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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊德良(Der-Liang Young) | |
dc.contributor.author | Chi-Wei Chen | en |
dc.contributor.author | 陳哲維 | zh_TW |
dc.date.accessioned | 2021-06-13T03:18:26Z | - |
dc.date.available | 2006-07-31 | |
dc.date.copyright | 2006-07-31 | |
dc.date.issued | 2006 | |
dc.date.submitted | 2006-07-28 | |
dc.identifier.citation | 1.1. V.D. Kupradze and M.A. Aleksidze, The method of functional equations for the approximate solution of certain boundary value problems, USSR Computational Mathematics and Mathematical Physics, 4, 82-126, 1964.
1.2. R. Mathon and R.L. Johnston, The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM Journal on Numerical Analysis, 14, 638-650, 1977. 1.3. P.K. Kythe, An Introduction to Boundary Element Methods, CRC Press, New York, 1995. 1.4. D.L. Young, C.M. Fan, C.C. Tsai and C.W. Chen, The method of fundamental solutions and domain decomposition method for degenerate seepage flownet problems, Journal of the Chinese Institute of Engineers, 29, 63-73, 2006. 1.5. G. Burgess and E. Mahajerin, The fundamental collocation method applied to the non-linear Poisson equation in two dimensions, Computers & Structures, 27, 763-767, 1987. 1.6. M.A. Golberg, The method of fundamental solutions for Poisson’s equations, Engineering Analysis with Boundary Elements, 16, 205-213, 1995. 1.7. K. Balakrishnan and P.A. Ramachandran, A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer, Journal of Computational Physics, 150, 239-267, 1999. 1.8. K. Balakrishnan and P.A. Ramachandran, Osculatory Interpolation in the method of fundamental solution for nonlinear Poisson problems, Journal of Computational Physics, 172, 1-18, 2001. 1.9. C.W. Chen, C.M. Fan, D.L. Young, K. Murugesan and C.C. Tsai, Eigenanalysis for membranes with stringers using the methods of fundamental solutions and domain decomposition, CMES: Computer Modeling in Engineering and Sciences, 8, 29-44, 2005. 1.10. D.L. Young, S.P. Hu, C.W. Chen and C.M. Fan, Analysis of elliptical waveguides by the method of fundamental solutions, Microwave and Optical Technology Letters, 44, 552-558, 2005. 1.11. A. Karageorghis, The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation, Applied Mathematics Letters, 14, 837-842, 2001. 1.12. A. Karageorghis and G. Fairweather, The method of fundamental solutions for the numerical solution of the biharmonic equation, Journal of Computational Physics, 69, 434-459, 1987. 1.13. A. Karageorghis and G. Fairweather, The Almansi method of fundamental solutions for solving biharmonic problems, International Journal for Numerical Methods in Engineering, 26, 1665-1682, 1988. 1.14. A. Poullikkas, A. Karageorghis and G. Georgiou, Methods of fundamental solutions for harmonic and biharmonic boundary value problem, Computational Mechanics, 21, 416-423, 1998. 1.15. A. Poullikkas, A. Karageorghis, G. Georgiou and J. Ascough, The method of fundamental solutions for Stokes flows with a free surface, Numerical Methods for Partial Differential Equations, 14, 667-678, 1998. 1.16. C.C. Tsai, D.L. Young and A.H.-D. Cheng, Meshless BEM for three-dimensional Stokes flows, CMES: Computer Modeling in Engineering and Sciences, 3, 117-128, 2002. 1.17. S.J. Jan, Meshless Methods for 2D and 3D Incompressible Viscous Flows, Ph.D. thesis, Department of Civil Engineering, National Taiwan University, Taiwan, 2004. 1.18. D.L. Young, C.W. Chen, C.M. Fan, K. Murugesan and C.C. Tsai, The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders, European Journal of Mechanics B/Fluids, 24, 703-716, 2005. 1.19. C.W. Chen, D.L. Young, C.C. Tsai and K. Murugesan, The method of fundamental solutions for 2D inverse Stokes problems, Computational Mechanics, 37, 2-14, 2005. 1.20. P.S. Kondapalli, D.J. Shippy and G. Fairweather, The method of fundamental solutions for transmission and scattering of elastic waves, Computer Methods in Applied Mechanics and Engineering, 96, 255-269, 1992. 1.21. G. Fairweather, A. Karageorghis and P.A. Martin, The method of fundamental solutions for scattering and radiation problems, Engineering Analysis with Boundary Elements, 27, 759-769, 2003. 1.22. D.L. Young and J.W. Ruan, Method of fundamental solutions for scattering problems of electromagnetic waves, CMES: Computer Modeling in Engineering and Sciences, 7, 223-232, 2005. 1.23. J. Raamachandran, Bending of plates with varying thickness by charge simulation method, Engineering Analysis with Boundary Elements, 10, 143-145, 1992. 1.24. R.L. Johnston and R. Mathon, The computation of electric dipole fields in conducting media, International Journal for Numerical Methods in Engineering, 14, 1739-1760, 1979. 1.25. M.A. Golberg and C.S. Chen, The method of fundamental solution for potential, Helmholtz and diffusion problems, In Boundary Integral Methods – Numerical and Mathematical Aspects, M.A. Golberg (ed.), Computational Mechanics Publications, Boston, 1998, 103-176. 1.26. C.S. Chen, Y.F. Rashed and M.A. Golberg, A mesh-free method for linear diffusion equations, Numerical Heat Transfer, Part B, 33, 469-486, 1998. 1.27. D.L. Young, C.C. Tsai, K. Murugesan, C.M. Fan and C.W. Chen, Time-dependent fundamental solutions for homogeneous diffusion problems, Engineering Analysis with Boundary Elements, 29, 1463-1473, 2004. 1.28. D.L. Young, C.C. Tsai and C.M. Fan, Direct approach to solve nonhomogeneous diffusion problems using fundamental solutions and dual reciprocity methods, Journal of the Chinese Institute of Engineers, 27, 597-609, 2004. 1.29. S.P. Hu, C.M. Fan, C.W. Chen and D.L. Young, Method of fundamental solutions for Stokes’ first and second problems, Journal of Mechanics, 21, 31-37, 2005. 1.30. C.C. Tsai, D.L. Young, C.M. Fan and C.W. Chen, MFS with time-dependent fundamental solutions for unsteady Stokes problems (Engineering Analysis with Boundary Elements in press, 2006). 1.31. S.P. Neuman, Eulerian-Lagrangian numerical scheme for the dispersion-convective equation using conjugate space-time grid, Journal of Computational Physics, 41, 270-294, 1981. 1.32. D.L. Young, C.M. Fan, C.C. Tsai, C.W. Chen and K. Murugesan, Eulerian-Lagrangian method of fundamental solutions for multi-dimensional advection-diffusion problem, International Mathematical Forum, 1, 687-706, 2006. 1.33. C.M. Fan, The Method of Fundamental Solutions for Advection-Diffusion, Burgers, and Navier-Stokes eEquations, PhD Thesis, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, 2005. 1.34. S.P. Hu, Applications of the Method of Fundamental Solutions to the Helmholtz, Diffusion and Burgers’ Equations, Master Thesis, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, 2005. 1.35. D.L. Young, C.M. Fan, S.P. Hu and C.W. Chen, Analysis of multi-dimensional Burgers’ equations by the method of fundamental solutions, International Conference on Computational & Experimental Engineering and Sciences, Chennai, India, Dec 1-10, 2005. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/31721 | - |
dc.description.abstract | 在本論文中,採用基本解法來分析反算及移動剛體之問題。在開始時,將基本解法結合矩陣的條件數來分析反算問題,包含二維拉普拉司方程式、柯西問題、遺失邊界條件和內部資料問題、散佈資料問題以及外型反算識別問題。再者,將基本解法結合穩態的史托克斯例來求解過度指定和不足指定部分邊界的反算史托克斯問題。史托克斯例的係數可以從任意兩個場域變數,例如速度、壓力、渦度或是流線函數來求得。將數值解和解析解加以比較均可以得到良好的結果。
接著,將基本解法與非穩態史托克斯例加以合併,加上對反算問題的數值經驗,可以直接分析半無窮域的非穩態史托克斯問題而不需任何的疊代或正規化處理。進一步的,基本解法結合非穩態史托克斯例可以成功模擬方形和圓形穴室流以及具有多種驅動邊界的非穩態史托克斯問題。模擬結果可清楚的呈現具有一段可動邊界、兩個轉動邊界以及兩個轉動的偏心圓流動現象。最後,將尤拉-拉格朗日基本解法與非穩態史托克斯例合併,用以求解有移動剛體的奈維爾-史托克斯方程式。首先,先驗證二維穴室流在雷諾數10和50的問題。接著,將此數值方法用以模擬有一移動圓柱的奈維爾-史托克斯方程式。尤拉-拉格朗日基本解法可以清楚且直接的描述移動剛體在流場中的現象。將數值方法與沈浸邊界有限元素法加以比較可得到良好的結果。 | zh_TW |
dc.description.abstract | The method of fundamental solutions (MFS) is proposed to deal with the inverse and moving rigid body problems. Firstly, the MFS with condition number analysis is carried out for the inverse problems in 2D Laplace equation, Cauchy problems, problem with missing boundary condition and internal data, problem with scattered data, and shape identification problem. Then, the MFS based on the steady Stokeslets has been employed to solve the inverse Stokes problems with over- and under-specified boundary segments. The coefficients of the Stokeslets can be obtained from any two field variables among the u, v velocity, pressure, vorticity or stream function. The numerical results are almost identical with the analytical solutions and other numerical results.
Furthermore, the unsteady Stokes flow in semi-infinite domain can be handled according to the experiences of dealing with the inverse problems. The MFS with unsteady Stokeslets can directly solve the semi-infinite domain problem without any iteration or regularization. In the next, the unsteady Stokes flow with various driven boundaries, square cavity and circular cavity will be solved. The variations also clearly demonstrate the phenomena of flow system with one moveable piece, two rotating belts and eccentric rotating cylinder. Finally, the Eulerian-Lagrangian method of fundamental solutions (ELMFS), which is a combination of the MFS and the Eulerian-Lagrangian method (ELM), is applied to solve the Navier-Stokes equations with moving rigid body. Further, the benchmark Navier-Stokes flow in lid-driven cavity is validated by the ELMFS based on the unsteady Stokelslets with Re=10 and Re=50. Finally, the phenomena of Navier-Stokes flow with a moving cylinder will be obtained and simulated. The ELMFS can be used clearly and directly to describe the moving rigid body phenomena in the fluid. The numerical results show good agreements with immersed-boundary finite element method (FEM). | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T03:18:26Z (GMT). No. of bitstreams: 1 ntu-95-F91521309-1.pdf: 8359270 bytes, checksum: 091840a36acc254d1ad654e0f160d5e9 (MD5) Previous issue date: 2006 | en |
dc.description.tableofcontents | 誌謝 i
摘要 ii Abstract iii Figurelist vi Tablelist xxii Chapter1 1 Introduction 1 The method of fundamental solutions(MFS) 2 Objectives of the thesis 4 Organization of the thesis 4 Chapter 2 13 The Method of Fundamental Solutions and Condition Number Analysis for Inverse Problems of Laplace Equation 13 Introduction 14 Governing equations 16 Application of the method of fundamental solutions (MFS) 17 Locations of source points and boundary collocation points 18 Condition number and error analysis 20 Numerical results 20 Conclusions 26 Chapter 3 51 The Method of Fundamental Solutions for Inverse 2D Stokes Problems 51 Introduction 52 Governing equations 54 Application of the method of fundamental solutions (MFS) for inverse problems 56 Numerical results 60 Conclusions 68 Chapter 4 95 The Method of Fundamental Solutions for Unsteady Stokes Problems with Semi-infinite Domain and Various Driven Boundaries 95 Introduction 96 Governing equations 98 Numerical results 102 Conclusions 109 Chapter 5 149 The Method of Fundamental Solutions for Navier-Stokes Problems with Moving Rigid Body 149 Introduction 150 Governing equations 151 Numerical results 155 Conclusions 159 Chapter 6 183 Conclusions and Suggestions 183 Conclusions 184 Suggestions 186 Some numerical experiences 188 Appendix A 195 The Method of Fundamental Solutions for Stokes Flow in a Rectangular Cavity with Cylinders 195 Introduction 196 Governing equations 198 Application of the method of fundamental solutions (MFS) 200 Numerical results 202 Conclusions 207 Appendix B 221 The Method of Fundamental Solutions with Eigenfunction Expansion Method for Nonhomogeneous Diffusion Equation 221 Introduction 223 Governing equation 226 Numerical method 227 Results and discussion 232 Conclusions 236 | |
dc.language.iso | en | |
dc.title | 以基本解方法求解反算及移動剛體之問題 | zh_TW |
dc.title | The Method of Fundamental Solutions for Inverse and Moving Rigid Body Problems | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 盧衍祺,卡艾瑋,洪宏碁,蔡加正,廖清標,范佳銘 | |
dc.subject.keyword | 基本解法,反算問題,半無窮域,非穩態史托克斯例,尤拉-拉格朗日基本解法,奈維爾-史托克斯方程式,移動剛體, | zh_TW |
dc.subject.keyword | method of fundamental solutions,inverse problem,semi-infinite domain,unsteady Stokeslets,Eulerian-Lagrangian method,Navier-Stokes equations,moving rigid body, | en |
dc.relation.page | 256 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2006-07-30 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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