شبیه‌سازی حرکت جسم جامد در یک سیال نیوتونی با استفاده از یک روش مرزمستور شبه‌طیفی موازی‌شده تاوایی‌مبنا

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه هوافضا- دانشگاه آزاد اسلامی-واحد علوم و تحقیقات

2 عضو هیئت علمی-گروه هوافضا-دانشگاه آزاد اسلامی-واحد علوم و تحقیقات- تهران

چکیده

در مقاله حاضر روشی عددی برای شبیه‌سازی اندرکنش‌ دوسویه یک جسم جامد صلب با یک سیال تراکم‌ناپذیر نیوتونی در یک پیکربندی دوبعدی تشریح می‌شود. در این روش مرزهای جامد متحرک توسط توابع پایه شعاعی مدل شده، به یک حل‌گر مرز مستور شبه­طیفی معادلات ناویر-استوکس در شکل تاوایی-سرعت اعمال شده‌اند. در ابتدای هر گام زمانی سرعت­هایی بقایی که شرایط مرز مستور متحرک را نیز ارضاء می­کنند، به همراه یک میدان تاوایی اصلاح شده، مستقیماً و بدون نیاز به تعریف یک تابع نیروی خارجی برای اصلاح جمله‌های جابجایی و پخش، مورد استفاده قرار می‌گیرند. با توجه به استقلال شرط‌مرزی‌های مؤلفه‌های سرعت از یکدیگر، در هر گام زمانی، معادلات پواسن سرعت به‌صورت موازی حل شده‌اند. دینامیک جسم جامد با دقت مرتبه دوم زمانی دنبال می‌شود که در آن نیروهای حاصل از اندرکنش مرز جامد و سیال از یک روش انتگرالی بر پایه تاوایی محاسبه شده‌اند. انتگرال­گیری زمانی از یک روش رانج کوتای مرتبه سوم موازی‌شده انجام شده است. استفاده از حل‌گر سریع شبه‌طیفی به‌همراه موازی‌سازی حل معادلات پواسون سرعت و موازی‌سازی انتگرال‌گیری زمانی؛ در ترکیب با مدل‌کردن مرز جامد با استفاده از توابع پایه شعاعی، الگوریتمی بسیار سریع و کارآمد را نتیجه می­دهد که شبیه‌سازی زمان واقعی را (که نیازمند حداقل 21 نمایش از میدان جریان در هر ثانیه است) امکان‌پذیر ساخته است. دقت و کارایی روش از طریق حل چند مسئله نمونه نشان داده ‌شده ‌است.

کلیدواژه‌ها

عنوان مقاله [English]

Simulation of Solid Body Motion in a Newtonian Fluid Using a Vorticity-Based Parallel Pseudo-Spectral Immersed Boundary Method

نویسندگان [English]

  • Ali Shahabaldini 1
  • Fereidoun Sabetghadam 2
1 Aerospace Dept., Science and Research branch, Islamic Azad University
2 Aerospace Dept., Science and Research Branch, Islamic Azad University, Tehran
چکیده [English]

A numerical method is presented for the simulation of the two-way interaction of a rigid body with an incompressible Newtonian fluid in a two-dimensional configuration. In this method, the moving boundaries which are modeled by the radial base functions, are implemented on a Fourier pseudo-spectral solver of the Navier-Stokes equations in the vorticity-velocity formulation. At the beginning of each time step, the conservative velocity fields, satisfying the immersed boundary conditions along with a modified vorticity field, are implemented to the pseudo-spectral solver. The Poisson equations are solved in parallel, because the velocity boundary conditions obtain independently. The dynamics of the solid body is followed by a second-order method in which the forces are obtained from a vorticity-based integral method. The time integration is performed using a third-order parallel Runge-Kutta method. Employing a parallel fast Fourier pseudo-spectral solver along with parallelization of the time integrations, in combination with modeling of the solid boundaries using the radial base functions result in a very fast and efficient solver that makes it possible real-time simulations (which requires at least 21 flow snapshots per second). The accuracy and efficiency of the method is demonstrated by solving some sample problems.

کلیدواژه‌ها [English]

  • Two-way fluid-solid interaction
  • Vorticity-velocity formulation
  • Pseudo spectral solver
  • Immersed boundary method
  • Radial basis functions
  • Parallel calculation

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سابقه مقاله

  • تاریخ دریافت: 02 دی 1398
  • تاریخ بازنگری: 16 تیر 1399
  • تاریخ پذیرش: 04 بهمن 1399
  • تاریخ انتشار: 01 تیر 1399

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