# 臺灣博碩士論文加值系統

(44.221.73.157) 您好！臺灣時間：2024/06/20 09:23

:::

### 詳目顯示

:

• 被引用:1
• 點閱:255
• 評分:
• 下載:0
• 書目收藏:0
 在這篇論文中，我們應用區域多元二次微分積分法求解卜易松、赫姆霍茲特徵值與穴室流場問題。無網格數值方法有許多種類﹐本方法是基於區域分解技術並結合多元二次法與微分積分法，也是無網格數值方法的一種。因此，本方法仍保有無網格法不需要建立網格組織的特性。在本論文中，我們使用此方法與傳統多元二次法、理論解析解、以及其他數值方法結果作比較。本論文主要貢獻在於應用此方法在不規則區域以及方法的行為分析。由比較結果可以看出此方法與其他方法的結果相當吻合。因此﹐我們認為此數值方法是一可信賴且有效率的方法。
 In this thesis, we employ the meshless local Multiquadric Differential Quadrature method (LMQDQ method) to deal with the Poisson, Helmholtz eigenvalue and cavity flow problems. Meshless methods can be classified as lots of categories. The numerical method in this thesis combines the Multiquadric method (MQ method) and the domain decomposition technique in Differential Quadrature (DQ) form. Thus, this method keeps the mesh-free property. We will discuss this method in the thesis and compare the results with those obtained by the conventional MQ method, analytic solutions or numerical solutions made by other methods. The main contribution of the thesis is to employ LMQDQ method to solve irregular domain problem and the behavior analysis of this method. These results indicate that this method is reliable and efficient.
 Table of contents摘要 IAbstract IITable of contents IIITable caption VFigure caption VIChapter 1 Introduction 11.1 Objective 11.2 Outline of the thesis 2Chapter 2 Literature review and formulation of LMQDQ method 42.1 DQ method 42.1.1 Advantages and weaknesses of DQ method 92.2 Meshless methods, RBFs and MQ method 142.2.1 RBFs 142.2.2 MQ RBF 162.2.3 Weaknesses of RBFs interpolation 172.3 Formulation of LMQDQ method 18Chapter 3 Numerical solutions of Poisson equation using LMQDQ method 213.1 Results of Dirichlet boundary condition 213.2 Results of Neumann boundary condition 31Chapter 4 Helmholtz eigenvalue problem 424.1 Governing equations and SVD technique 424.1.1 Governing equations 424.1.2 Singular value decomposition 454.2 Square eigenvalue problem 474.2.1 Results and comparisons for square TM case 484.2.2 Results and comparisons for square TE case 504.3 Circular eigenvalue problem 534.3.1 Results and comparisons for circular TM case 544.3.2 Results and comparisons for circular TE case 574.4 Multi-connected domain eigenvalue problem 604.5 Peanut-shaped eigenvalue problem 67Chapter 5 Cavity flow problem 725.1 The velocity-vorticity formulation 725.2 Steady Stokes cavity problem 745.3 Steady Navier-Stokes cavity problem 78Chapter 6 Conclusion, recommendations and further works 856.1 Conclusions 856.2 Recommendations and further works 86References 87