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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/16164

Title: 加權最小平方無網格法於熱傳之應用
Meshless Weighted Least Square Method Application in Heat Transfer
Authors: Chao-Feng Shih
Contributors: NTOU:Department of Marine Engineering
Keywords: 加權最小平方無網格法;形狀函數;移動最小平方近似;加權函數
MWLSM;Shape function;Least-square method;Weighting function
Date: 2008
Issue Date: 2011-06-30T08:33:47Z
Abstract: 有別於傳統網格或元素的架構,無網格法近似函數是建立在一系列離散點上,不需依賴背景網格。加權最小平方無網格法(MWLSM)則是一種新的高效無網格法。除了在現有的節點外又引入了一些輔助點,並使所有節點和輔助點處的殘餘值用最小平方法予以消除。所採用的形狀函數(Shape function)以移動最小平方(MLS)的模式來模擬真實解,因而比有限元素法具更高精確度。該方法不需要進行高斯積分,因而計算量小。本研究將加權最小平方無網格法應用於求解多維對流─擴散(Multi-dimensional convection-diffusion)問題,藉由修正加權函數(Modified weighted function)的構造形式以提升其準確度。所使用形狀函數之構造形式為橢圓形,經由測試題目驗證,其結果比圓形更具較佳的精確性。
Different from the traditional meshes or the elements, the approximate function is built on a series of dispersed nodes, and does not need to dependence on the limited meshes. MWLSM is based on least-squares method (LSM) and move least-squares (MLS) approximate foundation; it is a kind of high-efficient mesh-less method. The existing node leads into some auxiliary nodes, and eliminates the residuals with LSM between all nodes and some auxiliary places. The shape function fits and solves truly by MLS; therefore have higher accuracy than finite element method (FEM). This method does not need gauss integrations; therefore it is rapid to calculate. MWLSM is extended to solve multi-dimensional convection-diffusion problems; We revise modified weighting function structural form in order to raise their efficiency. Numerical examples indicate that the elliptically structural form of shape function has better than the round in convergence and accuracy.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M94660007
Appears in Collections:[輪機工程學系] 博碩士論文

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