正規化邊界積分法及邊界元素法對三維流場之研究

Abstract

本文利用正規化邊界積分法以及邊界元素法兩種數值分析方法對三維流場問題進行探討，並針對奇異點問題以不同方法進行計算，討論其在數值結果上之差異。本研究假設三維流場內之流體滿足勢流理論，並以兩種方法進行討論。其一，利用邊界元素法描繪幾何邊界上之物理量分佈情形，接著以高斯積分對離散後的積分方程式進行積分並組成核函數矩陣。其二，以邊界積分法的佈點概念結合面積權重的計算求得核函數矩陣之數值，以獲得模型表面上之未知物理量。利用此兩種方法結合不同元素之節點分佈方式，計算三維球體及橢球體模型之內、外流場問題，比較及討論其計算結果之均方根誤差、運算時間以及計算複雜度。

There are two numerical analysis methods are used in this paper to discuss the three-dimensional flow field problem. They are the regularized boundary integral method and the boundary element method respectively. We also use different methods to calculate the singular point problem and discuss the differences in numerical results. Assume the fluid in the three-dimensional flow field satisfies the potential flow theory. First, the boundary element method is used to describe the distribution of physical quantities on the boundary. Then, using Gaussian integral to integrate the discretized integral equation and form a kernel function matrix. Second, we use the point distribution concept of the boundary integral method combines with the calculation of weights to obtain the value of the kernel function matrix. With the matrix, we are able to obtain the unknown physical quantities on the model surface.These two methods are combines with the node distribution of different elements to calculate the internal and external flow field problems of the three-dimensional sphere and ellipsoid model. Furthermore, the root mean square error, calculation time and computational complexity of the calculation results are also compared.