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研究生: 洪培堯
論文名稱: 晶格波爾茲曼方法應用於多圖形顯示卡計算
Lattice Boltzmann model with multi-GPU implementation
指導教授: 林昭安
口試委員: 吳宗信
陳慶耀
林昭安
學位類別: 碩士
Master
系所名稱: 工學院 - 動力機械工程學系
Department of Power Mechanical Engineering
論文出版年: 2013
畢業學年度: 101
語文別: 英文
論文頁數: 55
中文關鍵詞: 晶格波茲曼圖形顯示卡計算
外文關鍵詞: Lid-driven cavity
相關次數: 點閱:2下載:0
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  • In this thesis, the implementation of GPU with CUDA architecture on lattice
    Boltzmann model is presented. Simulations of 3D lid-driven cavity flow is conducted
    as a test case with single GPU and multi-GPU. The optimization of single GPU
    and multi-gpu parallel efficiency is also discussed here. The numerical results are
    validated with benchmark solutions and the performance of the GPU implementation
    is scrutinized by comparisons with its CPU counterpart.


    1 Introduction 1 1.1 Introduction to lattice Boltzmann equation . . . . . . . . . . . . . . . 1 1.2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Theory of lattice Boltzmann models . . . . . . . . . . . . . . . 2 1.2.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.3 3-D lid driven cavity flows . . . . . . . . . . . . . . . . . . . . 4 1.2.4 GPU implementation . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Motivation and objective . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Methodology 8 2.1 The Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The BGK approximation . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 The low-Mach-number approximation . . . . . . . . . . . . . . . . . . 11 2.4 Discretization of the Boltzmann equation . . . . . . . . . . . . . . . . 12 2.4.1 Discretization of time . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Discretization of phase space . . . . . . . . . . . . . . . . . . . 14 2.5 The Chapman-Enskog expansion . . . . . . . . . . . . . . . . . . . . 16 2.6 The multi-relaxation-time lattice Boltzmann model . . . . . . . . . . 16 3 Numerical algorithm 21 3.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Boundary condition implementations . . . . . . . . . . . . . . . . . . 22 ii 3.3 GPU implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 Numerical results 29 4.1 Cavity flow simulations using GPU . . . . . . . . . . . . . . . . . . . 29 4.1.1 Numerical validation . . . . . . . . . . . . . . . . . . . . . . . 29 4.1.2 3D lid-driven cavity flow simulations . . . . . . . . . . . . . . 30 4.2 Performance with different implementation . . . . . . . . . . . . . . 30 4.2.1 Single GPU implementation . . . . . . . . . . . . . . . . . . . 30 4.2.2 Multi-GPU implementation . . . . . . . . . . . . . . . . . . . 32 5 Conclusions 46

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