臺灣博碩士論文加值系統

本研究的目的在於求出波音X37試驗機於不同攻角下在極音速流中的阻力係數、升力係數、和弓形震波與X37的距離。在本研究中，兩種根據有限體積法(FVM)的方法，對流迎風分裂法(AUSM)和分裂HLL(SHLL)法被使用來解尤拉方程式(Euler equations)。兩種方法將會藉由全差變遞減格式(TVD)及MUSCL法來使其空間精準度擴展到二階精準度，而Minmod通量限制器將使用來減少在空間中非物理性質的震盪。另一方面，在計算流體力學的多維度計算中，很多問題包含了不只大尺度的流場之外，也包括了小尺度的物理現象。為了得到更精確的結果，需要增加更多的計算網格。因此，自適應性網格細化(Adaptive Mesh Refinement) 演算法被運用在穩態模擬上。我們運用局部無因次化密度梯度和壓力係數的變化來判斷流場中哪部分的網格需要進一步地細化。然而，由於資料在切割網格的過程中必須頻繁地在CPU和GPU間傳遞，AMR的整體運算效率將受限於傳遞資料的頻寬。另外，正方體和球體的模型將被用來驗證這些方法在恆比熱完全氣體中的準確性，同時，運用牛頓-拉弗森方法(Newton-Raphson method)可將熱完全氣體的特性表現於模擬中。最後，AMR技術在圖型處理器GTX Titan X對比於單核心英特爾 i5-4590的加速表現將做比較。

The goal of the thesis is to obtain the drag coefficient, lift coefficient, as well as the bow shock standoff distance for the Boeing-X37 orbital test vehicle with different angles of attack in hypersonic flow using a Computational Fluid Dynamics (CFD) approach. Two methods, the advection upstream splitting method (AUSM) and Split HLL (SHLL) method, based on a Finite Volume Method (FVM) are used to solve the Euler equations in this study. With the TVD-MUSCL method, the spatial accuracy is extend to second order, with the Minmod flux limiter employed to avoid non-physical oscillations in the spatial domain. In Computational Fluid Dynamics (CFD), there are many problems including the flow field with not only large scale but also small scale physical phenomenon in the multiple dimensional computation. To obtain the more accurate results, finer grids are needed in the computation. Therefore, in this study an Adaptive Mesh Refinement (AMR) algorithm is employed in steady state simulations. We use the local dimensionless density gradient and pressure coefficient to detect where the grids need to be refined into smaller sub-grids. However, the computational efficiency of the AMR algorithm is limited by the GPU memory bandwidth since the data is transported between host and device frequently within the refinement procedure. For the sake of verification using a calorically perfect gas, the cube and sphere model are used to verify the difference between simulation results and the theoretical results in reference. Using a Newton-Raphson method, the characteristics of thermally perfect gas can be captured in the simulation. In the conclusion, a comparison of speedup between GTX Titan X and Intel i5-4590 is discussed.

中文摘要 ii
Abstract iv
Acknowledgements vi
Contents vii
List of Tables x
List of Figures xi
Chapter 1 - Introduction 1
1.1 Governing equation 1
1.1.1 Conservation Laws and differential equations 1
1.1.2Navier-Stokes and Euler equations 2
1.2 Finite Volume Method 4
1.2.1 CFL number 6
1.3 High resolution scheme 7
1.3.1 Advection upstream splitting method (AUSM) 7
1.3.2 SHLL (Split HLL) method 10
1.3.3 TVD and flux limiters 12
1.3.4 Adaptive Mesh Refinement method 14
1.4 Aerodynamics 16
1.4.1 Aerodynamic coefficient 16
1.4.2 Hypersonic flow 19
1.4.2.1 Normal shock wave 19
1.4.2.1.1 Isentropic stagnation ratio 20
1.4.2.1.2 Flow properties ratio across normal shock 21
1.4.2.1.3 Stagnation to static pressure ratio 23
1.4.2.1.4 Oblique shock wave 23
1.4.2.2 High-Temperature gas dynamics 24
1.4.2.3 Mach independence 28
1.5 Parallel Computing 29
1.5.1 Parallelization Theory 30
1.6 Graphical Processing Unit 34
1.6.1 GPU memory 34
1.6.2 CUDA threads, Blocks, Grids 36
1.6.3 CUDA API 40
Chapter 2 – Methodology 42
2.1 Implementation 42
2.1.1 Implementation of ray casting method 42
2.1.2 Thermally perfect gas implementation 43
2.1.3 Implementation of AUSM and SHLL 44
2.1.4 Flux calculation- extension of 2nd spatial accuracy 45
2.1.5 AMR Implement 47
2.1.5.1 Refinement criterion 47
2.1.5.2 Cell generation 48
2.1.5.3 Organization of cell Neighbors 49
2.1.6 Calculate aerodynamic characteristic 49
2.2 Data structure 50
2.2.1 Structured Cartesian grids 50
2.2.2 Adaptive Mesh Refinement data structure 51
2.3 Average difference and Performance 51
2.4 GPU parallelization 52
2.4.1 Memory management on the GPU with CUDA API 52
2.4.2 CPU-Launched GPU kernels 53
2.4.3 GPU-Launched GPU kernels 54
2.4.4 Compiling the code 54
Chapter 3 – Results 55
3.1 One dimensional shock tube problem 55
3.2 Three dimension bluff bodies in steady hypersonic flow 57
3.3 Calorically perfect gas versus thermally perfect gas in hypersonic flow 59
3.4 X37 spacecraft in steady hypersonic flow at different angle of attack 61
3.5 The accuracy and performance of AMR algorithm in steady hypersonic flow 62
Chapter 4 – Conclusion 65
Reference 67
Tables 70
Figures 85

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