ارائه یک مدل عددی-ریاضی برای پدیده شکست سد به روش حجم محدود با استفاده از شبکه بندی ورونوی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، دانشگاه آزاد اسلامی، واحد تهران جنوب

2 دانشجوی دکتری، دانشگاه آزاداسلامی، واحد علوم و تحقیقات

3 دانشجوی دکتری، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات

چکیده

در این مقاله حرکت سیل ناشی از شکست سد به صورت دو بعدی مورد مطالعه قرار گرفته است. بدین منظور معادله آب های کم عمق به شیوه مرتبه دوم Local-Lax–Friedrich برای تسخیر شوک یا ناپیوستگی در شرایط اولیه و ارضای خاصیت ابقایی در چهارچوب روش احجام محدود و شبکه بندی ورونوی که تطابق مناسبی با محیط دارد٬ در قالب یک برنامه توسط نرم افزار توانمند MATLAB ارائه گردیده شده است. نتایج حاصله از برنامه با نتایج به دست آمده از چند آزمون شکست سد که به صورت نامتقارن و دایره ای در مراجع ارائه گردیده توسط نرم افزار آماری SPSS مقایسه شده که تطابق بسیار خوبی را بیان می کند.مدل ارائه شده قادر به مدل سازی هندسه های پیچیده با در نظر گرفتن اثر شیب و تسخیر موج شوک می باشد.

کلیدواژه‌ها

عنوان مقاله [English]

A high resolution finite volume scheme with a voronoi mesh for dam break simulation

نویسندگان [English]

  • Hamid Reza Vosoughifar 1
  • hamidreza jalalpour barfroush 2
  • seyedeh mona tabandeh 3
2 Ph.D. Studnet, Department of Civil Engineering, Science and Research Branch, Tehran, Iran
3 Ph.D. Student, Department of Civil Engineering, Science and Research Branch, Tehran, Iran
چکیده [English]

A high resolution finite volume method for solving the shallow water equations with voronoi mesh is developed applying MATLAB software in this paper. The scheme is formally uniformly second order accurate and satisfies maximum principles. The model is verified by comparing the model output with condition of anti-symmetric and circular dam break with documented results. For more investigation we utilized SPSS statistical software. Very good agreement has been achieved in the verification phase. It can be considered as an efficient implement for the computation of shallow water problems, especially concerning those having discontinuities. A simple example of the collapse of water supply reservoir in a valley is used to demonstrate the capability of the model. The presented model is able to resolving shocks, handling, complex geometry, including the influence of steep bed slopes.

کلیدواژه‌ها [English]

  • Finite volume method
  • voronoi mesh
  • dam break
  • high resolution Local Lax–Friedrich scheme

مراجع

[1] Aureli, F., Mignosa, P., Tomirotti, “Numerical simulation and experimental verification of Dam-Break flows with shocks” , Journal of Hydraulic Research, Vol. 38 , No. 3, pp. 197- 206, 2000.
[2] Chaudhry, M. H,, “Open-Channel Flow Prentice-Hall”, Englewood Cliffs, New Jersey, 1993.
[3] Zoppou, C., Roberts, S., “Numerical solution of the two dimensional unsteady dam break”, International Journal for Computational Methods in Engineering Science and Mechanics, 8, pp.1– 14, 2000.
[4] Drysdale. S, Voronoi Diagram, Lecture 4, 1996.
[5] Eleuterio F. Toro, “HLLC Riemann solver”, Laboratory Of Applied Mathematics University of Trento, Italy, 2010.
[6] Fennena, R.J., Chaudhry, M.H., “Explicit Numerical Schemes for Unsteady Free-Surface Flows with Shocks”, Water Resources Research, Vol22, n13, 1986.
[7] Fletcher, C.A.J., “Computational Techniques for Fluid Dynamics”, vol. 2, seconded. Springer, Berlin, 1991.
[8] G. Steinebach, R. Weiner, “ Peer methods for the one-dimensional shallow water equations with CWENO space Discretization ”, internet, 2009.
[9] Garcia-Navarro, P.,Brufau, P. “One-Dimensional Dam Break Flow Modeling: Some Results”, 1992.
[10] Hans De SterckوPaul Ullrich, “ Introduction To Computational PDES”, Course Notes for AMATH 442 / CM 452, Fall, 2009.
[11] M. ALIPARAST, “Two-dimensional finite volume method for dam-break flow simulation”, international Journal of Sediment Research 24, 99– 107, 2009.
[12] Murthy Jayathi Y, “Numerical Methods in Heat, Mass, and Momentum Transfer”, 2002.
[13] Patankar. S. V, “Numerical heat transfer and fluid flow”, MC Graw-Hill, New York, 1980.
[14] Prickett, T.A, “Modeling Techniques for groundwater Evaluation”, In: V.T. Chow (editor), Advances in Hydro science, Vol. 10. Academic Press, New York, 1975.
[15] R. Bernetti, “Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom Geometry”, University of Trento presently at: Polytechnic, 2008.
[16] Randall J. Leveque, “Finite Volume Methods for Hyperbolic Problems”, 2004.
[17] Robert Eymard, Thierry Gallaudet and Raphael Herbin, “Finite Volume Methods”, January ,This manuscript is An update of the preprint n0, pp. 97-19 du LATP, 2003.
[18] Sugihara. K., Iri. M., “Construction of the Voronoi diagram for ‘one million’ sites in single- recession arithmetic”, Proc. IEEE, Vol. 80, No. 9, pp. 1471-1484, 1992.
[19] Sung-Uk Choi and Joongcheol Paik, “Performance Test of High Resolution Schemes for ID Dam Break Problem”, KSCE Journal Of Civil Engineering, Vol 5, No~ 3, September, pp. 23- 280, 2001.
[20] Tseng, M.H, Chia R. Chu, “The simulation of dam break flows by an improved predictor-corrector T.V.D scheme”, Advances in Water Resources, Vol. 23 , pp. 637- 643, 2000.
[21] Loukili, Y. and Soulaımani, A., “Numeric
University of Marche Department of Mechanical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF
Approximation”, 2007.
[22] Yuling L.,Wenli W “High Resolution Mathematical Model for Simulating 2D Dam Break flow Wave”, XXXI IAHR Congress, 2005.
[23] Wang J.W Liu R.X., “A Comparative Study of Finite Volume Methods on Unstructured Meshes for Simulation of 2D Shallow Water Wave problems”. Mathematic and computers in simulation 2000.

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