應用GPU叢集與顯式多重網格方法求解不可壓縮流動問題

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研究生：	史曉磊 Shi, Xiaolei
論文名稱：	應用GPU叢集與顯式多重網格方法求解不可壓縮流動問題 An explicit multigrid scheme using artificial compressibility method for the simulation of unsteady incompressible flows on multi-GPU cluster
指導教授：	林昭安 Lin, Chao-An
口試委員:	牛仰堯 Niu, Yang-Yao 吳宗信 Wu, Jong-Shinn 陳慶耀 Chen, Ching-Yao
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：	2019
畢業學年度：	107
語文別：	英文
論文頁數：	41
中文關鍵詞：	人工壓縮方法、多重網格法、多GPU 、不可壓縮流動
外文關鍵詞：	artificial compressibility method, multigrid method, multi-GPU, incompressibility flow
相關次數：	點閱：3 下載：0
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基於人工可壓縮性方法，本研究提出了壹種在多GPU集群上工作的非穩態不可壓縮Navier-Stokes方程的顯式求解器。通過計算蓋驅動立方腔（LDC）內的三維（3D）層流和湍流流動，該求解器的數值精度得到了充分驗證。數值預測結果與基準解和實驗結果結果相比，不論是平均量和湍流統計平均量都十分吻合。對於雷諾數3200的LDC湍流流動，本研究對Taylor-Gortler-Like（TGL）渦旋進行了詳細分析，此算例中下遊的二次角渦（DSE）和TGL渦之間存在復雜的相互作用。
該求解器通過顯式FAS多重網格方案進行加速計算。數值測試結果表明與單層網格相比，7層多重網格可以提供高達250倍加速。此外，本研究討論了網格數量以及多重網格層數對FMG-FAS方法的性能影響。對於網格分辨率為256x256x256，采用4層多重網格的算例，GPU版本程序相對於串行的CPU程序加速值達到141倍。
此外，該研究中設計了細粒度重疊執行和通訊隱藏的代碼優化策略來輔助多GPU計算，weak scaling 的測試結果表明該GPU求解器在采用4層多重網格、32塊GPU的情況具有75%的並行效率。

An explicit solver for unsteady incompressible Navier-Stokes equations working on a multi-GPU cluster is presented, based on the artificial compressibility method. The numerical procedure is validated by computing three-dimensional (3D) laminar and turbulent flows within a lid-driven cubic cavity. The predicted results compare favorably with previous benchmark solutions and measurements, both in mean and turbulent quantities. For turbulent flow at Reynolds number 3200, the detailed analysis of the Taylor-G$\ddot{o}$rtler-Like (TGL) vortices are conducted, where there exist complex interactions between the downstream secondary corner eddy (DSE) and the TGL vortices. Computation is accelerated by an explicit FAS multigrid scheme. Up to 250 speedups for FAS Lev.7 is reported. Moreover, the influences of the grid number as well as the number of multigrid layers on the performance of FMG-FAS scheme are investigated. Significant GPU accelerations of the computations are achieved over CPU per core by a factor of 141 for FAS Lev.~4 for the resolution of $256^3$. Fine-grained overlapping strategies are designed to assist multi-GPU computations, weak scaling shows about 75\% for FAS Lev. 4 at 32 GPUs.

Abstract i
Dedication ii
Acknowledgments iii
List of Figures vii
List of Tables ix
Introduction 1
Numerical method 3
1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Multigrid methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Inter-grid transfer operation . . . . . . . . . . . . . . . . . . . . . . . 7
5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Multi-GPU implementation 10
1 Domain decomposition and communication . . . . . . . . . . . . . . . 10
2 Overlapping strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Numerical results 16
1 Laminar lid-driven cavity
ows . . . . . . . . . . . . . . . . . . . . . 16
2 Turbulent lid-driven cavity
ows . . . . . . . . . . . . . . . . . . . . . 18
3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Performance 22
1 Performance of FMG-FAS . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Single node performance . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Multiple node performance . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Conclusion 33
1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1 Inter-node communication . . . . . . . . . . . . . . . . . . . . 34
2.2 Multigrid implementation . . . . . . . . . . . . . . . . . . . . 35
Bibiography 37
Research achievement 41
                                

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