نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه شهید چمران اهواز

2 دانشگاه شهید چمران اهواز، مرکز تحقیقات شبکه گاز در دانشگاه شهید چمران اهواز

چکیده

در تحقیق حاضر یک روش المان مرزی چندقطبی سریع تک‏سطحی اصلاح شده (MSLFMM) برای حل مسائل انتقال حرارت هدایتی با مقیاس بزرگ ارائه شده است. این روش با کاربرد تقریب دوردست (FFA) در روش چندقطبی سریع تک‏سطحی متداول (SLFMM) حاصل شده است. از این تقریب جهت محاسبه ضرایب تاثیر المان‏های دور از هم درون سلول‏های همسایه و همچنین تعیین گشتاور المان‏های درون سلول‏های دور استفاده شده است. انجام این دو مهم نه‏تنها از دشواری روابط محاسباتی و پیچیدگی در برنامه‏نویسی کم می‏نماید، بلکه بر کاهش زمان محاسباتی تاثیر چشمگیری دارد. چندین مثال برای ارزیابی روش پیشنهادی در نظر گرفته شده است. زمان محاسباتی روش پیشنهادی در مقایسه با روش المان مرزی متداول (CBEM)، روش چندقطبی سریع تک‏سطحی متداول و روش چندقطبی سریع چندسطحی (MLFMM) نشان داده شده است. نتایج نشان می‌دهد که سرعت حل این روش بسیار بالاتر از روش تک‏سطحی متداول بوده و با توجه به سادگی کاربرد آن قابل مقایسه با روش چندسطحی است. در نهایت برای بررسی توانایی روش پیشنهادی جهت حل مسائل پیچیده، انتقال حرارت هدایت دائم درون یک بدنه موتور شبیه‎سازی شده است. مقایسه میان نتایج روش حاضر و نتایج روش حجم محدود (نرم‏افزار فلوئنت) بیانگر انطباق مناسب با خطای کمتر از 1/5 درصد است.

کلیدواژه‌ها

عنوان مقاله [English]

Analysis of Large-Scale Heat Conduction Problems Using a Modified Single-Level Fast Multipole Method

نویسندگان [English]

  • Mohammadhadi Motaghed 1
  • Morteza Behbahani-nejad 2
  • maziar changizian 2

1 Shahid Chamran University of Ahvaz

2 Shahid Chamran University of Ahvaz/ Gas Networks Research Center, Shahid Chamran University of Ahvaz

چکیده [English]

A Modified Single-Level Fast Multipole Method (MSLFMM) for large-scale heat conduction problems is presented. This method is obtained by embedding the far-field approximation (FFA) within the traditional single-level fast multipole method (SLFMM). The FFA is used to compute the influence coefficients of the far elements within adjacent cells, and also to determine the moments of the elements within far cells. This approximation not only reduces the difficulty of procedures and programming, but also causes a significant decrease in the CPU time. Several problems are considered to verify and evaluate the proposed method. The computational cost of the MSLFMM is demonstrated by comparing the Conventional Boundary Element Method (CBEM), the SLFMM, and the Multi-Level Fast Multipole Method (MLFMM). It is shown that the MSLFMM is much faster than the SLFMM, and comparable with the MLFMM due to its ease of use. Finally, to check the ability of the proposed method in modeling a complicated problem, steady-state heat conduction in an engine block is solved. The numerical results show a good agreement with those obtained by a Finite Volume Method (FVM), and its difference is less than 1.5%.

کلیدواژه‌ها [English]

  • Boundary Element Method
  • Fast Multipole Method
  • Far-Field Approximation
  • Heat Conduction
  • Large-Scale
  1. Jaswon, M., “Integral Equation Methods in Potential Theory. I”, Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, Vol. 275, No. 1360, pp. 23-32, 1963.
  2. Brebbia,, The Boundary Element Method for Engineers, Pentech Press, London, 1978.
  3. Browne, L. E., and Ashby, D. L., Study of the Integration of Wind Tunnel and Computational Methods for Aerodynamic Configurations, San Diego State University,
  4. Rokhlin, V., “Rapid Solution of Integral Equations of Classical Potential Theory”, Journal of Computational Physics, Vol. 60, pp. 187-207, 1985.
  5. Greengard, L. F., and Rokhlin, V., “A Fast Algorithm for Particle Simulations”, Journal of Computational Physics, Vol. 73, pp. 325-348, 1987.
  6. Greengard, L. F., The Rapid Evaluation of Potential Fields in Particle Systems, The MIT Press, Cambridge, MA, 1988.
  7. Nishimura, N., “Fast Multipole Accelerated Boundary Integral Equation Methods”, Applied Mechanics Reviews, Vol. 55, No. 4, 99. pp. 299-324, 2002.
  8. Liu, Y. J., Nishimura, N., and Yao, Z. H., “A Fast Multipole Accelerated Method of Fundamental Solutions for Potential Problems”, Engineering Analysis with Boundary Elements, Vol. 29, No. 11, pp. 1016-1024, 2005.
  9. Liu, Y. J., and Nishimura, N., “The Fast Multipole Boundary Element Method for Potential Problems: A Tutorial”, Engineering Analysis with Boundary Elements, Vol. 30, No. 5, pp. 371-381, 2006.
  10. Liu, Y. J., Fast Multipole Boundary Element Method-Theory and Applications in Engineering, Cambridge: Cambridge University Press, 2009.
  11. Shen, L., and Liu, Y. J. “An Adaptive Fast Multipole Boundary Element Method for Three-Dimensional Potential Problems”, Computational Mechanics, Vol. 39, No. 6, pp. 681-691, 2007.
  12. Coifman, R., Rokhlin, V., and Wandzura, S., “The Fast Multipole Method for the Wave Equation: A Pedestrian Prescription”, IEEE Antennas and Propagation Magazine, Vol. 35, No. 3, pp. 7-12, 1993.
  13. Kreuzer, W., Majdak, P., and Chen, Z. S., “Fast Multipole Boundary Element Method to Calculate Head-Related Transfer Functions for A Wide Frequency Range”, The Journal of the Acoustical Society of America, Vol. 126, No. 3, pp. 1280-1290, 2009.
  14. López-Portugués, M., López-Fernández, J. A., Menéndez-Canal, J., Rodríguez-Campa, A., and Ranilla, J., “Acoustic Scattering Solver Based on Single Level FMM for Multi-GPU Systems”, Journal of Parallel and Distributed Computing, Vol. 72, No. 9, pp.1057-1064, 2012.
  15. Landesa, L., Taboada, J. M., Obelleiro, F., Rodriguez, J. L., Mourino, C., and Gomez, A., “Solution of Very Large Integral Equation Problems with Single Level FMM”, Microwave and Optical Technology Letters, Vol. 51, No. 10, pp. 2451-2453, 2009.
  16. Lu, C. C., and Chew, W. C., “Fast Far-Field Approximation for Calculating the RCS of Large Objects”, Microwave and Optical Technology Letters, Vol. 8, No. 5, pp. 238-241, 1995.
  17. Chew, W. C., Cui, T. J. and Song, J. M., “A FAFFA-MLFMA Algorithm for Electromagnetic Scattering”, IEEE Transactions on Antennas and Propagation, Vol. 50, No. 11, pp.1641-1649, 2002.
  18. McCowen, A., “A Far-Field Approximation for the Fast-Multipole Method Applied to the Combined Field Integral Equation”, IEEE Transactions on Magnetics, Vol. 39, No. 3, pp.1254-1256, 2003.
  19. Morino, L., Chen, L.T., and Suciu, E.O., “Steady and Oscillatory Subsonic and Supersonic Aerodynamics Around Complex Configurations”, American Institute of Aeronautics and Astronautics, vol. 13, No. 3, pp. 1932-1936, 1975.
  20. Katz, J., and Plotkin, A., Low-Speed Aerodynamics, 2nd Edition, Cambridge University Press, UK, 2001.
  21. Chen, Z. S., Waubke, H., and Kreuzer, W., “A Formulation of the Fast Multipole Boundary Element Method (FMBEM) for Acoustic Radiation and Scattering from Three-Dimensional Structures”, Journal of Computational Acoustics, Vol. 16, No. 2, pp. 303-320, 2008.
  22. Liu, Y. J., “A Fast Multipole Boundary Element Code for Solving General 3-D Potential Problems Governed by the Laplace Equation, Including Thermal and Electrostatic Problems, Using the Dual BIE Formulation (α CBIE + β HBIE)”, http://www.yijunliu.com

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