یک روش بدون شبکه موضعی برای شبیه سازی عددی رشد دندریتی کریستال

نویسنده
محمد ایلاتی
دانشگاه صنعتی سهند تبریز
چکیده
فرآیندهای انجماد در طیف گسترده‌ای از روش‌های ساخت و تولید، از متالورژی گرفته تا فرآوری مواد غذایی، وجود دارند. در سال‌های اخیر، مدل‌های میدان-فاز به طور فزاینده‌ای برای شبیه‌سازی و پیش‌بینی شکل‌گیری و تکامل ریزساختار مواد و سینتیک سطحی تغییر فاز مورد استفاده قرار گرفته‌اند. در این مقاله، مدل میدان-فاز انجماد را برای شبیه‌سازی عددی رشد دندریتی کریستال که در طی ریخته‌گری فلزات و آلیاژها بر اساس مدل کوبایاشی رخ می‌دهد، مطالعه می‌کنیم. ابتدا با استفاده از روش تفاضلات متناهی، این مدل را در جهت زمانی گسسته‌سازی می‌کنیم. سپس روش بدون شبکه کریجینگ متحرک را برای گسسته‌سازی مدل در راستای متغییر مکان اعمال می‌کنیم. روابط کیفی بین اشکال کریستال و پارامترهای مدل، در شبیه‌سازی عددی مدل مورد مطالعه قرار می‌گیرند. روش کریجینگ متحرک یک روش کاملا بدون شبکه است که در آن تابع مجهول را می توان به صورت موضعی تقریب زد که این منجر به تنک شدن ماتریس ضریب می‌شود. با توجه به مزایای قابل توجه روش‌های بدون شبکه، این روش را می‌توان جایگزینی بر روش‌های مبتنی بر شبکه‌ای در نظر گرفت که تا قبل از این برای شبیه‌‍سازی این مدل‌ها به کار برده شده است.
کلیدواژه‌ها
رشد دندریتی کریستال
انجماد دندریتی
انجماد فلز خالص
تکامل ریزساختار
مدل میدان-فاز کوبایاشی
روش بدون شبکه
تقریب کریجینگ متحرک

عنوان مقاله English

A local meshless method for numerical simulation of dendritic crystal growth

نویسنده English

Mohammad Ilati
Sahand University of Technology
چکیده English

Solidification processes are present in a wide range of manufacturing methods and applications, from metallurgy to food processing. In recent years, Phase-Field models have been increasingly used to simulate and predict the formation and evolution of material microstructure and phase change interfacial kinetics. In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys based on the kobayashi model. At first, the kobayashi phase-field model, which describes the solidification of a pure material from an undercooled melt, is introduced in detail. In discretization process of this model, the time derivatives are approximated via finite difference method. Then the local meshless moving Kriging method is applied for discretization of the model in space direction. The moving Kriging method is a truly meshless method in which the unknown function can be approximated locally, and this leads to the sparsity of the coefficient matrix. As the shape functions possess the Kronecker delta function property, boundary conditions can be implemented without any difficulties. The model is simulated for various values of it’s parameters. Numerical simulations illustrate the applicability and effectiveness of the proposed method. As a consequence, it is found that the method is very efficient and accurate for phase-field models compared with those of other conventional methods. Therefore, this method can be considered as an attractive alternative to existing mesh-based methods in solving phase-field models.

کلیدواژه‌ها English

Dendritic crystal growth
Dendritic solidification
Pure metal solidification
Microstructure evolution
kobayashi phase-field model
meshless method
Moving Kriging approximation
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