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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74765完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
| dc.contributor.author | "Ken, Ting-Jui, Nieh" | en |
| dc.contributor.author | 聶廷叡 | zh_TW |
| dc.date.accessioned | 2021-06-17T09:07:11Z | - |
| dc.date.available | 2019-12-25 | |
| dc.date.copyright | 2019-12-25 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-12-11 | |
| dc.identifier.citation | [1]A. Dai, “Experiments on two-layer density-stratified inertial gravity currents”, ”Physical Review Fluids” 2, 073802 (2017).
[2]F. Necker, C. Härtel, L. Kleiser, and E. H. Meiburg, “High-resolution simulations of particle-driven gravity currents”, International Journal of Multiphase Flow 28, 279–300 (2002). [3]E. Biegert, B. Vowinckel, R. Ouillon, and E. Meiburg, “High-resolution simulations of turbidity currents”, Progress in Earth and Planetary Science 4, 33 (2017). [4]C. H. Yu, L. Zhao, H. L. Wen, T. W. H. Sheu, and R. D. An, “Numerical study of turbidity current over a three-dimensional seafloor”, Communications in Computational Physics 25, 1177–1212 (2019). [5]L. Zhao, C. H. Yu, and Z. He, “Numerical modeling of lock-exchange gravity/turbidity currents by a high-order upwinding combined compact difference scheme”, International Journal of Sediment Research 34, 240–250 (2019). [6]P. H. Chiu and T. W. H. Sheu, “On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection–diffusion equation”, Journal of Computational Physics 228, 3640–3655 (2009). [7]C. H. Yu, Y. G. Bhumkar, and T. W. H. Sheu, “Dispersion relation preserving combined compact difference schemes for flow problems”, Journal of Scientific Computing 62, 482–516 (2015). [8]C. H. Yu, D. Wang, Z. He, and T. Pähtz, “An optimized dispersion–relation-preserving combined compact difference scheme to solve advection equations”, Journal of Computational Physics 300, 92–115 (2015). [9]C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatory shockcapturing schemes”, Journal of Computational Physics 77, 439–471 (1988). [10]A. J. Chorin, “Numerical solution of the Navier-Stokes equations”, Mathematics of Computation 22, 745–762 (1968). [11]B. P. Leonard, “A stable and accurate convective modelling procedure based on quadratic upstream interpolation”, Computer Methods in Applied Mechanics and Engineering 19, 59–98 (1979). [12]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, 387–411 (1982). [13]G. de Vahl Davis, “Natural convection of air in a square cavity: a bench mark numerical solution”, International Journal for Numerical Methods in Fluids 3, 249–264 (1983). [14]H. N. Dixit and V. T. Babu, “Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method”, International Journal of Heat and Mass Transfer 49, 727–739 (2006). [15]P. L. L. Quéré, “Accurate solutions to the square thermally driven cavity at high Rayleigh number”, Computers and Fluids 20, 29–41 (1991). [16]M. M. Nasr-Azadani and E. H. Meiburg, “Turbidity currents interacting with threedimensional seafloor topography”, Journal of Fluid Mechanics 745, 409–443 (2014). [17]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, 833–846 (1992). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74765 | - |
| dc.description.abstract | 本論文採用高階數值方法模擬因浮力而造成的二維流動，藉由推導其控制方程以求得數值近似解，並探討其結果。其中，「數值方法」包括五階dispersion-relation-preserving upwinding combined compact difference scheme (DRPCCD5)、四階龍格－庫塔法(Runge-Kutta method)、投影法(projection method)、三階quadratic upstream interpolation for convective kinematics scheme (QUICK)和二階中央差分法(central difference scheme)；而測試的「模型」題目包括拉穴流(lid-driven cavity)、空穴自然對流(natural convection in a cavity)、定界交換異重流(lock-exchange turbidity current)以及雙擴散空穴對流(double-diffusive convection in a cavity)；「方程」包含不可壓縮納維－斯托克斯方程(incompressible Navier-Stokes equation)和顆粒濃度、溫度及鹽度的傳遞方程。透過和對流－擴散方程(convection-diffusion equation)做實解驗證以及和前人的數值結果做一比較，以確保吾人所提數值方法的正確性與泛用性。爾後，將此一數值模型應用於求解雙擴散定界交換異重流問題(double-diffusive lock-exchange turbidity current problem)。透過改變模型內的溫度條件以瞭解溫差對異重流隨時間變化的基準量值之影響。 | zh_TW |
| dc.description.abstract | In this thesis, several high-order numerical schemes are used to simulate the two-dimensional flow induced by buoyancy forces, which includes the fifth-order dispersion-relation-preserving upwinding combined compact difference scheme (DRPCCD5), the fourth-order Runge-Kutta (RK4) method, the projection method, the third-order quadratic upstream interpolation for convective kinematics scheme (QUICK) and the second-order central difference scheme. Next, the governing equations are derived, the approximated solutions are obtained and the results are demonstrated and discussed. The models adopted are the lid-driven cavity, the natural convection in a cavity, the lock-exchange turbidity current and the double-diffusive convection in a cavity. Also, the incompressible Navier-Stokes equations and the solutal, thermal and saline transport equations are solved numerically. Through the verification of the convection-diffusive equation and the validation of other numerical results, it can be ensured the correctness and generality of the proposed mathematical models. Lastly, the result of the double-diffusive lock-exchange turbidity current problem is presented numerically, which is compared with the single-diffusive lock-exchange problem. Especially, the influence of the temperature on the benchmark quantities for two cases is also exhibited and discussed in detail. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T09:07:11Z (GMT). No. of bitstreams: 1 ntu-108-R06525014-1.pdf: 2807434 bytes, checksum: 9e9e86265abbae773b11da5624dfd693 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 誌謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Table of contents . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . xii List of Tables . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 Modelling problems . . . . . . . . . . . . . . . . . . 3 2.1 Lid-driven cavity flow . . . . . . . . . . . . . . . . . . . 3 2.2 Natural convection in a cavity . . . . . . . . . . . . . . . 4 2.3 Lock-exchange turbidity current flow . . . . . . . . . . . . 6 2.4 Double-diffusive convection in a cavity . . . . . . . . . . 8 2.5 Double-diffusive lock-exchange turbidity current flow . . . 10 Chapter 3 Numerical method . . . . . . . . . . . . . . . . . . 12 3.1 Solution algorithm . . . . . . . . . . . . . . . . . . . . 12 3.2 Schemes for the transport equations . . . . . . . . . . . . 12 3.2.1 5th DRP- upwinding Combined Compact Difference scheme . . 13 3.2.2 4th Runge-Kutta scheme . . . . . . . . . . . . . . . . . 14 3.3 Schemes for momentum equations . . . . . . . . . . . . . . 15 3.3.1 Projection method . . . . . . . . . . . . . . . . . . . . 15 3.3.2 Schemes for spatial discretization . . . . . . . . . . . 16 Chapter 4 Verification studies. . . . . . . . . . . . . . . . . 17 Chapter 5 Validation studies . . . . . . . . . . . . . . . . . 19 5.1 Lid-driven cavity flow . . . . . . . . . . . . . . . . . . 19 5.2 Natural convection in a cavity . . . . . . . . . . . . . . 20 5.3 Lock-exchange turbidity current . . . . . . . . . . . . . . 22 5.4 Double-diffusive convection in a cavity . . . . . . . . . . 24 Chapter 6 Discussion of results . . . . . . . . . . . . . . . . 45 Chapter 7 Concluding remarks . . . . . . . . . . . . . . . . . 52 Chapter 8 Appendix . . . . . . . . . . . . . . . . . . . . . . 54 8.1 Normalization of equations . . . . . . . . . . . . . . . . 54 8.1.1 Lid-driven cavity flow . . . . . . . . . . . . . . . . . 55 8.1.2 Natural convection in a cavity . . . . . . . . . . . . . 55 8.1.3 Lock-exchange turbidity current flow . . . . . . . . . . 57 8.1.4 Double-diffusive convection in a cavity . . . . . . . . . 59 8.1.5 Double-diffusive lock-exchange turbidity current flow . . 61 | |
| dc.language.iso | en | |
| dc.subject | 自然對流 | zh_TW |
| dc.subject | 定界交換 | zh_TW |
| dc.subject | 高階數值方法 | zh_TW |
| dc.subject | 拉穴流 | zh_TW |
| dc.subject | 納維－斯托克斯方程 | zh_TW |
| dc.subject | 雙擴散流 | zh_TW |
| dc.subject | 異重流 | zh_TW |
| dc.subject | lock-exchange | en |
| dc.subject | turbidity current | en |
| dc.subject | natural convection | en |
| dc.subject | double-diffusive flows | en |
| dc.subject | lid-driven cavity | en |
| dc.subject | Navier-Stokes equations | en |
| dc.subject | High-order numerical scheme | en |
| dc.title | 以高階方法模擬浮力引導流 | zh_TW |
| dc.title | High-order scheme development in simulating buoyancy force induced fluid flows | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 戴璽恆,羅弘岳,蔡順?,高仕超 | |
| dc.subject.keyword | 高階數值方法,納維－斯托克斯方程,拉穴流,自然對流,異重流,雙擴散流,定界交換, | zh_TW |
| dc.subject.keyword | High-order numerical scheme,Navier-Stokes equations,lid-driven cavity,natural convection,turbidity current,double-diffusive flows,lock-exchange, | en |
| dc.relation.page | 65 | |
| dc.identifier.doi | 10.6342/NTU201904377 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-12-11 | |
| 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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