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Title: 應用修正型Trefftz法求解非線性二維沖激問題
Applications of the Modified Trefftz Method on Solving Non-linear Two-dimensional Sloshing Problems
Authors: Yung-Wei Chen
陳永為
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
國立臺灣海洋大學:系統工程暨造船學系
Keywords: 拉普拉斯方程;混合邊界值問題;沖激
Laplace equation;Mixed-boundary value problem;Sloshing
Date: 2009
Issue Date: 2011-06-30T07:35:18Z
Abstract: 本論文發展修正型Trefft法結合保群算法處理二維非線性沖激問題。對於非線性沖激行為,傳統數值方法將因為係數矩陣的病態與非線性動力自由液面效應將造成數值不穩定與數值結果的耗散。為了克服以上的問題,本文引入控制體積概念於數值程序中來避免自由液面計算的耗散,且同時考慮多尺度特徵長度來保持數值方法之穩定性。此外,數值計算中利用保群算法可以避免因泰勒展開式所產生之二階導微來增加數值計算效率,且同時由保群算法之權重因子可以明顯觀查到非線性動力自由液面效應造成速度勢的耗散。因此,由數值結果比較可知,本文提出之修正型程序的數值結果遠優於目前比較之文獻,且由本文可看出修正型Trefft法結合保群算法既簡單且穩定尤其對於處理非線性沖激問題。
This dissertation develops a modified Trefftz method (MTM) associated with the group-preserving scheme (GPS) to deal with two-dimensional non-linear sloshing problems. For non-linear sloshing phenomena, the conventional numerical method may encounter numerical instabilities and numerical dissipation, as the coefficient matrix obtained by the conventional numerical method is ill-posed, and the free surface exhibits nonlinear kinematics. To overcome these problems, we introduce the concept of the controlled volume into the numerical procedure to prevent the elevation from vanishing, and we take the multi scaling characteristic lengths into account to maintain the stability of the new numerical method. Besides, the use of the GPS eliminates the need to use second-order derivatives for increasing the numerical efficiency and weighting factors can be used to observe the vanishing of the velocity potential. Comparisons of the present study with those in the literature show that the numerical results are better than those obtained by using previous methods. The method developed here is a simple and stable way to cope with the non-linear sloshing problems.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0D93510004
http://ntour.ntou.edu.tw/ir/handle/987654321/14275
Appears in Collections:[系統工程暨造船學系] 博碩士論文

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