臺灣博碩士論文加值系統

本研究運用分散式平行運算系統，以最小平方有限元素法(LSFEM)模擬腹主動脈系統的流場。在本文中建立了兩分岔血管位於動脈的同側以及兩分岔血管之間不同間距的模型。著重點在於三維分岔血管質傳現象和流場分析，觀察其速度向量、流線、濃度分佈。當兩分岔血管之間的距離 時，兩分岔血管交互影響越低，兩分岔血管之間的腹主動脈血管管壁上的迴流區域也越來越小。質傳方面，迴流區域是影響氧濃度的最大關鍵，在第一與第二根分岔血管中的迴流造成了低氧濃度的產生，而且低氧濃度會一直延伸至出口處。在腹主動脈血管管壁上的迴流區域同樣也造成了低濃度區的產生，並且當 時，低濃度區也隨之遞減。其他正常區域則是接近入口氧濃度 。運用平行化所得之結果，使用不同數量的CPU可以提昇100％以上的平行效益，對於複雜的數值計算相當有幫助。基於此數值模擬方式，本研究可以有效的利用數值模擬來處理整個複雜的流場與質傳現象。

A parallel computation system is applied for the numerical simulation in association with the least-squares finite element method (LSFEM) to study the flow fields and mass transfer in the abdominal aorta with two branches, which are on the same side of the artery with diameter D. The effects on flow field and mass transfer in relation to the distance (S) between two branches are investigated. From the distribution of velocity vector, streamline and concentration, it can be found when the distance between two branches is greater than one time of the diameter of the artery ( ) the interaction of flow field is small. The distribution of mass transfer of oxygen concentration is closely related to the existence of the vortex flow. The distribution of low concentration of oxygen is in the circulation zone near the wall of arteries, besides that the concentration is the same as the one in the inlet section. The area of low concentration could be the place of the intimal hyperplasia. This numerical model can be used to have a better understanding of the whole complicated flow field and mass transfer. Based on the parallel system, the computational CPU time can be improved by 100% for the complicated domain.

目 錄
摘 要 I
英文摘要.................................................II
致　謝..................................................III
目 錄 IV
表 目 錄 VI
圖 目 錄 VII
符號說明..................................................X
第一章 緒論 1
1-1 研究動機 1
1-2 研究方法和目的 2
1-3 文獻回顧 4
第二章� 理論分析 6
2-1歷史回顧 6
2-2 理論推導 7
2-3 控制方程式 10
第三章 模型建立與邊界條件給定 17
3-1 模型建立與網格產生 17
3-2 邊界條件給定 19
3-3 平行電腦的模式簡介 21
第四章 結果分析與討論 22
4-1 三維分岔血管之流場分析 22
4-2 三維分岔血管之質傳分析 25
4-3 平行效益 27
第五章 結論與建議 28
5-1結論 28
5-2建議 29
參考文獻 30


表 目 錄
表4-1： 分岔血管模型(網格數166608) 27
表4-2： 分岔血管模型(網格數205223) 27


圖 目 錄
圖3.1 腹主動脈系統及其分支群 32
圖3.2 腹主動脈系統模型說明 33
圖3.3分岔血管採用數值模型均勻網格系統 33
圖3.4 8-node MPP 架構示意圖 34
圖4.1 之XY平面上速度 的分佈圖 35
圖4.2 之XY平面上速度 的分佈圖 35
圖4.3 之XY平面上速度 的分佈圖 35
圖4.4 之XY平面上速度 的分佈圖 36
圖4.5 之XY平面上速度 的分佈圖 36
圖4.6 之XY平面上速度 的分佈圖 36
圖4.7 之三維流場分佈圖 37
圖4.8 之三維流場分佈圖 37
圖4.9 之三維流場分佈圖 37
圖4.10 之三維流場分佈圖 38
圖4.11 之三維流場分佈圖 38
圖4.12 之三維流場分佈圖 38
圖4.13 箭頭所指的區域為迴流區域 39
圖4.14 模型中各斷面位置示意圖 39
圖4.15 斷面a之速度分佈與速度向量圖 40
圖4.16 斷面b之速度分佈與速度向量圖 40
圖4.17 斷面c之速度分佈與速度向量圖 40
圖4.18 斷面d之速度分佈與速度向量圖 41
圖4.19 斷面e之速度分佈與速度向量圖 41
圖4.20 之XY平面上氧濃度 的分佈圖 42
圖4.21 之XY平面上氧濃度 的分佈圖 42
圖4.22 之XY平面上氧濃度 的分佈圖 43
圖4.23 之XY平面上氧濃度 的分佈圖 43
圖4.24 之XY平面上氧濃度 的分佈圖 44
圖4.25 之XY平面上氧濃度 的分佈圖 44
圖4.26 之YZ平面的氧濃度剖面圖 45
圖4.27 兩分岔血管Y=2.5斷面的速度向量圖............45
圖4.28 兩分岔血管Y=4斷面的速度向量圖..............45
圖4.29 之YZ平面的氧濃度剖面圖.....................46
圖4.30 之YZ平面的氧濃度剖面圖 46
圖4.31 兩分岔血管Y=2.5斷面的速度向量圖............47
圖4.32 兩分岔血管Y=4斷面的速度向量圖..............47
圖4.33 之YZ平面的氧濃度剖面圖.....................47
圖4.34 之YZ平面的氧濃度剖面圖.....................48
圖4.35 之YZ平面的氧濃度剖面圖.....................48
圖4.36 之兩分岔血管的氧濃度剖面圖..................49
圖4.37斷面1∼3..........................................49
圖4.38 斷面4∼6.........................................50
圖4.39 、 加速比示意圖 50

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