臺灣博碩士論文加值系統

本研究主要是利用個人電腦叢集(PC Cluster)之平行電腦搭配平行演算法，將使用體心共位有限體積法(Collocated Cell-Centered Finite Volume Method)之三維模擬循序程式平行化，以加快整個模擬分析之效率。並應用此平行化程式來模擬三維非恆溫泛牛頓流體於押出成型模頭中流動行為，以了解其速度場、壓力、溫度在三維空間中的分佈情形，且藉由改變網格元素數目的多寡來分析及討論其對平行計算效率的影響。
本研究在平行計算的施行方式上是採用區域分割(domain decomposition)方式將資料預先作切割，並配合SPMD(Single Program Multiple Data)平行程式的撰寫來進行平行計算，平行程式中所需資料的交換則使用MPI(Message Passing Interface)傳輸標準。另外在線性聯立方程組疊代求解上，則使用Jacobi前置處理之CG法及BICGSTAB法。
在循序程式及平行程式的模擬驗證上，程式的計算結果皆與文獻中的計算結果相當吻合，可證明此數值計算方法之正確性。而在不同網格元素的衣架形模具模擬上顯示，隨著分析的網格元素增加，其平行計算效率就會愈好，因此對於愈複雜的三維幾何分析上愈值得利用平行計算方式來減少分析計算時間。

The study is to improve efficiency of three-dimensional flow simulation by parallel Collocated Cell-Centered Finite Volume Method by PC Cluster and parallel algorithm. We apply the parallel program to simulate extrusion process of the non-isothermal generalized Newtonian fluid in extrusion die. And will predict the distribution of velocity, pressure, and temperature in the three-dimensional space. We also change the number of elements of the grid and discuss its affection on efficiency of parallel simulation.
In research, we adopt domain decomposition method to separate data previously, and use SPMD(Single Program Multiple Date) parallel program type to process parallel code. The data needed to exchange in simulation is achieved by MPI(Message Passing Interface). Besides, CG and GICGSTAB methods accompanied with Jacobi pre-conditioned method are used to solve linear equations.
The parallel simulation is of accuracy for results obtained from sequential and parallel algorithm, are almost the same with the references. On the other hand, since the simulation results of different number of elements reveal that parallel simulation is more efficient as elements increase, it''s worthwhile to adopt parallel simulation in cases with more complicated geometry.

摘要 I
ABSTRACT II
目錄 III
圖目錄 VI
表目錄 X
符號說明 XI
重要名詞中英對照 XIII
第一章、緒論 1
1-1研究目的與動機 1
1-2個人電腦叢集與平行計算 2
1-2-1個人電腦叢集之發展 2
1-2-2平行計算原理 5
1-2-3 MPI平行計算架構 7
1-3押出成型簡介 11
第二章、文獻回顧 14
2-1押出成型分析 14
2-2數值計算方法 15
2-3線性聯立方程組求解法 17
2-4區域分割計算方法 18
第三章、研究方法 19
3-1押出成形理論分析 19
3-1-1基本假設 19
3-1-2統御方程式 20
3-1-3邊界條件 21
3-2共位體心式有限體積法推導 22
3-2-1動量方程式的離散計算 23
3-2-2連續方程式的離散計算 24
3-2-3 SIMPLE去耦合疊代法 26
3-2-4能量方程式的離散計算 27
3-2-5循序計算流程 27
3-3區域分割方法 29
3-3-1分割流程 30
3-3-2界面資料交換處理 32
3-4線性聯立方程組求解之平行處理 33
3-5平行計算流程 36
第四章、結果與討論 39
4-1個人電腦叢集系統CAEPCC 39
4-1-1硬體設備 39
4-1-2軟體架構 42
4-1-3傳輸性能測試 43
4-2模擬計算之驗證 44
4-2-1循序計算結果正確性驗證 44
4-1-2平行計算結果正確性驗證 51
4-3衣架形平板押出模具之模擬 54
4-4平行計算效率探討 60
4-4-1效率值與加速比定義 60
4-4-2衣架形模頭模擬結果之平行效率探討 61
第五章、結論與展望 72
參考文獻 74
附錄 78
附錄A 衣架形押出模具之設計圖 78

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