請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60042
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 黃美嬌(Mei-Jiau Huang) | |
dc.contributor.author | Li-Chieh Chen | en |
dc.contributor.author | 陳立杰 | zh_TW |
dc.date.accessioned | 2021-06-16T09:52:23Z | - |
dc.date.available | 2017-02-16 | |
dc.date.copyright | 2017-02-16 | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017-01-12 | |
dc.identifier.citation | [1] C.S. Peskin, Numerical-Analysis of Blood-Flow in Heart, J Comput Phys, 25 (1977) 220-252.
[2] C.S. Peskin, D.M. Mcqueen, Modeling Prosthetic Heart-Valves for Numerical-Analysis of Blood-Flow in the Heart, J Comput Phys, 37 (1980) 113-132. [3] C.S. Peskin, D.M. Mcqueen, A 3-Dimensional Computational Method for Blood-Flow in the Heart .1. Immersed Elastic Fibers in a Viscous Incompressible Fluid, J Comput Phys, 81 (1989) 372-405. [4] J. Mohd-Yusof, Combined immersed boundary/B-spline methods for simulations of flow in complex geometries, Annual Research Briefs, Center for Turbulence Research, Stanford University, 1999, (1999) 317-327. [5] E.A. Fadlun, R. Verzicco, P. Orlandi, J. Mohd-Yusof, Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J Comput Phys, 161 (2000) 35-60. [6] D.Z. Noor, M.J. Chern, T.L. Horng, An immersed boundary method to solve fluid-solid interaction problems, Comput Mech, 44 (2009) 447-453. [7] R.D. Guy, D.A. Hartenstine, On the accuracy of direct forcing immersed boundary methods with projection methods, J Comput Phys, 229 (2010) 2479-2496. [8] M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J Comput Phys, 209 (2005) 448-476. [9] J.M. Yang, F. Stern, A simple and efficient direct forcing immersed boundary framework for fluid-structure interactions, J Comput Phys, 231 (2012) 5029-5061. [10] J.M. Yang, F. Stern, A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows, J Fluid Eng-T Asme, 136 (2014). [11] J.M. Yang, F. Stern, A non-iterative direct forcing immersed boundary method forstrongly-coupled fluid-solid interactions, J Comput Phys, 295 (2015) 779-804. [12] T. Ikeno, T. Kajishima, Finite-difference immersed boundary method consistent with wall conditions for incompressible turbulent flow simulations, J Comput Phys, 226 (2007) 1485-1508. [13] R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier fictitious domain method for particulate flows, Int J Multiphas Flow, 25 (1999) 755-794. [14] R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow, Comput Method Appl M, 184 (2000) 241-267. [15] R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, J. Periaux, A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J Comput Phys, 169 (2001) 363-426. [16] Z.S. Yu, N. Phan-Thien, R.I. Tanner, Dynamic simulation of sphere motion in a vertical tube, J Fluid Mech, 518 (2004) 61-93. [17] C. Diaz-Goano, P.D. Minev, K. Nandakumar, Fictitious domain/finite element method for particulate flows, J Comput Phys, 192 (2003) 105-123. [18] C. Veeramani, P.D. Minev, K. Nandakumar, A fictitious domain formulation for flows with rigid particles: A non-Lagrange multiplier version, J Comput Phys, 224 (2007) 867-879. [19] Z.S. Yu, X.M. Shao, A direct-forcing fictitious domain method for particulate flows, J Comput Phys, 227 (2007) 292-314. [20] S. Gallier, E. Lemaire, L. Lobry, F. Peters, A fictitious domain approach for the simulation of dense suspensions, J Comput Phys, 256 (2014) 367-387. [21] N. Sharma, N.A. Patankar, A fast computation technique for the direct numerical simulation of rigid particulate flows, J Comput Phys, 205 (2005) 439-457. [22] S.V. Apte, M. Martin, N.A. Patankar, A numerical method for fully resolved simulation (FRS) of rigid particle-flow interactions in complex flows, J Comput Phys, 228 (2009) 2712-2738. [23] S.V. Apte, J.R. Finn, A variable-density fictitious domain method for particulate flows with broad range of particle-fluid density ratios, J Comput Phys, 243 (2013) 109-129. [24] L. Zhang, A. Gerstenberger, X.D. Wang, W.K. Liu, Immersed finite element method, Comput Method Appl M, 193 (2004) 2051-2067. [25] L.T. Zhang, M. Gay, Immersed finite element method for fluid-structure interactions, J Fluid Struct, 23 (2007) 839-857. [26] W.K. Liu, D.W. Kim, S.Q. Tang, Mathematical foundations of the immersed finite element method, Comput Mech, 39 (2007) 211-222. [27] Z.Q. Zhang, J.Y. Yao, G.R. Liu, An Immersed Smoothed Finite Element Method for Fluid-Structure Interaction Problems, Int J Comp Meth-Sing, 8 (2011) 747-757. [28] X.S. Wang, C. Wang, L.T. Zhang, Semi-implicit formulation of the immersed finite element method, Comput Mech, 49 (2012) 421-430. [29] T.R. Lee, Y.S. Chang, J.B. Choi, D.W. Kim, W.K. Liu, Y.J. Kim, Immersed finite element method for rigid body motions in the incompressible Navier-Stokes flow, Comput Method Appl M, 197 (2008) 2305-2316. [30] M. Coquerelle, G.H. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, J Comput Phys, 227 (2008) 9121-9137. [31] M. Gazzola, P. Chatelain, W.M. van Rees, P. Koumoutsakos, Simulations of single and multiple swimmers with non-divergence free deforming geometries, J Comput Phys, 230 (2011) 7093-7114. [32] S. Haeri, J.S. Shrimpton, A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer, J Comput Phys, 237 (2013) 21-45. [33] X.M. Shao, Y. Shi, Z.S. Yu, Combination of the fictitious domain method and the sharp interface method for direct numerical simulation of particulate flows with heat transfer, Int J Heat Mass Tran, 55 (2012) 6775-6785. [34] Z.S. Yu, X.M. Shao, A. Wachs, A fictitious domain method for particulate flows with heat transfer, J Comput Phys, 217 (2006) 424-452. [35] S.J. Sherwin, G.E. Karniadakis, A Triangular Spectral Element Method - Applications to the Incompressible Navier-Stokes Equations, Comput Method Appl M, 123 (1995) 189-229. [36] T.C. Warburton, S.J. Sherwin, G.E. Karniadakis, Basis functions for triangular and quadrilateral high-order elements, Siam J Sci Comput, 20 (1999) 1671-1695. [37] G.E. Karniadakis, S.J. Sherwin, Spectral/hp element methods for CFD , Numerical Mathematics and Scientific Computation, Oxford University Press, (1999). [38] L. Parussini, V. Pediroda, Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow, J Comput Phys, 228 (2009) 3891-3910. [39] X.L. Yang, X. Zhang, Z.L. Li, G.W. He, A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, J Comput Phys, 228 (2009) 7821-7836. [40] P. Angot, C.H. Bruneau, P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer Math, 81 (1999) 497-520. [41] C. Bost, G.H. Cottet, E. Maitre, Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid, Siam J Numer Anal, 48 (2010) 1313-1337. [42] G.E. Karniadakis, M. Israeli, S.A. Orszag, High-Order Splitting Methods for the Incompressible Navier Stokes Equations, J Comput Phys, 97 (1991) 414-443. [43] J. Happel, H. Brenner, Low Reynolds number hydrodynamics : With special applications to particulate media, Prentice-Hall, 1965. [44] A. Wachs, A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions, Comput Fluids, 38 (2009) 1608-1628. [45] D. Calhoun, A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions, J Comput Phys, 176 (2002) 231-275. [46] D. Russell, Z.J. Wang, A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow, J Comput Phys, 191 (2003) 177-205. [47] B. Fornberg, A Numerical Study of Steady Viscous-Flow Past a Circular-Cylinder, J Fluid Mech, 98 (1980) 819-855. [48] S.C.R. Dennis, G.Z. Chang, Numerical Solutions for Steady Flow Past a Circular Cylinder at Reynolds Numbers up to 100, J Fluid Mech, 42 (1970) 471-&. [49] C. Liu, X. Zheng, C.H. Sung, Preconditioned multigrid methods for unsteady incompressible flows, J Comput Phys, 139 (1998) 35-57. [50] A. Roshko, On the development of turbulent wakes from vortex streets, NACA Rep., 1191 (1954). [51] C.H.K. Williamson, Defining a Universal and Continuous Strouhal-Reynolds Number Relationship for the Laminar Vortex Shedding of a Circular-Cylinder, Phys Fluids, 31 (1988) 2742-2744. [52] Y. Maday, E. Tadmor, Analysis of the Spectral Vanishing Viscosity Method for Periodic Conservation-Laws, Siam J Numer Anal, 26 (1989) 854-870. [53] G.S. Karamanos, G.E. Karniadakis, A spectral vanishing viscosity method for large-eddy simulations, J Comput Phys, 163 (2000) 22-50. [54] R.M. Kirby, S.J. Sherwin, Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling, Comput Method Appl M, 195 (2006) 3128-3144. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60042 | - |
dc.description.abstract | 在本論文中整合了沉浸邊界法與寬頻元素法,用以模擬二維之流固耦合問題。沉浸邊界法用以快速捕捉移動固體與流體之間的交互作用,固定且複雜的邊界則利用寬頻元素法的幾何彈性捕捉。在本方法中使用了非均勻密度的虛擬區域法(fictitious domain method)以及直接力量-虛擬區域法(direct forcing fictitious domain)兩種不同類型的沉浸邊界法以模擬剛體與不可壓縮流體間的交互作用。前者在固體區域內填入與固體密度相同的流體,將整個計算區域視為一非均勻密度的流場,再以固體區域內的動量估算剛體運動,最後以懲罰模型強制固體範圍內流體以剛體方式運動。後者同樣將流體延伸進固體區域,但填入與外部流體相同之流體,並在流體範圍內加入一假想力以耦合流固行為。為了解決流固邊界上性質的不連續,本論文提出了一分晶胞法將不連續性平滑化。此分晶胞法也同時幫助我們執行固體範圍內各性質的積分。經由模擬各類經典的流場實驗以及比對文獻或解析解的結果,本方法的準確性得到了驗證。最後根據研究剛體的經驗,我們將本方法延伸至處理可變形固體上,並在論文中簡單介紹初步結果。 | zh_TW |
dc.description.abstract | To simulate two-dimensional two-way coupling problems between a rigid body and a fluid, we combine the immersed-boundary type method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. Two immersed-boundary type methods are chosen in this work. The first one is the FD (fictitious domain) method. In this method, the solid region is filled with a fictitious fluid having a density as the same as the solid, and the entire fluid-solid domain is treated as an incompressible fluid with non-uniform density. The momentum inside the solid region is used to estimate the rigid-body motion and the no-slip boundary condition at the rigid body surface is enforced by the penalization method. The second one is the DFFD (direct forcing fictitious domain) method. The fluid in the fluid region is extended into the solid region and pseudo body force is imposed within the solid domain to enforce the rigid body motion in this method. In particular, a so-called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literature. Meanwhile, besides the rigid body, we also attempt to deal the deformable material. Some preliminary results are shown in the thesis. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T09:52:23Z (GMT). No. of bitstreams: 1 ntu-106-D99522015-1.pdf: 3979366 bytes, checksum: 101783241da943e8fa70b0bbc56fe2f6 (MD5) Previous issue date: 2017 | en |
dc.description.tableofcontents | 摘要 i
Abstract ii Contents iii List of Table v List of Figure v 1. Introduction 1 1.1 Background and Motivation 1 1.2 Thesis Outline 5 2. Governing Equations and FD Methods 6 2.1 Governing Equations 6 2.2 Non-uniform density FD method 7 2.3 DFFD method 8 3. Numerical Scheme 11 3.1 Spatial discretization 11 3.1.1 Expansion function 11 3.1.2 Sub-cell grid and Numerical Integration 12 3.2 Temporal Discretization and Time-Splitting Solver 15 3.2.1 Non-uniform density FD method 15 3.2.2 DFFD Method 17 4. Results and discussions 23 4.1 Typical flows 23 4.1.1 Uniform flow past a circular cylinder 23 4.1.2 Free falling circular cylinder 24 4.1.2.1 FD Method 25 4.1.2.2 DFFD method 25 4.1.2.3 Discussions 27 4.2 Convergence and efficiency study 28 4.2.1 FD method 28 4.2.2 DFFD method 29 4.3 A circular cylinder in a simple shear flow 30 4.4 Other applications 31 4.4.1 A freely falling square/triangular cylinder 32 4.4.2 Channels with varying width 33 5. Deformable Solid 56 5.1 Governing equations and IFEM 56 5.2 Numerical Procedure 57 5.3 Results 59 6 Conclusions and future work 63 6.1 Conclusions 63 6.2 Future work 64 Reference 65 Appendix A: Differential Operators 69 A-1. 1D collocation derivative 69 A-2. Differential operation in 2D triangular element 72 Appendix B: Mass matrix 75 Appendix C: Laplacian matrix 77 Appendix D: Jacobi polynomials 79 Appendix E: Divergence free condition in DFFD method 81 | |
dc.language.iso | en | |
dc.title | 整合沉浸邊界法與寬頻元素法之流固耦合數值模擬工具 | zh_TW |
dc.title | Development of a Spectral Element-Immersed Boundary Method for Fluid-Structure Interaction Problems | en |
dc.type | Thesis | |
dc.date.schoolyear | 105-1 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 許文翰,蕭述三(Shu-San Hsiau),林昭安(Chao-An Lin),洪子倫(Tzyy-Leng Horng),楊馥菱(Fu-Ling Yang) | |
dc.subject.keyword | 沉浸邊界法,寬頻元素法,流固耦合,分晶胞法,虛擬區域法, | zh_TW |
dc.subject.keyword | immersed boundary method,spectral element method,fluid-structure interaction,sub-cell,fictitious domain, | en |
dc.relation.page | 86 | |
dc.identifier.doi | 10.6342/NTU201700046 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2017-01-12 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
顯示於系所單位: | 機械工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-106-1.pdf 目前未授權公開取用 | 3.89 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。