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作者(中文):黃立民
作者(外文):Huang, Li-Min
論文名稱(中文):應用二維切割和多圖形顯示卡叢集電腦於晶格波茲曼法數值模擬
論文名稱(外文):Implementation of Lattice Boltzmann method simulations on multi-GPU cluster using two-dimensional domain decomposition
指導教授(中文):林昭安
口試委員(中文):吳宗信
何正榮
學位類別:碩士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
學號:101033511
出版年(民國):103
畢業學年度:102
語文別:英文
論文頁數:46
中文關鍵詞:GPU
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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 multi-GPU. The optimization of multi-GPU with two-dimensional domain decomposition is also discussed here. The numerical results are validated with benchmark solutions and the performance of the GPU implementation is also discussed. In the present work, we can achieve 17664.23 MLUPS for 384X384X384 grids with 96 nVIDIAr Tesla M2070 GPU cards.
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 . . . .... . . . . . . . . 5
1.3 Motivation and objective . . . . . . . . . . . 6
2 Methodology 7
2.1 The Boltzmann equation . . . . .............. . 7
2.2 The BGK approximation . . . . . . . . . . . . . . . . 8
2.3 The low-Mach-number approximation . . . . . . . . . 10
2.4 Discretization of the Boltzmann equation . . . . . . 11
2.4.1 Discretization of time . . . . . . . . . . . . . . 11
2.4.2 Discretization of phase space . . . . . . . . . . 13
2.5 The Chapman-Enskog expansion . . . . . . . . . . . . 15
2.6 The multi-relaxation-time lattice Boltzmann model. . 15
3 Numerical algorithm 20
3.1 Simulation procedure . . . . . . . . . . . . . . . . 20
3.2 Boundary condition implementations . . . . . . . . . 21
3.3 GPU implementation . . . . . . . . . . . . . . . . . 22
3.4 Two-dimensional domain decomposition . . . . . . . . 24
4 Numerical results 29
4.1 Cavity flow simulations using GPU . . . . . . . . . 29
4.2 Performance with multi-GPU implementation . . . . . 29
5 Conclusions 38
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