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研究生： 馮勝瑋
Feng, Sheng-Wei
論文名稱： 透過插值晶格波茲曼法模擬具壁面之紊流
Simulations of Wall Bounded Turbulent Flow via Interpolation-Based Lattice Boltzmann Method
指導教授： 林昭安
Lin, Chao-An
口試委員: 牛仰堯
Niu, Yang-Yao
吳毓庭
Wu, Yu-Ting
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： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 68
中文關鍵詞： 晶格波茲曼法 、直接數值模擬 、非均勻網格 、紊流模擬
外文關鍵詞： lattice Boltzmann method, direct numerical simulation, non-uniform grids, turbulent flow
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    • 本研究採用了插值晶格玻爾茲曼方法（IBLBM）在非均勻網格上求解各種流場，包括渠道紊流和渠道內週期性山坡層流。在渠道紊流中，我們比較了SRT和MRT模型在Reτ = 180 的表現。結果顯示，在相對簡單的邊界條件下，SRT模型能夠保持準確性，同時在計算時間上更具優勢。在中等雷諾數Reτ = 395 和 640，6階IBLBM的結果與文獻中的數據高度一致。在高雷諾數Reτ = 1000，6階IBLBM的結果在湍流強度和渦度方面與文獻相比有些許差異，但其他湍流特徵的結果表現良好，展示了IBLBM在模擬中的可行性。
    在渠道內週期性山坡層流中，由於邊界形狀較為複雜，採用了MRT模型。IBLBM計算
    的結果與LBM的結果幾乎一致。儘管IBLBM需要額外進行插值計算，但相較於LBM需要在
    大量網格上進行計算，IBLBM還是具有顯著的優勢，能夠通過使用非均勻網格生成來節省計算資源。為了提高計算效率，本研究使用了多GPU叢集進行並行處理，並使用了重疊技術、MPI和CUDA並行程序結構來加速運算。

    This study employs the Interpolation-Based Lattice Boltzmann Method (IBLBM) to solve various flow fields on non-uniform grids, including Poiseuille channel flow and channel flow over a periodic hill. For Poiseuille channel flow, we compared the performance of the SRT and
    MRT models using a case with Reτ = 180. It was found that under relatively simple boundary conditions, the SRT model maintains accuracy while being more advantageous in terms of computational time. At moderate Reynolds numbers, Reτ = 395 and 640, the results from the
    6th-order IBLBM showed excellent agreement with the literature. At a high Reynolds number, Reτ = 1000, the 6th-order IBLBM results had slight discrepancies in turbulent intensity and vorticity compared to the literature, but other turbulent characteristics were well captured, demonstrating the feasibility of IBLBM for simulations.

    In the case of flow over a periodic hill, the MRT model was used due to the complex boundary
    shapes. The IBLBM results were nearly identical to those of the LBM. Although IBLBM requires additional interpolation calculations, it offers significant advantages over LBM, which requires extensive calculations on a large number of grids. IBLBM can save computational
    resources by utilizing non-uniform grid generation. To enhance computational efficiency, this study employed multi-GPU clusters for parallel processing, overlapping techniques, MPI and CUDA parallel program structures.

    Abstract i Acknowledgments iii List of Figures vi List of Tables viii Chapter 1 Introduction 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Simulation of 3-D turbulent channel flow with the lattice Boltzmann method in non-uniform grids . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Flow over periodic hills . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2 Methodology 7 2.1 The Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Basic assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 The Bhatnagar-Gross-Krook approximation . . . . . . . . . . . . . . . . 9 2.1.3 The low-Mach-number approximation . . . . . . . . . . . . . . . . . . . . 11 2.2 Discretization of Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Discretization of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Discretization of phase space . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter 3 Numerical algorithm 15 3.1 Single-relaxation-time and multiple-relaxation-time lattice Boltzmann methods . 15 3.2 Forcing term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Flow over periodic hill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4 Interpolation-based lattice Boltzmann method . . . . . . . . . . . . . . . . . . . 19 3.4.1 Mesh setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4.2 Lagrange interpolation in Cartesian mesh . . . . . . . . . . . . . . . . . . 21 3.5 Boundary condition implementations . . . . . . . . . . . . . . . . . . . . . . . . 24 3.5.1 Halfway bounce-back boundary condition . . . . . . . . . . . . . . . . . . 24 3.5.2 Interpolated boundary condition . . . . . . . . . . . . . . . . . . . . . . . 25 3.5.3 Mass conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.6 Parallel Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Chapter 4 Numerical results and discussion 31 4.1 Turbulent Poiseuille channel flow . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1.1 Comparative Analysis of SRT and MRT Models . . . . . . . . . . . . . . 33 4.1.2 Performance of Results under Different Reynolds Numbers . . . . . . . . 40 4.2 Flow over Periodic hill in channel . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 5 Conclusions and future work 59 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.1 Poiseuille channel flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.2 Flow over periodic hill in channel . . . . . . . . . . . . . . . . . . . . . . 60 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Bibliography 62

    [1] Cyrus K Aidun and Jonathan R Clausen. Lattice-Boltzmann method for complex flows.
    Annual review of fluid mechanics, 42:439–472, 2010.
    [2] U Frisch, B Hasslacher, and Y Pomeau. Lattice-gas automata for the navier-stokes equation. Physical Review Letters, 56(14):1505–1508, 1986.
    [3] Stephen Wolfram. Cellular automaton fluids 1: Basic theory. Journal of Statistical Physics, 45(3-4):471–526, 1986.
    [4] Che-Yu Lin and Chao-An Lin. Direct numerical simulations of turbulent channel flow with polymer additives. Journal of Mechanics, 36(5):691–698, 2020.
    [5] Fran ̧cois Dubois, Chao-An Lin, and Mohamed Mahdi Tekitek. Anisotropic thermal lattice Boltzmann simulation of 2D natural convection in a square cavity. Computers & Fluids, 124:278–287, 2016.
    [6] Tzu-Chun Huang, Chien-Yi Chang, and Chao-An Lin. Simulation of droplet dynamic with high density ratio two-phase lattice Boltzmann model on multi-GPU cluster. Computers & Fluids, 173:80–87, 2018.
    [7] Yusuke Kuwata, Koji Tsuda, and Kazuhiko Suga. Direct numerical simulation of turbulent conjugate heat transfer in a porous-walled duct flow. Journal of Fluid Mechanics, 904:A9,2020.
    [8] MD Deshpande and S George Milton. Kolmogorov scales in a driven cavity flow. Fluid dynamics research, 22(6):359, 1998.
    [9] Olga Filippova and Dieter H ̈anel. Grid refinement for lattice-BGK models. Journal of computational Physics, 147(1):219–228, 1998.
    [10] Chung-Ming Wu, You-Sheng Zhou, and Chao-An Lin. Direct numerical simulations of turbulent channel flows with mesh-refinement lattice Boltzmann methods on GPU cluster. Computers & Fluids, 210:104647, 2020.
    [11] Xiaoyi He, Li-Shi Luo, and Micah Dembo. Some progress in lattice Boltzmann method. Part I. Nonuniform mesh grids. Journal of computational Physics, 129(2):357–363, 1996.
    [12] Xiaoyi He and Gary Doolen. Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder. Journal of Computational Physics, 134(2):306–315, 1997.
    [13] Bo-Xiao Jin. Investigating the performance of interpolation-based lattice boltzmann method in complex flows. Master’s thesis, National Tsing Hua University, 2023.
    [14] Dazhi Yu, Renwei Mei, and Wei Shyy. A multi-block lattice boltzmann method for viscous fluid flows. International journal for numerical methods in fluids, 39(2):99–120, 2002.
    [15] JMVA Koelman. A simple lattice Boltzmann scheme for Navier-Stokes fluid flow. Europhysics Letters, 15(6):603, 1991.
    [16] Vanja Zecevic, Michael P Kirkpatrick, and Steven W Armfield. Rectangular lattice Boltzmann method using multiple relaxation time collision operator in two and three dimensions. Computers & Fluids, 202:104492, 2020.
    [17] Lian-Ping Wang, Haoda Min, Cheng Peng, Nicholas Geneva, and Zhaoli Guo. A lattice-Boltzmann scheme of the Navier–Stokes equation on a three-dimensional cuboid lattice. Computers & Mathematics with Applications, 78(4):1053–1075, 2019.
    [18] Peng Wang, Lian-Ping Wang, and Zhaoli Guo. Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows. Physical Review E, 94(4):043304, 2016.
    [19] Yuntian Bo, Peng Wang, Zhaoli Guo, and Lian-Ping Wang. DUGKS simulations of three-dimensional Taylor–Green vortex flow and turbulent channel flow. Computers & Fluids, 155:9–21, 2017.
    [20] Misun Min and Taehun Lee. A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows. Journal of Computational Physics, 230(1):245–259, 2011.
    [21] Andreas Kr ̈amer, Dominik Wilde, Knut K ̈ullmer, Dirk Reith, Holger Foysi, and Wolfgang Joppich. Lattice Boltzmann simulations on irregular grids: Introduction of the NATriuM library. Computers & Mathematics with Applications, 79(1):34–54, 2020.
    [22] Robert R Long. The motion of fluids with density stratification. Journal of Geophysical Research, 64(12):2151–2163, 1959.
    [23] PS Jackson and JCR Hunt. Turbulent wind flow over a low hill. Quarterly Journal of the Royal Meteorological Society, 101(430):929–955, 1975.
    [24] GP Almeida, DFG Durao, and MV Heitor. Wake flows behind two-dimensional model hills. Experimental Thermal and Fluid Science, 7(1):87–101, 1993.
    [25] CP Mellen, J Fr ̈ohlich, and W Rodi. Large eddy simulation of the flow over periodic hills. In 16th IMACS world congress, pages 21–25. Lausanne, Switzerland, 2000.
    [26] Bruno Chaouat and Roland Schiestel. Hybrid rans/les simulations of the turbulent flow over periodic hills at high reynolds number using the pitm method. Computers & Fluids, 84:279–300, 2013.
    [27] Po-Hua Chang, Chuan-Chieh Liao, Hsin-Wei Hsu, Shih-Huang Liu, and Chao-An Lin.
    Simulations of laminar and turbulent flows over periodic hills with immersed boundary method. Computers & Fluids, 92:233–243, 2014.
    [28] Michael Breuer, Nikolaus Peller, Ch Rapp, and Michael Manhart. Flow over periodic hills–numerical and experimental study in a wide range of reynolds numbers. Computers & Fluids, 38(2):433–457, 2009.
    [29] Ch Rapp and M Manhart. Flow over periodic hills: an experimental study. Experiments in fluids, 51(1):247–269, 2011.
    [30] Wei Gao, Wan Cheng, and Ravi Samtaney. Large-eddy simulations of turbulent flow in a channel with streamwise periodic constrictions. Journal of Fluid Mechanics, 900:A43, 2020.
    [31] Laslo T Diosady and Scott M Murman. Dns of flows over periodic hills using a discontinuous galerkin spectral-element method. In 44th AIAA Fluid Dynamics Conference, page 2784, 2014.
    [32] P Balakumar, GI Park, and B Pierce. Dns, les, and wall-modeled les of separating flow over periodic hills. In Proceedings of the Summer Program, pages 407–415, 2014.
    [33] Benjamin Krank, Martin Kronbichler, and Wolfgang A Wall. Direct numerical simulation of flow over periodic hills up to re h= 10, 595 re h=10,595. Flow, turbulence and combustion, 101:521–551, 2018.
    [34] Chi-Wei Su. Mrt-lbm simulations of turbulent flows over periodic hills at different reynolds numbers. Master’s thesis, National Tsing Hua University, 2018.
    [35] Heng Xiao, Jin-Long Wu, Sylvain Laizet, and Lian Duan. Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations. Computers & Fluids, 200:104431, 2020.
    [36] Xiao-Ying Huang. Simulations of turbulent flow over periodic hills with multiple- relaxation-time lattice boltzmann method on multi-gpu cluster. Master’s thesis, National Tsing Hua University, 2017.
    [37] Wei-Jie Lin, Ming-Jiun Li, Chi-Wei Su, Xiao-Ying Huang, and Chao-An Lin. Direct numerical simulations of turbulent periodic-hill flows with mass-conserving lattice boltzmann method. Physics of Fluids, 32(11):115122, 2020.
    [38] De-Xiang Zeng. The flows over periodic hills in channel and duct simulations with multiple-relaxation time lattice boltzmann method on multi-gpu cluster. Master’s thesis, National Tsing Hua University, 2021.
    [39] Tamas I Gombosi and Atmo Gombosi. Gaskinetic theory. Number 9. Cambridge University Press, 1994.
    [40] Prabhu Lal Bhatnagar, Eugene P Gross, and Max Krook. A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Physical review, 94(3):511, 1954.
    [41] Xiaoyi He and Li-Shi Luo. Theory of the lattice boltzmann method: From the boltzmann equation to the lattice boltzmann equation. Physical review E, 56(6):6811, 1997.
    [42] Qisu Zou and Xiaoyi He. On pressure and velocity boundary conditions for the lattice boltzmann bgk model. Physics of fluids, 9(6):1591–1598, 1997.
    [43] Dominique d’Humi`eres. Multiple–relaxation–time lattice boltzmann models in three dimensions. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 360(1792):437–451, 2002.
    [44] Li-Shi Luo. Theory of the lattice boltzmann method: Lattice boltzmann models for nonideal gases. Physical Review E, 62(4):4982, 2000.
    [45] Hiroyuki Abe, Hiroshi Kawamura, and Yuichi Matsuo. Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. J. Fluids Eng., 123(2):382–393, 2001.
    [46] Xiaolei Shi and Chao-An Lin. Simulations of wall bounded turbulent flows using general pressure equation. Flow, Turbulence and Combustion, 105(1):67–82, 2020.
    [47] Xiaolei Shi, Tanmay Agrawal, Chao-An Lin, Feng-Nan Hwang, and Tzu-Hsuan Chiu. A parallel nonlinear multigrid solver for unsteady incompressible flow simulation on multi-GPU cluster. Journal of Computational Physics, 414:109447, 2020.
    [48] M’hamed Bouzidi, Mouaouia Firdaouss, and Pierre Lallemand. Momentum transfer of a boltzmann-lattice fluid with boundaries. Physics of fluids, 13(11):3452–3459, 2001.
    [49] Sathish KP Sanjeevi, Ahad Zarghami, and Johan T Padding. Choice of no-slip curved boundary condition for lattice boltzmann simulations of high-reynolds-number flows. Physical Review E, 97(4):043305, 2018.
    [50] Hung-Wen Chang, Pei-Yao Hong, Li-Song Lin, and Chao-An Lin. Simulations of flow instability in three dimensional deep cavities with multi relaxation time lattice Boltzmann method on graphic processing units. Computers & Fluids, 88:866–871, 2013.
    [51] Pei-Yao Hong, Li-Min Huang, Li-Song Lin, and Chao-An Lin. Scalable multi-relaxation-time lattice Boltzmann simulations on multi-GPU cluster. Computers & Fluids, 110:1–8, 2015.
    [52] You-Hsun Lee, Li-Min Huang, You-Seng Zou, Shao-Ching Huang, and Chao-An Lin. Simulations of turbulent duct flow with lattice Boltzmann method on GPU cluster. Computers & Fluids, 168:14–20, 2018.
    [53] Robert D Moser, John Kim, and Nagi N Mansour. Direct numerical simulation of turbulent channel flow up to re τ = 590. Physics of fluids, 11(4):943–945, 1999.
    [54] Myoungkyu Lee and Robert D Moser. Direct numerical simulation of turbulent channel
    flow up to. Journal of fluid mechanics, 774:395–415, 2015.

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