نویسندگان
1 دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان
2 گروه حرارت و سیالات، دانشکده مهندسی مکانیک، دانشگاه کاشان، کاشان
چکیده
روش بولتزمن شبکه‌ای یکی از زیرشاخه‌های دینامیک سیالات محاسباتی است. با وجود اینکه این روش زمینه ریاضی پیچیده‌ای دارد، روابط نهایی نسبتا ساده‌ای بر آن حکم‌فرماست، از این‌رو برنامه رایانه‌ای ساده‌تری نسبت به روشهای مرسوم دینامیک سیالات محاسباتی نیاز دارد. با توجه به ویژگی‌های روش بولتزمن شبکه‌ای برای پردازش موازی، این روش به‌‌عنوان روشی کارامد برای شبیه‌سازی جریان سیال در هندسه‌های پیچیده، که نیاز به حافظه محاسباتی زیادی دارند، در نظر گرفته می‌شود. به‌خاطر وجود مرزهای منحنی در هندسه‌های پیچیده، یافتن شرط مرزی مناسب در روش بولتزمن شبکه‌ای اجتناب‌ناپذیر است. برای این منظور پژوهش‌های زیادی انجام شده و شرایط مرزی مختلفی پیشنهاد شده است. در پژوهش حاضر، ابتدا تعدادی از شرایط مرزی منحنی مرور و سپس شرط مرزی ساده‌شده‌ای پیشنهاد شده است. برنامه‌ای به زبان فرترن، بر مبنای روش بولتزمن شبکه‌ای تهیه شده، که شرط مرزی پیشنهادی به‌همراه چند شرط مرزی دیگر در آن اعمال شده است. برای بررسی صحت و دقت شرط مرزی پیشنهادی، جریان داخل حفره دوبعدی شبیه‌سازی و با نتایج عددی موجود مقایسه شده است. تطابق نتایج حاصل از پژوهش حاضر با نتایج پژوهشگران قبلی، صحت برنامه تهیه شده را تأیید می‌کند. همچنین دو جریان سیال، یکی جریان اطراف استوانه ساکن در کانالی دوبعدی و دیگری جریان بین دو استوانه ساکن و متحرک، شبیه‌سازی شده‌اند. نتایج شبیه‌سازی‌ها با شرط مرزی پیشنهادی، به‌همراه نتایج شرایط مرزی قبلی، با نتایج در دسترس مقایسه شده است. مقایسه‌ها نشان می‌دهند که جواب‌هایی با دقت مناسب توسط شرط مرزی پیشنهادی به‌دست آمده است.
کلیدواژه‌ها
عنوان مقاله [English]
A Simplified Curved Boundary Condition in Stationary/Moving Boundaries for the Lattice Boltzmann Method
نویسندگان [English]
- S.M. Naghavi 1
- G.A. Sheikhzadeh 2
چکیده [English]
Lattice Boltzmann method is one of computational fluid dynamic subdivisions. Despite complicated mathematics involved in its background, end simple relations dominate on it; so in comparison to the conventional computational fluid dynamic methods, simpler computer programs are needed. Due to its characteristics for parallel programming, this method is considered efficient for the simulation of complex geometry flows, in which a large amount of computational memories is needed. Because of the curved boundaries in the complex geometries, detecting the proper curved boundary condition is unavoidable for the lattice Boltzmann method. For this purpose, more works have been done, and different curved boundary conditions have been proposed. At the present work, first, some curved boundary conditions have been reviewed; then a simplified curved boundary condition is proposed. A computer program based on the lattice Boltzmann method, in FORTRAN language, has been prepared; in this program, the boundary condition along with some others applied on it is proposed. To verify the accuracy and correctness of the proposed boundary condition, 2D cavity flow has been simulated and compared to the available numerical results. Adaptation of the achieved results with those of previous researchers verifies the prepared program correctness. Also, two fluid flows have been simulated, a flow around a stationary cylinder in a 2D channel and one between two stationary and moving cylinders. The results of simulations with the proposed boundary condition, along with the previous boundary conditions, have been compared to the available results. Comparisons demonstrate that solutions with proper accuracy could be obtained by the proposed boundary condition.
کلیدواژه‌ها [English]
- Lattice Boltzmann method
- boundary condition
- Bounce back
- Incompressible model
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