IJE TRANSACTIONS C: Aspects Vol. 27, No. 9 (September 2014) 1457-1466    Article Under Proof

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F. Sabetghadam, E. Soltani and H. Ghassemi
( Received: December 16, 2013 – Accepted: April 17, 2014 )

Abstract    Abstract The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to some other similar methods, there is not an explicit external forcing function in the present formulation. At the beginning of each time step, the solenoidal velocities (also satisfying the desired immersed boundary conditions), are obtained and fed into a conventional pseudo-spectral solver, together with a modified vorticity. The classical explicit fourth-order Runge-Kutta method is used in time integration, and the boundary conditions are set at the beginning of each sub-step, in order to increase the time accuracy. The method is employed in simulation of some different test cases, including the flow behind impulsively started circular cylinder, oscillating circular cylinder in fluid at rest and insect-like flapping wing motion. The results show accuracy and efficiency of the method.


Keywords    Immersed Boundary Method, Vorticity-Velocity Formulation, Pseudo-Spectral Method, Moving Obstacles



مقاله پيش­رو به حل شبه‌طيفي فوريه معادلات ناوير-استوکس تراکم‌ناپذير دوبعدي در فرم سرعت-تاوايي با استفاده از روش مرز مستور می­پردازد. شرايط مرزي مستور بدون اضافه کردن تابع نيرو و از طريق اصلاح مستقيم جملات جابجايي و پخش اعمال شده­است. در ابتداي هر گام زماني سرعت‌هاي بقايي ارضاکننده شرايط مرزي مستور به‌همراه تاوايي اصلاح‌شده در معادله انتقال تاوايي اعمال می­شوند. پيشروي زماني با استفاده از روش صريح رانج-کوتاي مرتبه چهار انجام شده است که در آن به منظور افزايش دقت، شرايط مرزي در ابتداي هر زيرگام اعمال شده­اند. روش به مسائل مرز متحرکي شامل استوانه با حرکت ناگهانی، حرکت نوسانی استوانه در يک سيال ساکن و حرکت شبه­بال يک حشره اعمال شده­است. نتايج مويد دقت و راندمان مناسب روش هستند



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