非結構性三角網格生成在車流模擬應用之研究

Abstract

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.