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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(TonyWen-Hann Sheu) | |
| dc.contributor.author | Ming-Chen Hsu | en |
| dc.contributor.author | 徐銘辰 | zh_TW |
| dc.date.accessioned | 2021-06-13T07:08:24Z | - |
| dc.date.available | 2005-07-29 | |
| dc.date.copyright | 2005-07-29 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-27 | |
| dc.identifier.citation | [1] O. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and breach, New York, 1969.
[2] P. D. Thomas and C. K. Lombard, Geometric conservation law and its application to flow computations on moving grids, AIAA J., 17 (1979), pp. 1030-1037. [3] I. Babuska, Error bounds for finite element methods, Numer. Math., 16 (1971), pp. 322-333. [4] I. Babuska, The finite element method with Lagrange multipliers, Numer. Math., 20 (1973), pp. 179-192. [5] F. Brezzi, On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers, RAIRO, Anal. Num., 8(R2) (1974), pp. 129-151. [6] F. Brezzi and J. Douglas, Stabilized mixed methods for the Stokes problem, Numer. Math., 53 (1988), pp. 225-235. [7] M. Bercovier and O. Pironneau, Error estimate for the finite element solution of the Stokes problem in the primitive variables, Num. Math., 33 (1979), pp. 211-244. [8] A. N. Brooks and T. J. R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 32 (1982), pp. 199-259. [9] A. Mizukami and T. J. R. Hughes, A Petrov-Galerkin finite element method for convection dominated flow: an accurate upwinding technique for satisfying the maximum principle, Comput. Methods Appl. Mech. Eng., 50 (1985), pp. 181-193. [10] M. Ahues and M. Telias, Petrov-Galerkin schemes for the steady state convectiondi usion equation. In K. P. Holz, editor, Finite Elements in Water Resources : proceedings of the 4th international conference, Springer-Verlag, 1982. [11] T. Ikeda, Maximal Principle in Finite Element Models for Convection-Di usion Phenomena, Lecture Notes in Numerical and Applied Analysis, 4, North-Holland, 1983. [12] T. Meis and U. Marcowitz, Numerical solution of partial di erential equations, Lecture Notes in Applied Mathematical Science, 32, Springer-Verlag, New York, 1981. [13] J. G. Rice and R. J. Schnipke, A monotone streamline upwind finite element method for convection-di usion flows, Comput. Methods Appl. Mech. Eng., 47 (1984), pp. 313-327. [14] D. L. Hill and E. A. Baskharone, A monotone streamline upwind method for quadratic finite elements, Int. J. Numer. Methods Fluids, 17 (1993), pp. 463-475. [15] C. K. W. Tam and J. C. Webb, Dispersion-relation-preserving finite di erence schemes for computational acoustics, J. Comput. Phys., 107 (1993), pp. 262-281. [16] F. Q. Hu, M. Y. Hussaini and J. L. Manthey, Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics, J. Comput. Phys., 124 (1996), pp. 177-191. [17] R. K. Lin, T. W. H. Sheu, Application of dispersion-relation-preserving theory to develop a two-dimensional convection-di usion scheme, J. Comput. Phys., 208 (2005), pp. 493-526. [18] J. Donea, An arbitrary Lagrangian-Eulerian finite element method for transient fluid-Vstructure interactions. Comput. Methods Appl. Mech. Eng. 33 (1982) pp. 689-723. [19] T. J. R. Hughes and G. J. Hulbert, Space-time finite element methods for elastodynamics: formulations and error estimates. Comput. Methods Appl. Mech. Eng. 66 (1988) pp. 339-363. [20] T. J. R. Hughes, W. K. Liu and T. K. Zimmerman, LagrangianVEulerian finite element formulation for incompressible viscous flow. Comput. Methods Appl. Mech. Eng. 29 (1981) pp. 329-349. [21] C. Bernardi, Y. Maday and A. T. Patera, Domain decomposition by the mortar element method. In Asymptotic and Numerical Methods for PDEs with Critical Parameters, vol. 384. Kaper HG, Garbey M. (eds), NATO ASI Series C: Mathematical and Physical Sciences, Kluwer: Dordrecht, 1993, pp. 169-186. [22] B. F. Ben and Y. Maday, The mortar fiinite element method for the three dimensional finite elements. RAIRO Analyse Numerique 31 (1997) pp. 289-302. [23] P. Hansbo, The characteristic streamline di usion method for the time-dependent incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 99 (1992), pp. 171-186. [24] M. Behr and T. E. Tezduyar, Finite element solution strategies for large-scale flow simulations, Comput. Methods Appl. Mech. Eng., 112 (1994), pp. 3-24. [25] S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30 (1998), pp. 329-361. [26] A. Esmaeeli and F. Tryggvasonm, Direct numerical simulation of bubbly flow, Part 2, moderate Reynolds number arrays, Journal of Fluid Mechanics, 385 (1999), pp.325-358. [27] H. H. Hu, N. A. Patankar and M. Y. Zhu, Direct numerical simulation of fluid-solid systems using the arbitrary LagrangianVEulerian technique, Journal of Computational Physics, 169 (2001), pp. 427-462. [28] J. von Neumann and R. D. Richtmyer, A method for the numerical calculation on hydrodynamic shock, J. Appl. Phys., 21 (1950), pp. 232-237. [29] R. F. Warming and B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite-di erence method, J. Comput. Phys., 14 (1974), pp. 159-179. [30] E. Burman and P. Hansbo, Edge stabilization for Galerkin approximations of convection-di usion-reaction problems, Comput. Method Appl. Mech. Engrg., 193 (2004), pp. 1437-1453. [31] R. M. Smith and A. G. Hutton, The numerical treatment of advection: a performance comparison of current methods, Numer. Heat Transf., 5 (1982), pp. 439-461. [32] H. Wang, H. K. Dahle, R. E. Ewing, M. S. Espedal, R. C. Sharpley and S. Man, An ELLAM scheme for advection-di usion equations in two dimensions. SIAM J. Sci. Comput., 20 (1999), pp. 2160-2194. [33] P. Tamamidis and D. N. Assanis, Evaluation for various high-order-accuracy schemes with and without flux limiters. Int. J. Numer. Methods Fluids, 16 (1993), pp. 931-948. [34] R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland, Amsterdam, 1979. [35] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986. [36] M.D. Gunzburger, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms, Academic Press, New York, 1989. [37] T. W. H. Sheu, S. F. Tsai and M. M. T. Wang, A Petrov-Galerkin formulation for incompressible flow at high Reynolds number, Comp. Fluid. Dyn., 5 (1995), pp. 213-230. [38] U. Ghia, K. N. Ghia and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48 (1982), pp. 387-411. [39] E. Erturk, T. C. Corke and C. G‥okc﹐ ‥ol, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, Int. J. Numer. Methods Fluids, 48 (2005), pp. 747-774. [40] M. T. Wang and T. W. H. Sheu, Implementation of a free boundary condition to Navier-Stokes equations, Int. J. Numer. Methods for Heat & Fluids Flow, 7 (1997), pp. 95-111. [41] D. K. Gartling, A test problem for outflow boundary conditons-flow over a backward-facing step, Int. J. Numer. Methods Fluids, 11 (1990), pp. 953-967. [42] P. M. Gresho, D. K. Gartling, K. H. Winters, T. J. Garratt, A. Spence and J. W. Goodrich, Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable?, Int. J. Numer. Methods Fluids, 17 (1993), pp. 501-541. [43] R. L. Sani and P. M. Gresho, R’esum’e and remarks on the open boundary condition ministmposium, Int. J. Numer. Methods Fluids, 18 (1994), pp. 983-1008. [44] I. E. Barton, The entrance e ect of laminar flow over a backward-facing step geometry, Int. J. Numer. Methods Fluids, 25 (1997), pp. 633-644. [45] J. Keskar and D. A. Lyn, Computations of a laminar backward-facing step flow at Re = 800 with a spectral domain decomposition method, Int. J. Numer. Methods Fluids, 29 (1999), pp. 411-427. [46] D. C. Wan, B. S. V. Patnail and G. W. Wei, Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows, J. Comput. Phys., 180 (2002), pp. 229-255. [47] S. Abide and S. Viazzo, A 2D compact fourth-order projection decomposition method, J. Comput. Phys., 206 (2005), pp. 252-276. [48] H. Zhang, M. Reggio, J. Y. Tr`epanier and R. Camarero, Discrete form of the GCL for moving meshes and its implementation in CFD schemes, Computers Fluids, 22(1) 1993), pp. 9-23. [49] H. Y. H. Chen and T. W. H. Sheu, Finite-element simulation of incompressible fluid flow in an elastic vessel, Int. J. Numer. Meth. Fluids, 42 (2003) pp. 131-146. [50] A. Okajima, Strouhal numbers of rectangular cylinders, J. Fluid Mech., 123 (1982), pp. 379-398. [51] R.W. Davis and E. F. Moore, A numerical study of vortex shedding from rectangles, J. Fluid Mech., 116 (1982), pp. 475-506. [52] R. Franke, W. Rodi and B. Sch‥onung, Numerical calculation of laminar vortexshedding flow past cylinders, J. Wind Eng. Ind. Aerodyn., 35 (1990), pp. 237-257. [53] M. P. Arnal, D. J. Goering and J. A. C. Humphrey, Vortex shedding from a bluff body adjacent to a plane sliding wall, J. Fluids Eng., 113 (1991), pp. 384-398. [54] G. LI and J. A. C. Humphrey, Numerical modelling of confined flow past a cylinder of square corss-section at vatious orientations, Int. J. Numer. Methods Fluids, 20 (1995), pp. 1215-1236. [55] A. Sohankar, C. Nurberg and L. Davidson, Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition, Int. J. Numer. Methods Fluids, 26 (1998), pp. 39-56. [56] A. N. Pavlov, S. S. Sazhin, R. P. Fedorenko and M. R. Heikal, A conservative finite difference method and its application for the analysis of a transient flow around a square prism, Int. J. Numer. Methods for Heat & Fluids Flow, 10 (2000), pp. 6-46. [57] D. C.Wan, B. S. V. Patnaik and G.W.Wei, Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows, J. Comput. Phys., 180 (2002), pp. 229-255. [58] N. Steggel and N. Rockli , Simulation of the e ects of body shape on lock-in characteristics in pulsating flow by the discrete vortex method, J. Wind Eng. Ind. Aerodyn., 69-71 (1997), pp. 317-329. [59] CFD Research Corporation (CFDRC), CFD Research Corp.(CFDRC)- Engineering Simulations Software, Services and R&D, 2005, <http://www.cfdrc.com/> (25 July 2005) [60] C. D. Munz, M. Dumbser and M. Zucchini, The multiple pressure variables method for fluid dynamics and aeroacoustics at low Mach numbers, submitted to Numerical methods for hyperbolic and kinetic problems, S. Cordier, T. Goudon, M. Gutnic, E. Sonnendrucker (eds.), IRMA series in mathematics and theoretical physics, de Gruyter. [61] S. Roller, T. Schwartzkop , R. Fortenbach, M. Dumbser and C. D. Munz, Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations, submitted to Mathematical Modelling and Numerical Analysis. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/35754 | - |
| dc.description.abstract | 本研究的目的是發展一保有色散關係之二維Petrov-Galerkin有限元模型，以期有效地去除錯誤的數值振蕩。此外，本文將任意的Lagrangian-Eulerian描述引入Navies-Stokes方程中，以便在移動的網格上得以求解高雷諾數之不可壓縮流體。為了強調所提出之精確色散捕捉能力，我們進行對流–擴散模型方程之基本分析。透過一系列的測試題目，得以證實本文所提出具保有色散關係之Petrov-Galerkin有限元模型確能有效地求解具移動網格問題。最後並將所開發之 DRP-PG有限元模型應用於生醫領域中有關聲帶震動的模擬，以瞭解聲道中流場所引起之發聲機制。 | zh_TW |
| dc.description.abstract | This thesis aims to develop a two-dimensional Petrov-Galerkin (PG) finite element model for effectively resolving erroneous oscillations in the simulation of incompressible viscous fluid flows at high Reynolds numbers in moving meshes by preserving the dispersion relation property. In order to stress the effectiveness of the developed test functions in providing better dispersive nature, we have conducted fundamental studies on the convection-diffusion equation. Several benchmark problems amenable to exact solutions are investigated for the sake of validation. The Navier-Stokes fluid flows in a lid-driven cavity and backward-facing step are also studied at different Reynolds numbers. For the incompressible flow problem with a moving boundary, the Arbitrary Lagrangian-Eulerian (ALE) method is developed in the formulation that is applicable to the time-varying domains. The flow over an oscillating square cylinder is chosen for validation. In order to apply our method in biomechanics area, we consider a vocal fold vibration problem and simplify the geometry as a contraction-and-expansion channel. By virtue of the fundamental analyses and numerical validations, the proposed dispersion-relation-preserving Petrov-Galerkin (DRP-PG) finite element model has been proven to be highly reliable and applicable to solve a wide range of incompressible flow problems in moving meshes. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T07:08:24Z (GMT). No. of bitstreams: 1 ntu-94-R92525018-1.pdf: 8732442 bytes, checksum: 81197609a5641687bd0a85612d34361b (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 1 Introduction 1 1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Working equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Working equations on fixed meshes . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Working equations on moving grids . . . . . . . . . . . . . . . . . . . . . 2 1.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Finite element model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 Petrov-Galerkin (PG) model . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.3 Dispersion-relation-preserving theory . . . . . . . . . . . . . . . . . . . 5 1.3.4 Arbitrary Lagrangian-Eulerian (ALE) method . . . . . . . . . . . . . . . . 5 1.4 Outlines of this study . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Finite element model for two-dimensional convection-diffusion scalar equation . 8 2.1 Transport equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Interpolation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Weak statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Two-dimensional dispersion-relation-preserving Petrov-Galerkin model . . . . . 13 3.1 Petrov-Galerkin (PG) model . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Dispersion-relation-preserving PG model . . . . . . . . . . . . . . . . . . . 15 3.3 Dispersion and Fourier (or von Neumann stability) analyses . . . . . . . . . 18 3.4 Fundamental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5.1 Gaussian and hyperbolic tangent problem . . . . . . . . . . . . . . . . . . 21 3.5.2 Skew convection-diffusion problem . . . . . . . . . . . . . . . . . . . . . 22 3.5.3 Convection-diffusion problem of Smith and Hutton . . . . . . . . . . . . . 23 3.5.4 Rotation of a cone-shaped scalar field . . . . . . . . . . . . . . . . . . 23 3.5.5 Mixing of hot and cold fluids . . . . . . . . . . . . . . . . . . . . . . . 24 4 Two-dimensional incompressible Navier-Stokes equations 48 4.1 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.1 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.2 Lid-driven cavity flow problem . . . . . . . . . . . . . . . . . . . . . . 52 4.2.3 Backward-facing step flow problem . . . . . . . . . . . . . . . . . . . . . 52 5 Moving boundary problem 68 5.1 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2 Geometric conservation law and grid velocity . . . . . . . . . . . . . . . . 69 5.3 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.3.1 Flow over a square cylinder . . . . . . . . . . . . . . . . . . . . . . . . 71 5.3.2 Flow over a square cylinder oscillating along the x direction . . . . . . . 73 5.3.3 Contraction-and-expansion channel . . . . . . . . . . . . . . . . . . . . . 75 6 Concluding remarks 96 A DRP-PG coefficients τi 98 B Coefficient matrices for Φx 100 C Derivation for ki and kr 102 | |
| dc.language.iso | zh-TW | |
| dc.title | 以精確色散之Petrov-Galerkin有限元模型求解二維不可壓縮Navier-Stokes方程於移動網格 | zh_TW |
| dc.title | Two-dimensional Dispersively Accurate Petrov-Galerkin Model for Solving Incompressible Navier-Stokes Equations on Moving Meshes | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔣德普(Te-Pu Chiang),蔡順峰(Shun-Feng Tsai),王識貴(Shih-Kuei Wang) | |
| dc.subject.keyword | 不可壓縮,高雷諾數,保有色散關係,移動網格,聲帶, | zh_TW |
| dc.subject.keyword | two-dimensional,incompressible,high Reynolds numbers,dispersion-relation- preserving,Arbitrary Lagrangian-Eulerian,vocal folds, | en |
| dc.relation.page | 110 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-27 | |
| 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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