# 臺灣博碩士論文加值系統

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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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