博碩士論文 992201008 詳細資訊




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姓名 蘇逸鎮(Yi-Chen Su)  查詢紙本館藏   畢業系所 數學系
論文名稱 平行化非線性消去預調節法對牛頓演算法在跨音速流體的應用
(A Parallel Adaptive Nonlinear Elimination Preconditioned Inexact Newton Method for Transonic Full Potential Flow Problems)
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摘要(中) 本篇論文目中,我們使用全勢流的方程式,來描述一個跨音速流體,在離散的方法中我們使用了有限差分法和上風密度法,來推導出大型稀疏的非線性方程組。接著詳細說明平行化非線性消去預調節法對牛頓演算法的優勢。最後我們模擬了兩個不同情況的幾何圖形,為NACA0012 的機翼模型和內部通道流的模型,也給出了數值結果,其中包括演算法和總結本文的主要貢獻,並指出此演算法有哪一些潛在的應用。
摘要(英) We describe the model equation for modeling transonic flows based on full potential equation and the derivation of a large sparse nonlinear system of equations using the finite differences with the density upwind technique. And then give a detailed description of the proposed algorithm, a parallel adaptive nonlinear elimination preconditioned inexact Newton algorithm. Last, presents the numerical results, including parallel performance for the algorithm and the paper summarize the main contribution of this paper and point out some potential applications of the algorithm.
關鍵字(中) ★ 全勢流 關鍵字(英) ★ Full Potential Flow
論文目次 中文摘要i
英文摘要ii
圖目錄v
表目錄vii
1 導論1
2 全勢流方程式與離散化3
2.1 數學模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 NACA0012 機翼模型. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 底部凸起的通道模型. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 離散化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 演算法的說明9
3.1 RAS-Krylov 方法在全區域雅可比矩陣. . . . . . . . . . . . . . . . . . . . . 12
4 數值結果與討論14
4.1 參數的選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 平行程式碼的確認. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 傳統牛頓法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 INB-ANE 法中的非線性檢查. . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5 討論高比例的壞元素. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.6 參數研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.7 平行效能研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 結論與未來發展30
參考文獻32
附錄:全勢流離散成大型非線性系統35
參考文獻 [1] H.-B. An. On convergence of the additive Schwarz preconditioned inexact Newton method. SIAM J. Numer. Analy., 43:1850–1871, 2006.
[2] X.-C. Cai, W.D. Gropp, D.E. Keyes, R.G. Melvin, and D.P. Young. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation. SIAM J. Sci. Comput., 19, 1998.
[3] X.-C. Cai and D.E. Keyes. Nonlinearly preconditioned inexact newton algorithms. SIAM J. Sci. Comput., 24:183–200, 2002.
[4] X.-C. Cai, D.E. Keyes, and L. Marcinkowski. Nonlinear additive schwarz precon-ditioners and applications in computational fluid dynamics. Int. J. Numer. Meth.
Fluids, 40:1463–1470, 2002.
[5] X.-C. Cai, D.E. Keyes, and D.P. Young. A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flow. In Domain Decomposition Methods in
Science and Engineering. CIMNE, 2002.
[6] X.-C. Cai and X. Li. Inexact Newton methods with restricted additive schwarz based nonlinear elimination for problems with high local nonlinearity. SIAM J. Sci. Com-
put., 33:746–762., 2011.
[7] J.E. Dennis and R.B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996.
[8] G Groß and R. Krause. On the globalization of ASPIN employing trust-region control strategies–convergence analysis and numerical examples. preprint, 2011.
[9] C. Hirsch. Numerical Computation of Internal and External Flows, Vol. 2. Wiley, 1990.
[10] F.-N. Hwang and X.-C. Cai. A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations. J. Comput. Phys., 204:666–691, 2005.
[11] F.-N. Hwang and X.-C. Cai. A class of parallel two-level nonlinear Schwarz precondi-tioned inexact Newton algorithms. Comput. Meth. Appl. Mech. Eng., 196:1603–1611,
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[12] F-.N. Hwang, H.-L. Lin, and X.-C. Cai. Two-level nonlinear elimination-based pre-conditioners for inexact Newton methods with application in shoched duct flow cal-
culation. Electron. Trans. Numer. Anal., 37:239–251, 2010.
[13] J. Nocedal and S.J. Wright. Numerical Optimization. Springer Verlag, New York, 1999.
[14] B. Sanderse. Cartesian grid methods for preliminary aircraft design. 2008.
[15] S. Shitrit, D. Sidilkover, and A. Gelfgat. An algebraic multigrid solver for transonic flow problems. J. Comput. Phys., 230:1707–1729, 2011.
[16] Jan Ole Skogestad, Eirik Keilegavlen, and Jan M Nordbotten. Domain decomposition strategies for nonlinear flow problems in porous media. J. Comput. Phys., 234:439–
451, 2013.
[17] D.P. Young, W.P. Huffman, R.G. Melvin, C.L. Hilmes, and F. T. Johnson. Nonlinear elimination in aerodynamic analysis and design optimization. In L.T. L.T. Biegler, O. O. Ghattas, Heinkenschloss M., and van Bloemen Waanders B., editors, Large-Scale PDE-Constrained Optimization, volume 30 of Lect. Notes in Comp. Sci., pages 17–44. Springer-Verlag, 2003.
[18] D.P. Young, R.G. Melvin, M.B. Bieterman, F.T. Johnson, S.S. Samant, and J.E. Bussoletti. A locally refined rectangular grid finite element method: application to
computational fluid dynamics and computational physics. J. Computat.l Phys., 92:1–66, 1991.
[19] M. Ziani. Acceleration de la convergence des methodes de type Newton pour laresolution des systemes non-lineaires. PhD thesis, 2009.
指導教授 黃楓南(Fen-nan Hwang) 審核日期 2013-8-21
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