GPU加速數模於二維穩態不可壓縮穴流之研究

GPU ACCELERATED SIMULATIONS OF TWO-DIMENSIONAL STEADY INCOMPRESSIBLE CAVITY FLOW

10.6652/JoCICHE.201706_29(2).0004

謝東洲(Tung-Chou Hsieh)；葉克家(Keh-Chia Yeh)

GPGPU ； CUDA ； 穴流 ； 有限差分法 ； GPGPU ； CUDA ； cavity ； finite difference

中國土木水利工程學刊

29卷2期（2017 / 06 / 01）

97 - 107

繁體中文

圖形處理器（graphic processing unit，GPU）源自於處理電腦遊戲大量貼圖運算，現今透過計算統一架構（compute unified device architecture，CUDA）能夠有效的運用其高度計算能力、儲存器帶寬於科學計算方面。在水利方面所面臨的大量計算問題，如集水區淹水演算、三維水理及動床演算等，數據規模大小已經達到TB 甚至於PB 量級，對計算效能構成了嚴峻的挑戰。本研究藉GPU 以有限差分法求解二維穩態不可壓縮穴流，評估GPU 加速於數值模擬之效益。本研究以nVidia GeForce GTX 480、GTX 970 作為平行計算之GPU設備，CPU 方面選用Intel^® Core^(TM)2 i7-4790 進行串行計算，在長寬比為7，網格點數達257×1793 時，加速成效介於13 ~ 20 倍加速效果。

The development of graphic processing unit (GPU) originated from processing a great deal of mapping operation in computer games. Nowadays, GPU can apply its strong computing power and bandwidth of storage effectively to science computation by using compute unified device architecture (CUDA). There are a large amount of hydraulic computational problems we will face. For instance, model for watershed inundation, three-dimensional hydraulic model, three-dimensional mobile-bed model etc. The data size abovementioned has reached to TB even to PB, and it yields a rigorous challenge to computing efficiency. This study takes GPU combined with finite difference method to solve two-dimensional steady incompressible cavity flow, and evaluates the beneficial result of numerical simulation accelerated. This study implemented on nVidia parallel programming and computing platform with GTX 480 and 970 graphic cards. The results were compared with traditional serial computing results obtained by Intel^® Core^(TM)2 i7-4790. When the aspect ratio is 7 and grid number reaches to 257 × 1,793, there are 13 ~ 20 times acceleration effect.

1. (2014).NVIDIA CUDA Programming Guide.
2. Batchelor, G. K.(1956).A proposal concerning laminar wakes behind bodies at large Reynolds number.Journal of Fluids Mechanics,1,388-398.
3. Brandvik, T.,Pullan, G.(2008).Acceleration of a 3D Euler solver using commoditygraphics hardware.46th AIAA Aerospace Sciences Meeting and Exhibit
4. Burggraf, O. R.(1966).Analytical and numerical studies of the structure of steady separated flows.Journal of Fluids Mechanics,24,113-151.
5. Cheng, M.,Hung, K. C.(2006).Vortex structure of steady flow in a rectangular cavity.Computers and Fluids,35,1046-1062.
6. Fritzsche, M.(2009).Institut für Angewandte Mathematik, Friedrich-Schiller-Universität.
7. Ghia, U.,Chia, K. N.,Shin, C. T.(1982).High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid Method.Journal of Computational Physics,48,387-411.
8. Khorasanizade, S.,Sousa, J. M.(2014).A detailed study of lid-driven cavity flow at moderate Reynolds numbers using incompressible SPH.International Journal for Numerical Methods in Fluids,76,653-668.
9. Koseff, J. R.,Street, R. L.(1984).On end wall effects in a lid-driven cavity flow.Journal of Fluids Engineering, ASME,106,385-389.
10. Kuznik, F.,Obrecht, C.,Rusaouen, C.,Roux, J. J.(2010).LBM based flow simulation using GPU computing processor.Computers and Mathematics with Applications,59,2380-2392.
11. Pan, F.,Acrivos, A.(1967).Steady flows in rectangular cavitys.Journal of Fluid Mechanics,28,643-655.
12. Patil, D. V.,Lakshmisha, K. N.,Rogg, B.(2006).Lattice Boltzmann simulation of lid-driven flow in deep cavities.Omputers and Fluids,35,116-1125.
13. Ramaswamy, B.,Tue, T. C.,Akin, T. E.(1992).Finiteelement analysis of unsteady two-dimensional Navier-Stokes equations.Numerical Heat Transfer, Part B,21,147-182.
14. Spotz, W. F.(1998).Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible streamfuction vorticity.International Journal for Numerical Methods in Fluids,28,737-757.
15. Szewc, K.,Pozorski, J.,Minier, J. P.(2012).Analysis of the incompressibility constraint in the smoothed particle hydrodynamics method.International Journal for Numerical Methods in Engineering,92,343-369.
16. Thibault, J. C.,Senocak, I.(2009).CUDA implementation of a Navier-Stokes solver on Multi-GPUDesktop platforms for incompressible flows.47th AIAA Aerospace Sciences Meeting,Orlando FL:
17. Tölke, J.(2008).Implementation of a lattice boltzmann kernel using the computeunified device architecture developed by nVIDIA.Journal Computing and Visualization in Science,13(1),29-39.
18. Zhang, J.(2003).Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes.Computer and Mathematics with Applications,45,43-52.