IJE TRANSACTIONS A: Basics Vol. 23, No. 2 (April 2010) 169-176   

downloaded Downloaded: 64   viewed Viewed: 1484

T. K. Sheel
MEMA, University Catholique de Louvain, Batiment Euler, 4 Avenue Goerges Lemaitre
1348 Louvain-La-Neuve, Belgium
tarun.sheel@uclouvain.be - tksheel@sust.edu

S. Obi
Department of Mechanical Engineering, Keio University, Tokyo, Japan
( Received: August 18, 2009 – Accepted in Revised Form: October 05, 2009 )

Abstract    Bluff body calculation was accelerated by using a special-purpose computer, MDGRAPE-2, that was exclusively designed for molecular dynamics simulations. The three main issues were solved regarding the implementation of the MDGRAPE-2 on vortex methods. These issues were the efficient calculation of the Biot-Savart and stretching equation, the optimization of the table domain, and the round-off error caused by the partially single precision calculation in the MDGRAPE-2. Finally this technique was applied to calculation of flow around a circular cylinder. The drag and lift coefficient was investigated to check the validity of the proposed method.


Keywords    Vortex Method, MDGRAPE-2, Bluff Body, Drag and Lift Coefficient


چکیده    در این تحقیق محاسبه بدنه خالی با استفاده از یک کامپیوتر ویژه (MDGRAPE-2) که منحصراً برای شبیه‌سازی‌های دینامیک مولکولی طراحی شده است تسریع شد. سه مساله مهم مربوط به اجرای MDGRAPE-2 در روش‌های گردابی حل شد. این سه مساله محاسبه کارآمد Biot-Sarvat و معادله کشش، بهینه سازی حوزه جدول و خطای گرد کردن حاصل از محاسبه دقیق منقرد جزئی در MDGRAPE-2 بود. در نهایت این تکنیک برای محاسبه جریان در اطراف یک استوانه مدور به کار رفت. ضریب کشش و بلند کردن برای کنترل اعتبار مدل پیشنهادی مورد بررسی قرار گرفت.


1. Barba LA. Vortex Method for computing high-Reynolds number flows: Increased accuracy with a fully mesh-less formulation, PhD Thesis, California Institute of Technology, 2004.

2. Chatelain P. Contributions to the Three-Dimensional Vortex Element Method and Spinning Bluff Body Flows, PhD Thesis, California Insitute of Technology, 2005.

3. Cocle R, Winckelmans G, Daeninck G. Combining the vortex-in-cell and parallel fast multipole methods for efficient domain decomposition simulations, Journal of Computational Physics, Vol. 227, No. 21, (2008), 9091-9120.

4. Cottet GH, Koumoutsakos PD. Vortex Methods (Theory and Practice), Cambridge University Press, 2000.

5. Eldredge JD. Dynamically coupled fluid-body interactions in vorticity-based numerical simulations, Journal of Computational Physics, Vol. 227, No. 21, (2008), 9170-9194.

6. Fukushige T, Taiji M, Makino J, Ebisuzaki T, Sugimoto D. A highly parallelized special-purpose computer for many-body simulations with an arbitrary central force: MD-GRAPE, Astrophys. J., (1996), 468:51.

7. Huang MJ, Su H-X , Chen L-C. A fast resurrected core-spreading vortex method with no-slip boundary conditions, Journal of Computational Physics, Vol. 228, No. 6, (2009), 1916-1931.

8. Leonard A. Vortex Methods for Flow Simulations. J Comput Phys, Vol. 37, (1980), 289-335.

9. Liu CH, Doorly DJ. Vortex particle-in-cell method for three-dimensional viscous undbounded flow computations, Int. J. Numer. Meth. Fluids, Vol. 32, (2000), 29-50.

10. Narumi T. Special-Purpose Computer for Molecular Dynamics Simulations, Doctoral Thesis, College of Arts and Sciences, University of Tokyo, 1997.

11. Ploumhans P, Winckelmans GS, Salmon JK, Leonard A, and Warren MS. Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows: Application to the Sphere at Re = 300, 500, and 1000. J. Comp. Phys., Vol. 178, (2002), 427-463.

12. Poncet P. Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation, Journal of Computational Physics, Vol. 228, No. (19), (2009), 7268-7288.

13. Ramachandran P, Ramakrishna M, Rajan SC. Efficient random walks in the presence of complex two- dimensional geometries, Computers & Mathematics with Applications, Vol. 53, No. 2, (2007), 329-344.

14. Sbalzarini IF, Walther JH, Bergdorf M, Hieber SE, Kotsalis EM, Koumoutsakos P. PPM - A Highly Efficient Parallel Particle-Mesh Library for the Simulation of Continuum Systems. J. Comp. Phys. Vol. 215, (2006), 566-588.

15. Sheel TK, Yasuoka K, Obi S. Fast vortex method calculation using a special-purpose computer, Computers and Fluids, Vol. 36, (2007), 1319-26.

16. Susukita R, Ebisuzaki T, Elmegreen B G, Furusawa H, Kato K, Kawai A, Kobayashi Y, Koishi T, McNiven GD, Narumi T, Yasuoka K. Hardware accelerator for molecular dynamics: MDGRAPE-2. Comput Phys Comm, Vol. 155, (2003), 115-131.

17. Winckelmans GS, Leonard A. Contributions to Vortex Particle Methods for the Computation of Three- Dimensional Incompressible Unsteady Flows. J Comput Phys, Vol. 109, (1993), 247-273.

18. Yatsuyanagi Y, Ebisuzaki T, Hatori T, Kato T. Filamentary magneto hydrodynamic simulation model, current vortex method. Physics of Plasmas, Vol. 10, (2003),3181-3187.

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir