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DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
dc.contributor.author | Chin-Wei Wang | en |
dc.contributor.author | 王晉偉 | zh_TW |
dc.date.accessioned | 2021-06-16T06:54:16Z | - |
dc.date.available | 2020-07-27 | |
dc.date.copyright | 2020-07-27 | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020-07-24 | |
dc.identifier.citation | [1] J. S. Turner. Buoyancy Effects in Fluids. Cambridge University Press, 1979. [2] F. Necker, C. Hartel, L. Kleiser, and E. Meiburg. High-resolution simulations of particle-driven gravity currents. International Journal of Multiphase Flow, 28(2):279-300, 2002. [3] E. Meiburg, S. Radhakrishnan, and M. Nasr-Azadani. Modeling gravity and turbidity currents: Computational approaches and challenges. Applied Mechanics Reviews, 67(4), 2015. [4] A. Dai. Experiments on two-layer density-stratified inertial gravity currents. Physical Review Fluids, 2(7):073802, 2017. [5] M. Cantero, J.R. Lee, S. Balachandar, and M. Garcia. On the front velocity of gravity currents. Journal of Fluid Mechanics, 586:1-39, 2007. [6] W. L. Briggs, V. E. Henson, and S. F. McCormick. A Multigrid Tutorial, 2nd Edition. Society for Industrial and Applied Mathematics, 2000. [7] F. Wan, Y. Yin, and S. Zhang. 3D parallel multigrid methods for real-time fluid simulation. 3D Research, 9:8, 2018. [8] M. Zingale. pyro: A teaching code for computational astrophysical hydrodynamics. Astronomy and Computing, 6:52, 2014. [9] P. H. Chiu and Tony W. H. Sheu. On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation. Journal of Computational Physics, 228(10):3640-3655, 2009. [10] C. H. Yu, Yogesh G. Bhumkar, and Tony W. H. Sheu. Dispersion relation preserving combined compact difference schemes for flow problems. Journal of Scientific Computing, 62(2):482-516, 2015. [11] P. C. Chu and C. W. Fan. A three-point combined compact difference scheme. Journal of Computational Physics, 140(2):370-399, 1998. [12] P. Moin. Fundamentals of Engineering Numerical Analysis. Cambridge University Press, 3 edition, 2010. [13] A. J. Chorin. Numerical solution of the Navier-Stokes equations. Mathematics of Computation, 22(104):745-762, 1968. [14] M. J. Quinn. Parallel Programming in C with MPI and OpenMP. McGraw-Hill Education Group, 2003. [15] U. Ghia, K. N. Ghia, and C. T. Shin. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48(3):387-411, 1982. [16] G. De Vahl Davis. Natural convection of air in a square cavity: A benchmark numerical solution. International Journal for Numerical Methods in Fluids, 3(3):249-264, 1983. [17] M. Hortmann, M. Peric, and G. Scheuerer. Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions. International Journal for Numerical Methods in Fluids, 11(2):189-207, 1990. [18] P. LeQuere. Accurate solutions to the square thermally driven cavity at high Rayleigh number. Computers Fluids, 20(1):29-41, 1991. [19] 聶廷叡, 以高階方法模擬浮力引導流. Thesis, 國立臺灣大學, 2019. [20] C. Beghein, F. Haghighat, and F. Allard. Numerical study of double-diffusive natural convection in a square cavity. International Journal of Heat and Mass Transfer, 35(4):833-846, 1992. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57616 | - |
dc.description.abstract | 本論文採用多重網格架構以改善求解壓力 Poisson 方程的計算效率,在數值方法中,本論文實作在兩種不同網格系統下的多重網格法,並且將此方法推廣到任意階層,同時比較 V 循環以及 Full 循環的計算效率。此外,本論文使用 OpenMP 架構,並利用簡易的區域分割以平行化程式,更進一步地加速求解。在物理問題方面,本論文採用拉穴流、自然對流以及雙擴散浮力引導流,以進行數值方法以及程式整體的驗證,同時比較使用多重網格法以及傳統迭代法的運算時間差別。 在開放水閘所引致的異重流問題中,本論文比較在層流與紊流的條件下,探討 Kelvin-Helmholtz instability 以及 Lobe and cleft 不穩定性 (instability) 的模擬結果,另外,本論文也比較了在二維水槽以及兩種不同寬度的三維水槽問題中,其寬度對於流場的影響以及邊界所造成的渦度變化。 | zh_TW |
dc.description.abstract | In this thesis, multigrid method is used to improve the computational efficiency of solving the pressure Poisson equation. The multigrid method with arbitrary level under two different grid systems is implemented, and the comparison of computational efficiency between V-cycle and Full-cycle is also made. In addition, OpenMP architecture and a simple domain decomposition are used to parallelize the program so as to accelerate the computation. The models of lid-driven cavity, the natural convection in a cavity and the double-diffusive convection in a cavity are adopted to verify the numerical method and compare the execution time between the multigrid method and the traditional iterative method. In the lock-exchange gravity current problem, this thesis investigates the Kelvin-Helmholtz instability and the lobe-and-cleft instability under laminar and turbulent conditions. In addition, the wall effect and the vorticity are also compared in the two-dimensional and three-dimensional problems with different channel widths. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T06:54:16Z (GMT). No. of bitstreams: 1 U0001-2007202009115300.pdf: 9430712 bytes, checksum: 496be791d4f490fcd4bc8bb5d7ffd9f1 (MD5) Previous issue date: 2020 | en |
dc.description.tableofcontents | 口試委員會審定書 i 誌謝 ii 中文摘要 iii 英文摘要 iv 圖示目錄 vii 表格目錄 viii 第一章 序論 1.1 文獻回顧 1 1.2 研究動機 2 1.3 研究目標 2 第二章 數學模型之建立 2.1 拉穴流問題 4 2.2 自然對流問題 5 2.3 雙擴散浮力引導流的問題 7 第三章 數值模型 3.1 求解輸送方程所使用的數值方法 9 3.1.1 保持頻散關係的五階迎風緊緻差分方法 9 3.1.2 四階龍格-庫塔法 10 3.2 求解動量方程所使用的數值方法 11 3.2.1 投影法 11 3.2.2 QUICK 方法 12 3.3 求解演算法 13 第四章 高效能計算 4.1 多重網格加速 14 4.1.1 Restriction 與 Prolongation 運算子 16 4.1.2 循環演算法 20 4.1.3 邊界值問題 22 4.2 平行計算加速 29 第五章 程式驗證 5.1 具理論解問題之驗證 33 5.2 基準問題之驗證 41 5.2.1 拉穴流問題 41 5.2.2 自然對流問題 42 5.2.3 雙擴散浮力引導流的問題 43 第六章 開放水閘所引致的異重流模擬 6.1 問題描述 55 6.2 數值模擬結果 57 第七章 結論 7.1 研究結果與討論 69 7.2 未來工作與展望 70 參考文獻 71 | |
dc.language.iso | zh-TW | |
dc.title | 在多重網格架構下加速求解異重流方程的三維平行計算 | zh_TW |
dc.title | Multigrid acceleration of three dimensional lock-exchange gravity current flow simulation in parallel | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 羅弘岳(Hong-Yueh Lo),蔡順峰(Shun-Feng Tsai),沈立軒(Li-Syuan Shen),高仕超(Shih-Chao Kao) | |
dc.subject.keyword | 多重網格法,Neumann 邊界,Poisson 方程,異重流,Kelvin-Helmholtz instability,Lobe and cleft instability, | zh_TW |
dc.subject.keyword | Multigrid method,Neumann B.C.,Pressure Poisson equation,Lock-exchange gravity current,Kelvin-Helmholtz instability,Lobe and cleft instability, | en |
dc.relation.page | 72 | |
dc.identifier.doi | 10.6342/NTU202001632 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2020-07-24 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
顯示於系所單位: | 工程科學及海洋工程學系 |
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