. The order reduction method has been widely used in recent years to reduce computational time. In this way, by reducing the constraints of the system, without changing the inherent features of the problem, the computational efficiency will dramatically increase. In this study, using the basic concepts of dynamical systems, two problems of thermal diffusion and convection-diffusion are investigated independently and by using the proper orthogonal analysis method, a reduced order model is established for the equations governing these phenomena created. Accordingly, for each of the problems, based on the projection of the governing equation in the vector space of modes, by using more energetic modes, a reduced order model is obtained with respect to the orthogonal basis properties. The model obtained in order to simulate the process time variations can properly replace the original equation and predict the behavior of the system with very good accuracy.

کلیدواژه‌ها [English]

  • Proper Orthogonal Decomposition
  • Diffusion Equation
  • Convection-Diffusion equation
  • Reduced Order Model
  • Surrogate model
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