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研究生： 吳培綸
Wu, Pei Lun
論文名稱： 利用GPU平行計算在非結構性網格下的真實流向靜態直接模擬法
True Direction QDS Simulations on Unstructured Grids Using GPU
指導教授： 李汶樺
Matthew Smith
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2018
畢業學年度： 106
語文別： 中文
論文頁數： 130
中文關鍵詞： 計算流體力學 、有限體積法 、靜態直接模擬法 、非結構性網格 、平行計算 、圖形處理器 、CUDA
外文關鍵詞： Computational Fluid Dynamics, Finite Volume Method, Quiet Direction Simulation, Unstructured grid, Parallel Computing, Graphics Processing Unit(GPU), CUDA
相關次數： 點閱：114  下載：2 
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    • 隨著工程問題漸趨複雜，傳統的計算流體力學不再只是著重在結構性的卡氏座標網格，本研究提出一新方法稱為三角網格下的靜態直接模擬法(QDS Triangular Meshes method, QDS-tri)，其改良自以往的靜態直接模擬法(Quiet Direct Simulation, QDS)。QDS方法利用數值積分的方式取代了平衡通量法(Equilibrium Flux Method, EFM)經由積分速度機率分布函數之通量計算，並且由於其真實流向的特性，通量的計算不再受限於像以往傳統的有限體積法(Finite Volume Method, FVM)只能存取於網格間的介面通量。儘管過往有發展過於三角網格下之QDS方法，但是卻是利用方向解耦(direction decoupling)之通量計算。因此在此研究中我們延伸發展了三角網格下的QDS方法，同時保留著其真實流向的特性。為了確認QDS-tri方法之可行性，該方法運用偽一維震波管問題、二維爆炸波問題以及高超速流場問題來驗證，同時也和其他的方法之結果比較。
    此外，我們運用圖形處理器(Graphics Processing Unit, GPU)的平行運算架構透過CUDA技術來加快計算速度。從最佳結果來看，利用輝達(Nvidia)的GTX Titan X計算下約比單核心的Intel Xeon E5 2650搭配著SSE向量化及最佳化的計算快上了9.6倍。

    As the engineering problems become more and more complicated, the conventional Computational Fluid Dynamics are no longer focused on the structured Cartesian grids. This study present an adaptation of the Quiet Direct Simulation (QDS), named the “Quiet Direct Simulation on Triangular meshes (QDS-tri) method. The QDS method is an approximation of the Equilibrium Flux Method (EFM) whereas replaces analytical moments of molecular velocity distribution functions with the numerical integrals. Also with the true directional nature of QDS, the fluxes can be delivered among the diagonal cells which they do not share the interface while the conventional finite volume method compute the fluxes across the interface shared by adjacent cells. Although previous research have developed on unstructured (triangular) grids, it was performed by directionally decoupled variation of QDS with pseudo one-dimensional fluxes. This study extend to develop the QDS method on 2D triangular meshes while retaining direction coupling. In order to demonstrate the QDS-tri method, there are several benchmark studies applied by QDS-tri method to verify the physical phenomenon. These studies include pseudo one-dimensional shock tube and two dimensional blast wave and hypersonic flow problems, which are compared with other solvers.
    Furthermore, we apply Graphics Processing Unit (GPU) parallel computing architecture to improve the computation speed through the application of Compute Unified Device Architecture (CUDA). The maximum speed up is approximately 9.6x compared with Nvidia GTX Titan X and Intel Xeon E5 2650 CPU core using SSE vectorization / optimization.

    Contents 摘要 i Abstract iii Acknowledgements v Contents vi List of Tables ix List of Figures x Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Governing Equation 3 1.2.1 Continuity Equation 4 1.2.2 Navier-Stokes and Euler equation 5 1.3 Finite Volume Methods in Computational Fluid Dynamics 7 1.3.1 Finite Volume Method 7 1.3.2 CFL number 9 1.3.3 Direction Decoupling 11 1.3.4 Riemann Problem 12 1.3.5 Equilibrium Flux Method 19 1.3.6 Particle Flux Method 22 1.3.7 Quiet Direct Simulation Method 23 1.4 Parallel Computing and Graphics Processing Units 26 1.4.1 GPU Memory 28 1.4.2 CUDA Threads, Blocks and Grids 29 1.4.3 CUDA Application Programming Interface 30 Chapter 2 Methodology 33 2.1 Data Construction 33 2.1.1 Model and Parameters Construction 33 2.1.2 Data Transfer 35 2.2 QDS Triangular Meshes method 36 2.2.1 Introduction of the QDS-tri method 36 2.2.2 The Concept of QDS-tri method Algorithm 38 2.2.3 Implementation of QDS-tri method 42 2.3 GPU Parallelization 44 2.3.1 Memory Management on the GPU using CUDA 45 2.3.2 GPU Kernels Launched by CPU 47 2.3.3 GPU Kernels Launched by GPU 48 2.3.4 Compilation of CUDA in Linux 49 2.3.5 QDS-tri method Parallelization Implementation 49 Chapter 3 Results 51 3.1 Shock Tube Problem 51 3.2 Blast Wave Problem 54 3.3 Hypersonic Flow Over a Forward Facing Step 56 3.4 Hypersonic Flow Over a Wedge 58 3.5 Analysis of Parallel Performance 59 Chapter 4 Conclusion 62 References 64 Tables 66 Figures 73  

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