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研究生:陳立杰
研究生(外文):Li-Jie Chen
論文名稱:快速面積擴散渦漩法之開發與平行化
論文名稱(外文):Development and Parallel Application of a Fast Core-Spreading Vortex Method
指導教授:黃美嬌黃美嬌引用關係
指導教授(外文):Mei-Jiau Huang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
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:2008
畢業學年度:96
語文別:中文
論文頁數:70
中文關鍵詞:快速渦漩法自適晶胞切割勞倫茲級數多極法面積擴散渦漩法
外文關鍵詞:Fast vortex methodAdaptive domain decompositionLaurent seriesMultipole methodCore spreading vortex method
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在本篇論文中,我們以修正過後之面積擴散渦漩法以及多極法(multipole method)成功地發展出一套快速面積擴散渦漩法。在此快速渦漩法中,我們首先依渦漩粒子分佈密集程度,利用自適晶胞切割的方式自動將流域切割成各種不同尺寸的晶胞,再依晶胞間的相對關係與位置,分別選用點對點計算或群對點計算方式來計算渦漩粒子相互引致的速度。前者乃直接計算畢歐-沙伐定理,計算量與晶胞內渦漩粒子總數的平方成正比;後者則以有限項的勞倫茲級數近似之,可將計算量大幅降低,若將後者做適當的再展開近似(群對群計算),可稍微再提昇計算速度。方法中我們並設計了一套二進位晶胞編號系統,藉由此編號系統,我們可以快速的分辨晶胞間的關係,並找出晶胞的鄰居;另設計一速度加總邏輯,可有效率地將所有渦漩粒子交互引致的速度全部算出。最後,我們徹底檢視這套方法的效率以及準確性,研究其中重要參數的影響,尋求最佳的參數值。最後以模擬兩漩渦融合過程為真實流場模擬測試,同步分析並比較整個快速面積擴散渦漩法一時步中各個步驟所花費的CPU時間。研究發現本快速渦漩法可將計算速度提高一個數量級之多,而為了進一步提升程式效率,我們也開發了平行化的程式邏輯。
In this study, a fast vortex method is successfully developed based on a resurrected core-spreading vortex method and on a multipole method. In this fast vortex method, the flow domain is first divided into cells of various levels via an adaptive-domain-decomposition technique. The mutually-induced velocities among vortex blobs are calculated either directly by the Biot-Savart law (point-to-point formula) or by a truncated Laurent series (box-to-point formula). The judgment is made according to the cell-to-cell relation with the help of a binary numbering system of cells, which is designed to quickly figure out the neighbors of a cell and of its mother. A fast summation algorithm is also developed to sum over all mutually-induced velocities efficiently. If we rearrange the truncated Laurent series properly, the efficiency can be increased. The accuracy and the efficiency of this fast algorithm are then examined thoroughly. The influences of relevant parameters are explored and optimum values are proposed. The CPU times spent in each substep of the vortex method in a simulation of vortex merger are finally measured and analyzed.
摘要 i
Abstract ii
目錄 iii
表目錄 v
圖目錄 v
1.緒論 1
1.1研究背景 1
1.2 研究目的 6
1.3論文架構 6
2.面積擴散渦旋法 7
2.1 理論基礎 7
2.2渦泡分裂 8
2.3 渦泡融合 9
3.快速渦旋法(一) 12
3.1「群對點」計算與勞倫茲級數展開 12
3.2自適晶胞切割 13
3.3 晶胞編號與鄰居搜尋邏輯 14
3.4 速度加總邏輯設計 16
3.5 勞倫茲係數疊加邏輯 17
3.6群對點快速渦旋法程式流程 18
4. 群對群快速面積渦旋法 20
4.1「群對群」計算與勞倫茲級數再展開 20
4.2速度加總邏輯 21
4.3群對群快速渦旋法程式流程 22
5.結果與討論 24
5.1 群對點快速面積渦旋法 24
5.1.1 基本測試(點渦源粒子) 24
5.1.2 基本測試(高斯渦泡) 25
5.1.3 流場測試 27
5.2 群對群快速渦旋法 29
5.2.1 基本測試(高斯渦泡) 29
5.2.2 流場測試 30
6.平行化處理 31
6.1平行化簡介 31
6.2 平行化設計要點 31
6.3 速度加總邏輯 33
6.4 平行化邏輯設計 33
6.5 平行化程式測試 34
7.結論與未來展望 36
參考文獻 38
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