跳到主要內容

臺灣博碩士論文加值系統

(44.210.237.158) 您好!臺灣時間:2022/09/25 21:31
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:蘇逸鎮
研究生(外文):Yi-Chen Su
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
論文名稱(外文):A Parallel Adaptive Nonlinear Elimination Preconditioned Inexact Newton Method for Transonic Full Potential Flow Problems
指導教授:黃楓南
指導教授(外文):Fen-nan Hwang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:47
中文關鍵詞:全勢流
外文關鍵詞:Full Potential Flow
相關次數:
  • 被引用被引用:0
  • 點閱點閱:242
  • 評分評分:
  • 下載下載:10
  • 收藏至我的研究室書目清單書目收藏:0
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。
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.
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
[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,
2007.
[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.
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top