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研究生:陳璞
研究生(外文):Pu Chen
論文名稱:非結構性三角網格生成在車流模擬應用之研究
論文名稱(外文):Unstructured Triangular Mesh Generation and Application to Traffic Flow Simulation
指導教授:卓訓榮卓訓榮引用關係李義明李義明引用關係
指導教授(外文):Hsun-Jung ChoYiming Li
學位類別:碩士
校院名稱:國立交通大學
系所名稱:運輸科技與管理學系
學門:運輸服務學門
學類:運輸管理學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:83
中文關鍵詞:三角網格單不規則點網格結構網格網格加切車流模擬
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網格(Mesh)是近代電腦模擬與數值計算中不可或缺的一環,一個好的網格不但可以提升答案的準確度,同時也可以大大地降低計算所需的時間。對於網格生成方法來說,加切網格幾何比的品質好壞,以及處理複雜區域問題的能力決定了演算法的適用與效率性。本研究針對不同的網格結構如:結構網格(Structured mesh)、單不規則點網格(1-Irregular mesh)、三角網格(Triangular mesh)的生成以及加切演算法作系列探討與優缺點比較。同時針對數個不同之工程問題發展出事先猜測加切技術,以減少計算時間的浪費,提昇科學計算的準確性。事先猜測加切技術是指在電腦模擬前先針對問題之特性加以分析,約略判斷解變化劇烈的區域,並在此區域中作有效的網格加切,以得到一個符合工程效益的密集網格,減少實際計算時間、提升答案的準確度。
本研究發展之三角網格和事先猜測加切技術已經成功應用於數個不同工程問題之模擬與分析上。對於道路平面幾何上如T字形路口、十字型路口、具有安全島的十字型路口、外側車道封閉路段、彎曲路段以及三叉路口,運用吾人所發展之方法其所生成與加切的網格完全符合交通車流之意義。本研究對於電腦模擬大型網路與車流具有正面之幫助,同時亦具有實際問題應用之價值。

The quality of mesh is an essential element in modern numerical computation. It is known that a well-designed and -generated mesh structure can increase the accuracy of solution and reduce the time cost of simulation process in various science and engineering problems. The mesh structure and refinement algorithm for multidimensional complicated geometries play important roles in developing any cost effective mesh generation schemes. In this work three most popular mesh structures, structured mesh, 1-irregular mesh, and triangular mesh have been investigated and compared comprehensively. Before performing a large-scale computing, a prior predictive refinement technique is applied to reduce simulation CPU time. This approach is mainly relied on the prediction of the solution shape and variation for a specified model problem. Based on the developed refinement algorithm, a triangular mesh generation program has been successfully developed and tested on different model problems, such as semiconductor nano devices, structure design and optimization, and traffic flow simulation. The developed program has also been applied to various network linking topologies, for example crossroad, crossroad with safety island, outside road closed, winding road, and road junction. By considering the driver`s responses and traffic flow phenomena, the generated meshes for these cases here precisely located the variations of traffic density and velocity.

中文摘要 I
英文摘要 II
誌 謝 IV
目 錄 V
圖目錄 VII
表目錄 IX
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
1.3 研究內容 6
1.4 研究方法與流程 7
第二章 文獻回顧 9
第三章 數學模式與電腦模擬 13
3.1 數學模式 13
3.1.1 橢圓型偏微分方程式 13
3.1.2 拋物型偏微分方程式 14
3.1.3 雙曲型偏微分方程式 14
3.1.4 車流波動方程式 15
3.2 電腦模擬 17
3.2.1 有限差分法 18
3.2.2 有限元素法 19
3.2.3 有限體積法 20
第四章 網格的性質與網格生成 22
4.1 網格的性質 22
4.2 結構網格 25
4.3 單不規則點網格 26
4.4 三角網格 29
第五章 網格加切方法比較與應用 32
5.1 網格加切方法比較 32
5.2 事先猜測加切方法 39
第六章 實際應用範例 43
6.1 T字型路口 43
6.2 十字型路口 46
6.3 具有安全島的十字型路口 48
6.4 外側車道封閉路段 51
6.5 彎曲路段 52
6.6 三叉路口 53
第七章 結論與建議 56
7.1 結論 56
7.2 建議 57
參考文獻 58
附錄A 三角化的性質 60
附錄B 網格生成程式架構圖 70
附錄C 網格生成程式類別定義 71
附錄D 有限體積法程式架構圖 74
附錄E 有限體積法程式類別定義 75
附錄F 本研究於半導體元件模擬之應用 77
簡 歷 82

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