使用多圖形顯示卡叢集與晶格波茲曼法模擬氣泡上升動力學問題

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研究生：	張健益 Chang, Chien-Yi
論文名稱：	使用多圖形顯示卡叢集與晶格波茲曼法模擬氣泡上升動力學問題 Lattice Boltzmann Simulations of Bubbles Rising Dynamics on Multi-GPU Cluster
指導教授：	林昭安 Lin, Chao-An
口試委員:	陳慶耀 Chen, Ching-Yao 林洸銓 Lin, Kuang-C
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：	2017
畢業學年度：	105
語文別：	英文
論文頁數：	51
中文關鍵詞：	晶格波茲曼法、多相流模型、高密度差、假性速度、氣泡上升、圖形顯示卡
外文關鍵詞：	multi-phase, large density ratio, spurious velocity, Bubble rising
相關次數：	點閱：2 下載：0
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在本研究中使用Lee所提出的晶格波茲曼模型進行三維的多相流模擬計算，並在多張圖形顯示卡叢集上運行以獲得高效率的結果。其中驗證的例子有消除氣泡周圍由於數值誤差而產生的假性速度。在單球上升的模擬中，討論在不同無因次參數bond number和Morton number下，對於氣泡上升過程的變形過程以及終端速度的影響，不論是模擬的變形過程以及雷諾數都與實驗結果相符合。而雙球上升的模擬中，無論初始氣泡是在同軸或非同軸的狀態，都可以觀察到下方氣泡由於上方氣泡產生的尾流而加速上升的現象。經由不同氣泡大小的設定，也能發現體積大的氣泡受到流場的影響也較大。此外，將二維平行切割應用在多圖形顯示卡叢集，效能測試的結果顯示即使使用多張圖形顯示卡計算，依舊能維持高平行效率。

In this thesis, a three-dimensional two-phase lattice Boltzmann model [28] is adopted on multi graphic processing unit (GPU) cluster. Such a binary system at high density ratio is carried out with high performance of computation. In the study, The spurious velocity caused by the force imbalance near the two-phase interface can be successfully suppressed in the simulation. A single bubble rising in a rectangular domain is discussed with different regimes of Bond number (Bo) and Morton number (Mo). The terminal Reynolds number (Re) and the deformed shape are consistent with both experimental results [23] and simulation results obtained by Lee et al. [28]. The phenomenon of the trailing bubble catching up the leading bubble is observed. Further, an efficient multi-GPU cluster implementation with two
dimensional decomposition is examined and the program maintains good scalability even in the case with high GPU number.

Introduction                                                   1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Lattice Boltzmann method . . . . . . . . . . . . . . . . . 1
1.2 Multiphase fluid systems . . . . . . . . . . . . . . . . . 2
1.3 Graphics processing unit . . . . . . . . . . . . . . . . . 2
2 Literature survey . . . . . . .  . . . . . . . . . . . . . . 3
2.1 Lattice Boltzmann multiphase model . . . . . . . . . . . . 3
2.2 Bubble dynamics. . . . . . . . . . . . . . . . . . . . . . 4
2.3 GPU implementation . . . . . . . . . . . . . . . . . . . . 6
3 Objective and motivation . . . . . . . . . . . . . . . . . . 7
Theory and governing equations                                 8
1 The Boltzmann equation . . . . . . . . . . . . . . . . . . . 8
2 The BGK approximation. . . . . . . . . . . . . . . . . . . . 9
3 The low-Mach-number approximation . . . . . . . . . . . . . 11
4 Discretization of the Boltzmann equation. . . . . . . . . . 12
4.1 Discretization of phase space . . . . . . . . . . . . . . 12
4.2 Dicretization of time . . . . . . . . . . . . . . . . . . 13
5 The free-energy model . . . . . . . . . . . . . . . . . . . 14
6 Lattice Boltzmann model for multiphase flow . . . . . . . . 15
6.1 The governing equations . . . . . . . . . . . . . . . . . 15
6.2 Discrete Boltzmann equation . . . . . . . . . . . . . . . 15
6.3 Interface capturing equation. . . . . . . . . . . . . . . 17
Numerical algorithm                                           20
1 Simulation procedure. . . . . . . . . . . . . . . . . . . . 20
2 Gradient treatments . . . . . . . . . . . . . . . . . . . . 21
3 Boundary condition. . . . . . . . . . . . . . . . . . . . . 22
4 GPU implementation. . . . . . . . . . . . . . . . . . . . . 23
4.1 Memory access . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Multi-GPU implementation. . . . . . . . . . . . . . . . . 24
Numerical results                                             28
1 Spurious velocity elimination . . . . . . . . . . . . . . . 28
2 One bubble rising . . . . . . . . . . . . . . . . . . . . . 29
3 two bubbles rising. . . . . . . . . . . . . . . . . . . . . 30
3.1 In-line case. . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Off-line case . . . . . . . . . . . . . . . . . . . . . . 32
4 Performance of GPU implementation . . . . . . . . . . . . . 33
Conclusions                                                   45
                                

[1] U. Frisch, B. Hasslacher, and Y. Pomeau, “Lattice-gas automata for the Navier- Stokes equation,” Phys. Rev. Lett. 56, 1505, (1986).
[2] S. Wolfram, “Cellular automaton fluids 1: Basic theory,” J. Stat. Phys. 45, 471, (1986).
[3] F. J. Higuera, S. Sussi, and R. Benzi, “3-dimensional flows in complex geometries with the lattice Boltzmann method,” Europhys. Lett. 9, 345, (1989).
[4] F. J. Higuera, and J. Jem´enez, “Boltzmann approach to lattice gas simulations,” Europhys. Lett. 9, 663, (1989).
[5] P. L. Bhatnagar, E. P. Gross, and M. Grook, “A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems,” Phys. Rev. E 94, 511, (1954).
[6] S. Harris, “An introduction to the throry of the Boltzmann equation,” Holt, Rinehart and Winston, New York, (1971).
[7] U. Frisch, D. d’Humi`eres, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.
P. Rivet, “Lattice gas hydrodynamics in two and three dimensions,” Complex Syst. 1, 649, (1987).
[8] D. O. Martinez, W. H. Matthaeus, S. Chen, and D. C. Montgomery, “Comparison of spectral method and lattice Boltzmann simulations of two- dimensional hydrodynamics,” Phys. Fluids. 6, 1285, (1994).
[9] S. Osher and R. P. Fedkiw, “Level set method: An overview and some recent results,” J. Comput. Phys. 169, 463, (2001).
[10] R. Scardovelli and S. Zaleski, “Direct numerical simulation of free-surface and interfical flow,” Annu.Rev.Fluid Mech. 31, 567, (1999).
[11] T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, “Boundary integral methods for multicomponent fluids and multiphase materials,” J. Comput.Phys. 169, 302, (2001).
[12] P. Y. Hong, L. M. Huang, L. S. Lin, and C.A. Lin, “Scalable multi-relaxation- time lattice Boltzmann simulations on multi-GPU cluster,” Computers & Fluids. 110, 1-8, (2015).
[13] X. Shan and H. Chen, “Lattice Boltzmann model for simulating flows with multiple phases and components,” Phys. Rev. E. 47, 1815-1819, (1993).
[14] X. Shan and H. Chen, “Simulation of Nonideal Gases and Liquid-GasPhase Transitions by the Lattice Boltzmann Equation,” Phys. Rev. E. 49, 2941-2948, (1994).
[15] X. Shan, and G. D. Doolen, “Multicomponent Lattice-Boltzmann Model With Interparticle Interaction,” J. Stat. Phys. 52, 379-393, (1995).
[16] M. R. Swift, W. R. Osborn, and J. M. Yeomans “Lattice Boltzmann simulation of nonideal fluids,” Phys. Rev. Lett. 75(5), 830-833, (1995).
[17] M. R. Swift, W. R. Osborn, and J. M. Yeomans “Lattice Boltzmann simulations of liquid-gas and bunary-fluid systems,” Phys. Rev. E,54, 5041-5052, (1996).
[18] T. Inamuro, T. Ogata, S. Tajima, and N. Konishi, “A lattice Boltzmann method for incompressible two-phase flows with large density diﬀerences,” J. Comput. Phys. 198, 628, (2004).
[19] T. Lee and C. L. Lin, “A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio,” J. Comput. 206, 16-47, (2005)
[20] T. Lee and P. F. Fischer, “Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases,” Phys. Rev.E. 74, 046709, (2006).
[21] T. Lee and L. Liu, “Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces,” J. Comput. Phys. 229, 8045-8063, (2010).
[22] D. Bhaga and M. E. Weber, “In-line interaction of a pair of bubbles in a viscous liquid,” Chem. Eng. Sci. 35, 2467-2474, (1980).
[23] D. Bhaga and M. E. Weber, “Bubbles in viscous liquids: shapes, wakes and velocities,” J. Fluid Mech. 105, 61-85, (1981).
[24] R. Krishna, M.I. Urseanu, J. M. van Baten, and J. Ellenberger, “Rise velocity of a swarm of large gas bubbles in liquids,” Chem. Eng. Sci. 54, 171-183, (1999).
[25] N. Takada, M. Misawa, A. Tomiyama, and S. Fujiwara, “Numerical simulation of two- and three-dimensional two-phase fluid motion by lattice Boltzmann method,” Comput. Phys. Commun. 129, 233-246, (2000).
[26] M. Cheng, J. Hua, and J. Lou, “Simulation of bubble–bubble interaction using a lattice Boltzmann method,” Comput. Fluids. 39, 260-270, (2010).
[27] H. W. Zheng, C. Shu, and Y. T. Chew, “Lattice Boltzmann interface capturing method for incompressible flows,” Phys. Rev. E 72, 056705, (2005).
[28] L. Amaya-Bower, T. Lee, “Single bubble rising dynamics for moderate Reynolds number using Lattice Boltzmann Method,” Comput. Fluids. 39, 1191-1207, (2010).
[29] J. Bolz, I. Farmer, E. Grinspun, and P. Schro¨der, “Sparse matrix solvers on the GPU: Conjugate gradients and multigrid,” ACM Trans. Graph. (SIGGRAPH) 22, 917, (2003).
[30] F. A. Kuo, M. R. Smith, C. W. Hsieh, C. Y. Chou, and J. S. Wu, “GPU acceleration for general conservation equations and its application to several engineering problems,” Comput. Fluids. 45, 147, (2011).
[31] J. T¨olke, and M. Krafczyk, “TeraFLOP computing on a desktop PC with GPUs for 3D CFD,” Comput. Fluid D. 22, 443-456, (2008).
[32] C. Obrecht, F. Kuznik, B. Tourancheau, and J. J. Roux, “A new approach to the lattice Boltzmann method for graphics processing units,” Comput. Math. Appl. 61, 3628, (2011).
[33] X. Wang, T. Aoki, “Multi-GPU performance of incompressible flow computation by lattice Boltzmann method on GPU cluster,” Parallel. Computing. 37, 521, (2011).
[34] J. Myre, S. D. C. Walsh, D. Lilja and M. O. Saar, “Performance analysis of single-phase, multiphase, and multicomponent lattice-Boltzmann fluid flow simulations on GPU clusters,” Concurrency Comput.: Pract. and Exper. 23, 332-350, (2010).
[35] X. Li, Y. Zhang, X. Wang, Wei Ge , “Performance analysis of single-phase, multiphase, and multicomponent lattice-Boltzmann fluid flow simulations on GPU clusters,” Concurrency Comput.: Pract. and Exper. 23, 332-350, (2010).
[36] T. C. Huang and C. A. Lin, “Lattice Boltzmann Simulations of Two-phase Flow at High Density Ratio on Multi-GPU CLuster,” National Tsing Hua University, Department of Power Mechanical Engineering, (2016).
[37] Tamas I. Gombosi, “Gas kinetic theorym,” Cambridge University Press, (1994).
[38] X. He, and L. S. Luo, “Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation,” Phys. Rev. E 56, 6811-6817, (1997).
[39] D. A. Wolf-Gladrow, “Lattice-gas cellular automata and lattice Boltzmann models - an introduction,” Springer, Lecture Notes in Mathematics, p.159, (2000).
[40] T. Lee, “Eﬀects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids ,” Comput. Math. Appl. 58, 987-994, (2009).
[41] L. Amaya-Bower, T. Lee, “Numerical simulation of single bubble rising in vertical and inclined square channel using lattice Boltzmann method,” Chem. Eng. Sci. 66, 935-952, (2011).
[42] H. W. Chang, P .Y. Hong, L. S. Lin and C. A. Lin, “Simulations of flow instability in three dimensional deep cavities with multi relaxation time lattice Boltzmann method on graphic processing units,” Comput. & Fluids. 88, 866- 871, (2013).
[43] R. Clift, J. R. Grace and M. E. Weber, “Bubbles, Drops, and Particles,” New York: Academic Press, (1978).

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