# 臺灣博碩士論文加值系統

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 本研究完成非結構調適網格(h-refinement)於三維直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)之應用。當網格內的Kn 小於標準值時，使用isotropic調適法建立新的網格。然而，這個簡易的方法會有多個重要的因素影響了蒙地卡羅法(DSMC)的表現。因此，我們應用了anisotropic調適法，移除懸掛點(hanging node)。它解決調適網格所會遇到懸掛點(hanging node)的所有困難。同時，這個方法所增加的工作量是可以忽略不計的。我們已然使用以氦氣，不同的網格:四面體的，六面體的，五面體的，或是三者混合的網格，測試高速度cavity流場，和超音流流經一圓球障礙物。結果證明，利用調適網格得到較好的改善。利用調適網格計算上的代價遠小於蒙地卡羅法(DSMC)本身。因此，我們得到一個結論，利用調適網格法較原始的非調適網格法有較正確的結果。
 The implementation of an adaptive mesh embedding (h-refinement) schemes using unstructured grid in three-dimensional Direct Simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new meshes where local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the three-dimensional DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the anisotropic refinement. This is completed by simply connect the hanging node(s) with the other non-hanging node(s) in the non-refined, interfacial cells. In contrast, this remedy increases negligible amount of work; however, it removes all the difficulties presented in the scheme with hanging nodes. We have tested the proposed scheme for Argon gas using different types of mesh, such as tetrahedron, hexahedron, and pyramid or mixed, to a high-speed driven cavity flow and, then, a hypersonic flow over a sphere. The results show an improved flow resolution as compared with that of unadaptive mesh.
 中文摘要 I ABSTRACT II LIST OF TABLES IV LIST OF FIGURES V NOMENCLATURE VII CHAPTER 1 INTRODUCTION 1 1.1 Rarefied Gas Dynamics 1 1.2 Solution Methodologies 1 1.3 Structured and Unstructured Mesh 3 1.4 Mesh Adaptation 3 1.5 Concerns Related to Mesh Adaptation 6 1.6 Objectives of the Thesis 9 1.7 Organization of the Thesis 9 CHAPTER 2 THE DSMC METHOD WITHMESH ADAPTATION 10 2.1 The Conventional DSMC Method 10 2.2 The DSMC Method with Mesh Adaptation 11 2.2.1 General Features 11 2.2.2 Adaptation Parameters and Criteria 12 2.2.3 Adaptation Procedures 13 2.2.4 Surface Representation 19 CHAPTER 3 BENCHMARK TESTS 21 3.1 A High-Speed Driven Cavity Flow 21 3.2 A Hypersonic Flow Over a sphere 23 CHAPTER 4 CONCLUSIONS AND FUTURE WORK 26 4.1 Conclusions 26 4.2 FUTURE WORK 26 REFERENCES 28