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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 許文翰(Tony Wen-Hann Sheu) | |
dc.contributor.author | Filip Ivancic | en |
dc.contributor.author | 伊菲利 | zh_TW |
dc.date.accessioned | 2021-05-20T00:49:33Z | - |
dc.date.available | 2020-08-21 | |
dc.date.available | 2021-05-20T00:49:33Z | - |
dc.date.copyright | 2020-08-21 | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020-08-19 | |
dc.identifier.citation | [1] P. G. Ciarlet. The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 2002. [2] Z. Chen. Finite Element Methods and Their Applications. Berlin Heidelberg: Springer-Verlag, 2005. [3] A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations. Berlin, Heidelberg: Springer–Verlag, 1994. [4] J. Donea and A. Huerta. Finite Element Methods for Flow Problems. The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England: John Wiley Sons Ltd, 2003. [5] L. Formaggia and F. Nobile. “A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements”. In: East–West Journal of Numerical Mathematics 7 (1999), pp. 105-132. [6] L. Formaggia and F. Nobile. “Stability analysis of the second–order time accurate schemes for ALE–FEM”. In: Computer Methods in Applied Mechanics and Engineering 193 (2004), pp. 4097-4116. [7] J. G. Trulio and K. R. Trigger. Numerical solution of the one-dimensional hydrodynamic equations in an arbitrary time–dependent coordinate system. Technical Report. California. Univ., Livermore, CA (United States). Lawrence Radiation Lab., 1961. [8] P. D. Thomas and C. K. Lombard. “The Geometric Conservation Law and Its Applications to Flow Computations on Moving Grids”. In: American Institute of Aeronautics and Astronautics (AIAA) Journal 17 (1979), pp. 1030-1037. [9] Y. Abe et al. “Geometric interpretations and spatial symmetry property of metrics in the conservative form for high-order finite-difference schemes on moving and deforming grids”. In: Journal of Computational Physics 260 (2014), pp. 163-203. [10] M. R. Visbal and D. V. Gaitonde. “On the use of higher-order finite-difference schemes on curvilinear and deforming meshes”. In: Journal of Computational Physics 181 (2002), pp. 155-185. [11] X. Deng et al. “Further studies on Geometric Conservation Law and applications to high-order finite difference schemes with stationary grids”. In: Journal of Computational Physics 239 (2013), pp. 90-111. [12] B. Sjögreen, H. C. Yee, and M. Vinokur. “On high order finite–difference metric discretizations satisfying GCL on moving and deforming grids”. In: Journal of Computational Physics 265 (2014), pp. 211-220. [13] H. Zhang et al. “Discrete form of the GCL for moving meshes and its implementation in CFD schemes”. In: Computers Fluids 22 (1993), pp. 9-23. [14] I. Demirdžić and M. Perić. “Space conservation law in finite volume calculations of fluid flow”. In: International Journal for Numerical Methods in Fluids 8 (1998), pp. 1037-1050. [15] M. Lesoinne and C. Farhat. “Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations”. In: Computer Methods in Applied Mechanics and Engineering 134 (1996), pp. 71-90. [16] B. Koobus and C. Farhat. “Second–order time–accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes”. In: Computer Methods in Applied Mechanics and Engineering 170 (1999), pp. 103-129. [17] H. Guillard and C. Farhat. “On the significance of the geometric conservation law for flow computations on moving meshes”. In: Computer Methods in Applied Mechanics and Engineering 190 (2000), pp. 1467-1482. [18] C. Farhat, P. Geuzaine, and C. Grandmont. “The Discrete Geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids”. In: Journal of Computational Physics 174 (2001), pp. 669-694. [19] D. Boffi and L. Gastaldi. “Stability and geometric conservation laws for ALE formulations”. In: Computer Methods in Applied Mechanics and Engineering 193 (2004), pp. 4717-4739. [20] S. Etienne, A. Garon, and D. Pelletier. “Geometric conservation law and finite element methods for 3D unsteady simulations of incompressible flow”. In: Journal of Computational Physics 228 (2009), pp. 2313-2333. [21] M. Solovchuk F. Ivancic T. W.–H. Sheu. “Arbitrary Lagrangian Eulerian-type finite element methods formulation for PDEs on time-dependent domains with vanishing discrete space conservation law”. In: SIAM Journal of Scientific Computing 41 (2019), A1548-A1573. [22] A. N. Brooks and T. J. R. Hughes. “Streamline Upwind/Petrov Galerkin method formulation for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations”. In: Computer Methods in Applied Mechanics and Engineering 32 (1982), pp. 199-259. [23] S. Ganesan and S. Srivastava. “ALE-SUPG finite element method for convection-diffusion problems in time-dependent domains: Conservative form”. In: Applied Mathematics and Computation 303 (2017), pp. 128-145. [24] T. J. R. Hughes, L. P. Franca, and G. M. Hulbert. “A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/Least–Squares method for advective diffusive equations”. In: Computer Methods in Applied Mechanics and Engineering 73 (1989), pp. 173-189. [25] J. Douglas Jr. and J. Wang. “An absolutely stabilized finite element method for the Stokes problem”. In: Mathematics of Computation 52 (1989), pp. 495-508. [26] L. P. Franca, S. L. Frey, and T. J. R. Hughes. “Stabilized finite element methods: I. Application to the advective-diffusive model”. In: Computer Methods in Applied Mechanics and Engineering 95 (1992), pp. 253-276. [27] L. P. Franca and C. Farhat. “Bubble function prompt unusual stabilized finite element methods”. In: Computer Methods in Applied Mechanics and Engineering 123 (1995), pp. 299-308. [28] J.A. Sethian. Level Set Methods and Fast Marching Methods; Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge: Cambridge University Press, 1999. [29] S. Osher and R. Fedkiw. “Level Set Methods and Dynamic Implicit Surfaces”. In: (2003). [30] C. W. Hirt and B. D. Nichols. “Volume of fluid (VOF) method for the dynamics of free boundaries”. In: Journal of Computational Physics 39 (1981), pp. 201-225. [31] W. Aniszewski, T. Ménard, and M. Marek. “Volume of fluid (VOF) type advection methods in two-phase flow: A comparative study”. In: Computers and Fluids 97 (2014), pp. 52-73. [32] S. Ganesan, G. Matthies, and L. Tobiska. “On spurious velocities in incompressible flow problems with interfaces”. In: Computer Methods in Applied Mechanics and Engineering 196 (2007), pp. 1193-1202. [33] S. Elgeti et al. “On the usage of NURBS as interface representation infree-surface flows”. In: International Journal for Numerical Methods in Fluids 69 (2012), pp. 73-87. [34] E. Gros, G. R. Anjos, and J. R. Thome. “Interface-fitted moving mesh method for axisymmetric two–phase flow in microchannels”. In: International Journal for Numerical Methods in Fluids 86 (2018), pp. 201-217. [35] S. Quan and D. P. Schmidt. “A moving mesh interface tracking method for 3D incompressible two-phase flows”. In: Journal of Computational Physics 221 (2007), pp. 761-780. [36] M. Botsch et al. Polygon Mesh Processing. AK Peters / CRC Press, Sept. 2010, p. 250. URL : https://hal.inria.fr/inria-00538098. [37] T. Z. Qian, X. P. Wang, and P. Sheng. “Molecular scale contact line hydrodynamics of immiscible flows”. In: Physical Review E 68 (2003), p. 016306. [38] T. Z. Qian, X. P. Wang, and P. Sheng. “Molecular scale contact line in two-phase immiscible flows”. In: Communications in Computational Physics 1 (2006),pp. 1-52. [39] F. Ivančić, T. W.-H. Sheu, and M. Solovchuk. “The free surface effect on a chemotaxis-diffusion-convection coupling system”. In: Computer Methods in Applied Mechanics and Engineering 356 (2019), pp. 387-406. [40] F. Ivančić, T. W.-H. Sheu, and M. Solovchuk. “Bacterial chemotaxis in thin fluid layers with free surface”. In: Physics of Fluids 32 (2020), p. 061902. [41] J. Donea et al. “Arbitrary Lagrangian-Eulerian Methods”. In: Encyclopedia of Computational Mechanics Second Edition. John Wiley Sons, Ltd., 2017. DOI:10.1002/9781119176817.ecm2009. [42] L. Formaggia et al. “Numerical treatment of defective boundary conditions for the Navier-Stokes equations”. In: SIAM Journal on Numerical Analysis 40 (2002), pp. 376-401. [43] J. Fouchet-Incaux. “Artificial boundaries and formulations for the incompressible Navier-Stokes equations: applications to air and blood flows”. In: SeMA Journal 64 (2014), pp. 1-40. [44] Y. J. Chou and O. B. Fringer. “Consistent discretization for simulations of flows with moving generalized curvilinear coordinates”. In: International Journal for Numerical Methods in Fluids (2009), DOI: 10.1002/fld.2046. [45] T. J. R. Hughes, M. Mallet, and A. Mizukami. “A new finite element formulation for computational fluid dynamics: II. Beyond SUPG”. In: Computer Methods in Applied Mechanics and Engineering 54 (1986), pp. 341-355. [46] A. C. Galeão and E. G. D. D. Carmo. “A consistent approximate upwind Petrov-Galerkin method for convection–dominated problems”. In:Computer Methods in Applied Mechanics and Engineering 68 (1988), pp. 83-95. [47] J. Volker and P. Knobloch. “On the choice of parameters in stabilization methods for convection-diffusion equations”. In: Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications. Graz, Austria, 2007, pp. 297-304. [48] J. Volker and P. Knobloch. “On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I - A review”. In: Computer Methods in Applied Mechanics and Engineering 96 (2007), pp. 2197-2215. [49] A. Sendur. “A Comparative Study on Stabilized finite element methods for the convection-diffusion-reaction problems”. In: Journal of Applied Mathematics 2018 (2018), pp. 1-16. [50] F. Hecht. “New development in freefem++”. In: Journal of Numerical Mathematics 3-4 (2012), pp. 251-265. [51] J.-F. Gerbeau and M. Bercovier C. Le Bris. “Spurious velocities in the steady flow of an incompressible fluid subjected to external forces”. In: International Journal for Numerical Methods in Fluids 25 (1997), pp. 679-695. [52] T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs. “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement”. In: Computer Methods in Applied Mechanics and Engineering 94 (2005), pp. 4135-4195. [53] I. Akkerman et al. “Isogeometric analysis of free-surface flow”. In: Journal of Computational Physics 230 (2011), pp. 4137-4152. [54] S. Ganesan and L. Tobiska. “Modelling and simulation of moving contact line problems with wetting effects”. In: Computing and Visualization in Science 12 (2009), pp. 329-336. [55] J.–F. Gerbeau and T. Lelièvre. “Generalized Navier boundary condition and geometric conservation law for surface tension”. In: Computer Methods in Applied Mechanics and Engineering 198 (2009), pp. 644-656. [56] S. Ganesan and L. Tobiska. “An accurate finite element scheme with moving meshes for computing 3D–axisymmetric interface flows”. In: International Journal for Numerical Methods in Fluids 57 (2008), pp. 119-138. [57] J. P. Ahrens, B. Geveci, and C. C. W. Law. “ParaView: An End-User Tool for Large-Data Visualization”. In: The Visualization Handbook. 2005. [58] E. W. Jenkins, C. Paribello, and N. E. Wilson. “Discrete mass conservation for porous media saturated flow”. In: Numerical Methods for Partial Differential Equations 30 (2014), pp. 625-640. [59] E. Burman and A. Linke. “Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements”. In: Applied Numerical Mathematics 58 (2008), pp. 1704-1719. [60] Ø. Wind-Willassen and M. P. Sørensen. “A finite element method model for droplets moving down a hydrophobic surface”. In: The European Physical Journal E 37 (2014), p. 65. [61] J. Xie et al. “Mode selection between sliding and rolling for droplet on inclined surface: Effect of surface wettability”. In: International Journal of Heat and Mass Transfer 122 (2018), pp. 45-58. [62] B. S. Yilbas et al. “Dynamics of a water droplet on a hydrophobic inclined surface: influence of droplet size and surface inclination angle on droplet rolling”. In: RSC Advances 7 (2017), p. 48806. [63] M. Sbragaglia et al. “Sliding droplets across alternating hydrophobic and hydrophilic stripes”. In: Physical Review E 89 (2014), p. 012406. [64] N. A. Hill and T. J. Pedley. “Bioconvection”. In: Fluid Dynamics Research 37 (2005), pp. 1-20. [65] M. A. Bees. “Advances in bioconvection”. In: The Annual Review of Fluid Mechanics 52 (2020), pp. 449-476. [66] K. Al-Khaled, S. U. Khan, and I. Khan. “Chemically reactive bioconvection flow of tangent hyperbolic nanoliquid with gyrotactic microorganisms and nonlinear thermal radiation”. In: Heliyon 6 (2020), e03117. [67] A. J. Hillesdon, T. J. Pedley, and J. O. Kessler. “The development of concentration in a suspension of chemotactic bacteria”. In: Bulletin of Mathematical Biology 57 (1995), pp. 299-344. [68] A. J. Hillesdon and T. J. Pedley. “Bioconvection in suspensions of oxytactic bacteria: linear theory”. In: Journal of Fluid Mechanics 324 (1996), pp. 223–259. [69] A. Chertock et al. “Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high resolution numerical approach”. In: Journal of Fluid Mechanics 694 (2012), pp. 155-190. [70] Y. Deleuze et al. “Numerical study of plume patterns in a chemotaxis–diffusion-convection coupling system”. In: Computers Fluids 126 (2016), pp. 58-70. [71] M. Hennes et al. “Active depinning of bacterial droplets: The collective surfing of Bacillus subtilis”. In: Proceedings of the National Academy of Sciences 23 (2017), pp. 5958-5963. [72] I. Tuval et al. “Bacterial swimming and oxygen transport near contact lines”. In: Proceedings of the National Academy of Sciences 102 (2005), pp. 2277-2282. [73] S. Chakraborty et al. “Stability and dynamics of a chemotaxis-diffusion-convection system in a shallow fluid layer”. In: Physics of Fluids 30 (2018), p. 071904. [74] D. Lopez and E. Lauga. “Dynamics of swimming bacteria at complex interfaces”. In: Physics of Fluids 26 (2014), p. 071902. [75] K. A. Cliffe and S. J. Tavener. “Marangoni-Bénard convection with a deformable free surface”. In: Journal of Computational Physics 145 (1998), pp. 193-227. [76] F. Roohbakhshan and R. A. Sauer. “A finite membrane element formulation for surfactants”. In: Colloids and Surfaces A 566 (2019), pp. 84-103. [77] M. C. Ruzicka. “On dimensionless numbers”. In: Chemical Engineering Research and Design 86 (2008), pp. 835-868. [78] O. Pironneau. “An energy preserving monolithic Eulerian fluid–structure numerical scheme”. In: hal-01348648 (2016). [79] R. Finn. Equilibrium Capillary Surfaces. New York: Springer-Verlag, 1986. [80] D. V. Lyubimov et al. “On the Boussinesq approximation for fluid systems with deformable interfaces”. In: Advances in Space Research 22 (1998), pp. 1159-1168. [81] L. Formaggia, A. Quarteroni, and A. Veneziani Eds. Cardiovascular Mathematics. Milano: Springer-Verlag Italia, 2009. [82] J. G. Heywood, R. Rannacher, and S. Turek. “Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations”. In: International Journal fo Numerical Methods in Fluids 22 (1996), pp. 325-352. [83] M. A. Fernandéz. “Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit”. In: Boletin de la Sociedad Espanola de Matematica Aplicada. SeMA 55 (2011), pp. 59-108. [84] I. Babuška. “The finite element method with Lagrange multipliers”. In: Numerical Mathematics 20 (1973), pp. 179-192. [85] J. Pitkäranta. “The finite element method with Lagrange multipliers for domainwith corners”. In: Mathematics of Computation 37 (1981), p. 155. [86] J. Pitkäranta. “Boundary subspaces for the finite element method with Lagrange multipliers”. In: Numerical Mathematics 33 (1979), pp. 273-289. [87] J. Pitkäranta. “Local stability conditions for the Babuška method of Lagrange multipliers”. In: Mathematics of Computation 35 (1980), pp. 1113-1129. [88] I. Babuška and G. N. Gatica. “On the mixed finite element method with Lagrange multipliers”. In: Numerical Methods for Partial Differential Equations 19 (2003), p. 192. [89] R. Stenberg. “On some techniques for approximating boundary conditions in the finite element method”. In: Journal of Computational and Applied Mathematics 63 (1995), pp. 139-148. [90] E. Burman and P. Hansbo. “Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems”. In: IMA Journal of Numerical Analysis 30 (2010), pp. 870-885. [91] E. Burman. “Projection stabilization of Lagrange multipliers for the imposition of constraints on interfaces and boundaries”. In: Numerical Methods for Partial Differential Equations 30 (2014), pp. 576-592. [92] H. J. C. Barbosa and T. J. R. Hughes. “Boundary Lagrange multipliers in finite element methods: error analysis in natural norms”. In: Numerical Mathematics 62 (1992), pp. 1-15. [93] H. J. C. Barbosa and T. J. R. Hughes. “The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition”. In: Computer Methods in Applied Mechanics and Engineering 85 (1991), pp. 109-128. [94] F.-X. Roux F. Magoulés. “Lagrangian formulation of domain decomposition methods: A unified theory”. In: Applied Mathematical Modelling 30 (2006), pp. 593-615. [95] C. Farhat, M. Lesoinne, and P. Le Tallec. “Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity”. In: Computer Methods in Applied Mechanics and Engineering 157 (1998), pp. 95-114. [96] M. A. Fernandez and M. Moubachir. “An exact block-Newton algorithm for solving fluid-structure interaction problems”. In: Comptes rendus de l’Académie des Sciences Paris 336 (2003), pp. 681-686. [97] M. A. Fernandez and M. Moubachir. “A Newton method using exact jacobians for solving fluid-structure coupling”. In: Computers and Structures 83 (2005), pp. 127-142. [98] P. Le Tallec and J. Mouro. “Fluid structure interaction with large structural displacements”. In: Computer Methods in Applied Mechanics and Engineering 190 (2001), pp. 3039-3067. [99] J. Hron and S. Turek. “A monolithic FEM solver for an ALE formulation of fluid-structure interaction with configuration for numerical benchmarking”. In: European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2006). [100] T. J. R. Hughes and G. M. Hulbert. “Space-time finite element methods for elastodynamics: Formulations and error estimates”. In: Computer Methods in Applied Mechanics and Engineering 66 (1988), pp. 339-363. [101] H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitex (UTX). 233 Spring Street, New York, NY 10013, USA: Springer Science+Business Media, LLC, 2011. [102] A. Decoene and B. Maury. “Moving meshes with FreeFem++”. In: Journal of Numerical Mathematics 20 (2012), pp. 195-214. [103] M. E. Gurtin. An Introduction to Continuum Mechanics. Pittsburgh, Pennsylvania: Academic Press, 1981. [104] J. O. Kessler. “Path and pattern - the mutual dynamics of swimming cells and their environment”. In: Journal of Theoretical Biology 1 (1989), pp. 85-108. [105] C. Klingenberg, G. Schnücke, and Y. Xia. “An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations”. In: Journal of Scientific Computing 73 (2017), pp. 906-942. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8172 | - |
dc.description.abstract | 本論文目的主要為發展一數值方法用以模擬在時變域上的多物理場系統。考慮此類問題的動機大部分來自於以時變域的偏微分方程式觀點所描述的生醫及生物流體力學問題。為此,我們將採用有限元素法來求解此類問題。此外,我們只考慮在演化過程中其場域拓樸不變的問題,此限制允許我們採用以對齊網格來顯式描述場域介面的任意拉格朗日-歐拉架構。因此,整個數值方法屬於顯式界面追蹤類別方法中的移動網格架構。論文的第一部分主要在守恆形式的ALE架構下推導出一個新穎的有限元數值方法,提供一個系統的方法用以消除由於移動網格下而產生的人工沉降及源項。即便此類人工數值沉降及源項已被眾所皆知,此問題仍是一個開放性且具挑戰性的主題。質量及離散空間律的守恆則為另外兩個需要被解決的問題,而所本論文的方法正是在結合此兩個特徵所發展出的。論文的第二部分將採用所提出的數值方法來解決真實的流體問題,將會著重在自由液面流跟流固耦合問題這兩類主題上,所選取的驗證問題中將會驗證所開發的方法具有良好靈活性及可信賴性。 | zh_TW |
dc.description.abstract | The purpose of this thesis is to develop a numerical method for simulations of multiphysical systems on evolving domains. Motivation for the problems considered in this work comes largely from the field of bio-medicine and bio--fluid mechanics. These multiphysical systems are described in terms of systems of partial differential equations (PDEs) posed on time dependent domains. Finite element method (FEM) is employed for numerical approximation of such problems. Furthermore, only a special class of 'domain-evolving' problems is considered - problems in which domain's topology does not change during its evolution. This restriction allows to work within the so-called arbitrary Lagrangian-Eulerian (ALE) framework in which the interface of domain is described explicitly by the aligned mesh. Thus, the complete numerical method employed falls under a moving mesh category within an explicit, so called interface tracking, approach. The first part of the thesis deals with derivation of a novelty approach in finite element method within ALE framework focused on conservative formulations. This approach offers a systematic way to eliminate artificial sinks and sources arising from the moving mesh. Although the numerical origins of these artificial sinks and sources are well known, this problematics still remains to be an active and challenging topic. The mass conservation problem and the discrete space conservation law (SCL) are the two major issues resolved; actually, the novelty approach is integrated upon these two characteristics. In the second part of the thesis, the newly proposed approach is applied to (academic) problems arising from the real world situations. The attention is on two particular class of problems: free-surface flows and fluid-structure interaction (FSI) problems. The flexibility and credibility of the methodology derived in the first part are demonstrated on selected examples. | en |
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dc.description.tableofcontents | List of Figures (xv) List of Tables (xxv) Introduction (xxvii) I FEM approximation of differential problems within ALE framework (1) 1 Parabolic equations in time-dependent domains (3) 1.1 The Arbitrary Lagrangian-Eulerian framework (4) 1.1.1 Fundamentals of ALE framework (5) 1.1.2 The ALE temporal derivative (8) 1.1.3 Euler expansion formula (9) 1.1.4 Test function spaces in ALE framework (10) 1.1.5 Strong forms of conservation laws (12) 1.1.6 Weak formulations of conservation laws (14) 1.1.7 The transformation of configurations (16) 1.1.8 Pullback of weak formulation to reference configuration (19) 1.2 ALE finite element formulation (20) 1.2.1 Finite element discretization of the ALE map (23) 1.2.2 Finite element formulation (24) 1.2.3 Remark on notation (25) 1.2.4 Example (28) 1.3 Artificial sinks/sources on moving meshes (30) 2 Volume preserving moving mesh method (37) 2.1 Motivation (37) 2.2 Construction of volume preserving deformation (41) 2.3 FEM formulation with Lagrange multiplier (48) 2.4 Numerical validation (52) 2.4.1 Volume gain/loss (53) 2.4.2 Accumulated volume oscillation during the simulation (53) 2.5 Discussion (56) 3. Space Conservation Law (57) 3.1 Space conservation law (59) 3.1.1 SCL in finite element method (62) 3.2 Mesh velocity calculation and vanishing discrete SCL (64) 3.2.1 Mesh velocity piecewise constant in time (64) 3.2.2 Mesh velocity continuous in time (67) 3.3 Discretization schemes (70) 3.3.1 Implicit Euler scheme (72) 3.3.2 Crank-Nicolson scheme (73) 3.3.3 Backward differentiation formula - BDF (73) 3.4 Numerical validation (77) 3.4.1 Stability (77) 3.4.2 Convergence (79) 3.4.3 Accuracy (82) 3.5 Discussion (84) 4. Stabilization methods for FEM on moving meshes (87) 4.1 S-SS decomposition of parabolic equations (89) 4.1.1 S-SS decomposition of differential operator on time–dependent domain (90) 4.2. Numerical diffusion based stabilizations (92) 4.2.1 Selection of the stabilization parameter on time-dependent domain (98) 4.3 Temporal discretization of stabilized conservative formulation (99) 4.4 Numerical validation for scalar conservation laws (102) 4.4.1 Heat equation on an oscillating domain (102) 4.4.2 Convergence of stabilized methods on moving meshes (108) 4.5 Stabilization of the Navier–Stokes equations (111) 4.5.1 S-SS decomposition of Navier-Stokes differential operator (111) 4.5.2 Ladyženskaya-Babuška-Brezzi (inf-sup) condition (113) 4.5.3 Flow past an oscillating cylinder (113) 4.6 Beyond convection stabilization (118) 4.6.1 Convection–diffusion equation on domain with a moving cylinder (118) 4.7 Discussion (120) 5. Curvature evaluation of mesh–fitted interface in FEM (123) 5.1 Curvature in weak form: employment of the Laplace-Beltrami operator (127) 5.2 Introduction of spurious velocities due to curvature approximation (129) 5.2.1 Model problem setup (129) 5.2.2 Finite element formulation (131) 5.3 Detour framework for Laplace-Beltrami operator in finite elements (136) 5.3.1 Finite element formulation for discrete curvature calculation (136) 5.3.2 Effect of finite element spaces on numerical curvature (138) 5.3.3 Beyond linear meshes (141) 5.4 FEM formulation with the numerically corrected curvature (145) 5.4.1 Decoupling the curvature evaluation from the primary problem (147) 5.4.2 Numerical validation - FEM on polygnal meshes (149) 5.4.3 Numerical validation - isoparametric concept (151) 5.5 Discussion (158) II Applications (161) 6. Dynamic contact line problem - sliding droplet (163) 6.1 Introduction (164) 6.2 Moving contact line problem (166) 6.3 Non-dimensionalization (168) 6.4 Weak and FEM formulation (170) 6.5 Numerical results (171) 6.5.1 Mesh adaptation (171) 6.5.2 Droplet on a horizontal solid surface (172) 6.5.3 Droplet on an inclined solid surface (174) 6.6 Discussion (176) 7. Chemotaxis (179) 7.1 Introduction (180) 7.2 Chemotaxis-diffusion-convection (CDC) coupling system with fixed free surface (183) 7.2.1 The dimensional CDC system (183) 7.2.2 The dimensionless CDC system (186) 7.3 Chemotaxis-diffusion-convection (CDC) coupling system with dynamic free surface (188) 7.3.1 The generalized Navier boundary conditions (188) 7.3.2 CDC system with dynamic free surface (191) 7.4 FEM formulation (194) 7.4.1 Weak formulation of system (7.14,7.15) (194) 7.4.2 Numerical (FEM) approach (196) 7.4.3 Multiscale to singlescale formulation (198) 7.5 Numerical simulations (199) 7.5.1 Two–dimensional setup (199) 7.5.2 Three–dimensional setup (202) 7.5.3 Bacterial chemotaxis in bacterial droplets (207) 7.6 Free (thermal) convection (209) 7.6.1 Mathematical model (209) 7.6.2 Non-dimensionalization (211) 7.6.3 Weak and FEM formulation (213) 7.6.4 Numerical results (214) 7.7 Discussion (215) 8. Fluid-Structure Interaction (219) 8.1 Introduction (220) 8.2 Mathematical models for blood and vessel wall (222) 8.2.1 Mathematical model for the blood (22) 8.2.2 Mathematical model for the vessel wall (223) 8.3 Fluid-structure interaction modeling (226) 8.3.1 Fluid–structure coupling (227) 8.3.2 Weak formulation and implicit coupling (228) 8.3.3 Implicit coupling in FEM formulation (231) 8.3.4 Implicit coupling through Lagrange multipliers (232) 8.4 Numerical validation (233) 8.5 Discussion (236) Conclusions (239) | |
dc.language.iso | en | |
dc.title | 在Arbitrary Lagrangian Eulerian架構下發展一具有守恆形式的有限元素法 | zh_TW |
dc.title | Development of an Arbitrary Lagrangian Eulerian Finite Element Formulation in Conservative Form | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-2 | |
dc.description.degree | 博士 | |
dc.contributor.author-orcid | 0000-0002-4711-9477 | |
dc.contributor.coadvisor | 馬克沁(Maxim Solovchuk) | |
dc.contributor.oralexamcommittee | 張建成(Chien-Cheng Chang),王安邦(An-Bang Wang),周逸儒(Yi-Ju Chou),陳宜良(I-Liang Chern),趙修武(Shiu-Wu Chau) | |
dc.subject.keyword | 有限元方法,任意拉格朗日歐拉方法,移動網格,人工沉降源,自由液面流,流固耦合, | zh_TW |
dc.subject.keyword | finite element method,arbitrary Langrangian-Eulerian,moving mesh,artificial sink/source,free-surface flow,fluid-structure interaction, | en |
dc.relation.page | 254 | |
dc.identifier.doi | 10.6342/NTU202003676 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2020-08-20 | |
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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U0001-1708202009102100.pdf | 43.74 MB | Adobe PDF | 檢視/開啟 |
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