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研究生:陳季聰
研究生(外文):Chen, Chi-Tsung
論文名稱:正交格點產生法之研究
論文名稱(外文):Development of Orthogonal Grid Generation
指導教授:鄭育能
指導教授(外文):Yih-Nen Jeng
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:84
中文關鍵詞:格點產生法正交格點目標函數
外文關鍵詞:Grid GenerationOrthogonal GridFunctional
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本文重新探討正交格點產生法,探討了固定邊界格點法和浮動邊界格法,
除了研究Ryskin和Leal所提出的線性橢圓型格點方程式也提出類似
Thompson,Thame和Mastin方程式的非線性格點方程式。本文發現這兩種
方程式都是特定之目標函數的Euler-Lagrange方程式。前人未能在所有的
例子得到收斂解,都可以由其目標函數不是凸函數(strictlyconvex
function)得到解釋。數值測試顯示,若邊界格點密度足以解析邊界曲率
時,浮動邊界法可以使扭曲函數(由起始猜測格點求得)的分佈大致適合邊
界格點分佈以及平滑的正交格點,經一次或數次的浮動邊界法後改用固定
邊界法,可以得到收斂解。此外本文也成功的由不同的起始猜測格點求得
兩組不同的正交格點之收斂解,顯示正交格點的不唯一性。其它的測試顯
示使用古典的線性格點方程式可以得到較好的正交性但平滑性略差。比起
固定邊界法,浮動邊界法可以有較好的格點平滑性,但若邊界格點使用
Chikhliwala和Yortsos的指數函數分佈法則平滑性則差不多。本文也針對
一個Laplace方程式之正解問題以及兩個自然對流問題,在不同方法之正
交格點上測試其精確度,發現若物理解為平滑分佈時,精確度與前面所提
的趨勢一致。

The dissertation studies both the fixed and floating
boundarypoint grid generation of orthogonal grids. In addition
to thelinear grid equations of Ryskin and Leal, the nonlinear
gridequations, which are similar to the well known TTM
equations,are also examined.It is found that both equations
arethe Euler-Lagrange equations of properly defined
functionalwhich are functions of (x,y,f) or (ξ, η,f). The
functionsare not a strictly convex function of the
correspondingvariables (x,y,f) or (ξ, η,f). Consequently, the
reason thatthe previous study of Eca can not always find a
convergentsolution is reasonable. Several test cases show that,
if theboundary grid density is dense enough to resolve all
theboundary curvature, the floating boundary point grid
generationmethod can provide the consistency between the
distortionfunction f and boundary grids and generates smooth
orthogonal grids. Subsequently, it is found that, by employing
thefloating point method one or several times and then switching
to the fixed boundary point grid generation method,convergent
orthogonal grids can be found. Based on differentinitial grids,
this new procedure can produce differentorthogonal grid systems
which reflects the non-uniquenessof the orthogonal grid systems
for a typical domain. The othertests show that the classical
linear grid equations cangenerate a better grid orthogonality
than that of the proposed nonlinear grid equations but the grid
smoothness is worse.As comparing with the fixed boundary point
method, thefloating boundary point method can provide a better
gridsmoothness. However, if the Chikhliwala and Yortsos'
exponential function distribution of the boundary grid
pointmethod is properly employed the grid smoothness is
similarto that of the floating boundary point method.This study
also examines a exact solution of the Laplaceequation and two
free convection problems on differentorthogonal grids, all the
results show a similar tendencyprovided that the solution is
relatively smooth.

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