邊界元素法及正規化邊界積分法對三維流體之計算分析

Abstract

本文對三維流場問題分別以邊界元素法以及正規化邊界積分法進行分析，並且針對不同方法的數值分析結果進行探討。其中，兩種分析方法皆以邊界積分方程式作為理論基礎。本研究假設流場內之流體滿足勢流理論之基本假設，並且針對單位球體分別以不同的數值分析方法計算出球體表面的未知物理量。邊界元素法計算方面，使用了二次元素以進行計算，並且探討不同階數形狀函數的分析結果。邊界積分法計算方面，透過不同的數值積分理論改變計算節點的分布方式，以及節點所對應的權重因子。針對不同分析方法的均方根誤差、計算時間進行互相比較，並且探討出計算效率最高的分析方法。

This paper analyzes the three-dimensional flow field problem using two numerical methods, and discusses the results of different methods. They are the boundary element method and the boundary integral method both of which use boundary integral equations as rationale, respectively. In the study, we assume the fluid in the flow field satisfies the potential flow theory, and calculate the unknown physical quantities on the surface of the unit sphere using different numerical analysis methods. In the boundary element method, quadratic elements are used for calculation, and the analysis results of different orders of shape functions are discussed. In the boundary integral method, different numerical integration theories are applied to change the distribution of calculation nodes and the weight factors corresponding to the nodes. The root mean square error and calculation time of different analysis methods are compared with each other to find out the analysis method with the highest calculation efficiency.