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DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 許文翰 | |
dc.contributor.author | Chen-Yu Chiang | en |
dc.contributor.author | 蔣承佑 | zh_TW |
dc.date.accessioned | 2021-06-17T06:03:52Z | - |
dc.date.available | 2020-02-12 | |
dc.date.copyright | 2019-02-12 | |
dc.date.issued | 2019 | |
dc.date.submitted | 2019-01-25 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71584 | - |
dc.description.abstract | The present work aims at developing a numerical solver for fluid–structure interac- tion (FSI) problems, especially those encountered in biology such as blood circulation in valved veins. Blood flow is investigated using anatomically and physically relevant models.
Computational procedures are conceived, designed, and implemented in a platform that couples the cheapest cost and the fastest processing using high-performance comput- ing. The first aspect of FSI problems is related to management of algorithm stability. An Eulerian monolithic formulation based on the characteristic method unconditionally achieves stability and introduce a first order in time approximation with two distinct hy- perelastic material models. The second aspect deals with between-solid domain contact such as that between valve leaflets during closure and in the closed state over a finite surface, which avoid vcusp tilting and back flow. A contact algorithm is proposed and validated using benchmarks. Computational study of blood flow in valved veins is investigated, once the solver was verified and validated. The 2D computational domain comprises a single basic unit or the ladder-like model of a deep and superficial veins communicating by a set of perforating veins. A 3D mesh of the basic unit was also built. Three-dimensional computation relies on high performance computing. Blood that contains cells and plasma is a priori a heterogeneous medium. However, it can be assumed homogeneous in large blood vessels, targets of the present study. Red blood capsules that represent the vast majority of blood cells (97%) can deform and aggregate, influencing blood rheology. However, in large veins, in the absence of stagnant flow regions, blood behaves as a Newtonian fluid. Blood flow dynamics is strongly coupled to vessel wall mechanics. Deformable vascular walls of large veins and arteries are composed of three main layers (intima, media, and adventitia) that consist of composite material with a composition specific to each layer. In the present work, the wall rheology is assumed to be a Mooney–Rivlin material. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T06:03:52Z (GMT). No. of bitstreams: 1 ntu-108-F01525007-1.pdf: 26925742 bytes, checksum: 922b915dc03e5bed558043ad70a21766 (MD5) Previous issue date: 2019 | en |
dc.description.tableofcontents | Acknowledgement i
Abstract iii List of Figures xi List of Tables xv Objectives 1 1 Introduction and state of the art 3 1.1 Biological materials 4 1.1.1 Blood—A flowing biological tissue 4 1.1.2 Vascular wall composition 8 1.2 Blood circulatory circuit 10 1.2.1 Heart 10 1.2.2 Windkessel effect 13 1.2.3 Macrocirculation 14 1.2.4 Microcirculation 14 1.3 Mechanical aspects 15 1.3.1 Main blood flow properties 15 1.3.2 Blood rheology 21 1.4 Fluid–structure interactions(FSI) 22 1.4.1 Fluid mechanics – Navier–Stokes equations 24 1.4.2 Vascular wall dynamics 25 1.4.3 Tube law 26 1.4.4 Numerical approaches of FSI problems 28 1.5 Computational aspects of blood flow 30 1.5.1 Modeling and simulation methods in distensible vessels 30 1.5.2 Modeling and simulation methods in collapsible vessels 32 1.5.3 Modeling and simulation methods in aortic valves 32 2 Numerical analysis of a monolithic formulation 35 2.1 Fluid dynamics and solid mechanics equations 37 2.1.1 Fully Eulerian description 38 2.1.2 Solid mechanics equations – incompressible material 39 2.1.3 Solid mechanics equations – compressible material 41 2.2 Monolithic formulation 42 2.2.1 Variational formulation 42 2.3 Numerical schemes and computational algorithm 43 2.3.1 Characteristic–Galerkin derivatives 43 2.3.2 A monolithic time–discrete variational formulation 44 2.3.3 Spacial discretization with finite elements 45 2.3.4 Solution algorithm 46 2.4 Stability analysis of monolithic formulation 47 2.4.1 Conservation of energy 47 2.4.2 Stability of the scheme discretized in time 47 2.4.3 Energy inequality for the fully discrete scheme 49 3 Implementation of a monolithic formulation in FreeFEM++ 51 3.1 Introduction 52 3.2 FreeFem++ and its interpreted language 52 3.2.1 The syntax 52 3.2.2 Meshing tools 54 3.2.3 Finite element method 61 3.3 Solving problems in FreeFem++ 65 3.3.1 Evolution problem 65 3.3.2 Incompressible Navier–Stokes equation 67 3.4 Concluding remarks 72 4 Verification and validation 73 4.1 Validation of Navier Stokes equations 74 4.1.1 Lid–driven cavity flow 74 4.1.2 Flow past a cylinder 78 4.2 Validation of structural equations 80 4.2.1 Bending beam 80 4.3 Validation of 2D monolithic formulation 83 4.3.1 A thin elastic plate clamped into a small rigid square body im- mersed in a flowing fluid 83 4.3.2 A thin elastic plate clamped to a rigid cylinder immersed in a flowing fluid 85 4.3.3 Flow past a flexible sheet with a rear mass attached to a rotatable cylinder 89 4.4 Validation of 3D monolithic formulation 92 4.4.1 Bending of a flexible plate in crossflow 92 4.4.2 Elastic structure in merging flow from two inlets 93 5 Computational contact mechanism 101 5.1 Numerical schemes 102 5.1.1 Penalty method: non–penetration method 103 5.1.2 Lagrange multiplier 103 5.2 Computational results 107 5.2.1 Simulations of contact problems 107 5.2.2 Validation: free falling disc 107 5.2.3 Validation: free falling disc on stairs 110 5.2.4 Falling ball hitting a fixed and rigid ball 112 5.2.5 Falling discs in a container 115 6 Blood flow in valved veins of inferior limbs 117 6.1 Introduction of venous blood flow 118 6.1.1 Vein architecture (anatomy–geometry) 118 6.1.2 Governing equations for blood flow 122 6.1.3 Governing equations for venous wall and valves 123 6.2 Modelling aspects 124 6.2.1 Computational domain – 2Dgeometry 124 6.2.2 Computational domain – meshing 125 6.2.3 Modelling and assumption from 3D to 2D 127 6.2.4 Boundary conditions 128 6.3 Tube law 130 6.4 Numerical results 131 6.4.1 One valved vein 132 6.4.2 Two connected valved veins 132 6.4.3 Network of valved veins in inferior limbs 134 Conclusion Appendices A Collapsible vessels 145 A.1 Flow in collapsible tubes and veins as example 146 A.2 Starling resistor 146 A.3 Collapsible tube law 148 A.4 Main results 152 B Summation of proposed monolithic formulation 155 B.1 Incompressible solid: Mooney–Rivlin model 155 B.1.1 2D formulation 155 B.1.2 3D formulation 156 B.2 Compressible solid: St–Venant–Kirchhoff model 156 B.2.1 2D formulation 156 B.2.2 3D formulation 157 C Domain decomposition methods 159 C.1 Schwarz method...............................160 C.1.1 Preliminary: original Schwarz method 160 C.1.2 Additive Schwarz method 162 C.1.3 Restricted additive Schwarz method 162 C.1.4 Optimized restricted additive Schwarz method 163 C.2 Krylov method – GMRES method 165 C.3 Scalability 165 C.4 Numerical test 167 C.5 Concluding remarks 168 D Computational domain – 3D geometry 169 Bibliography 171 | |
dc.language.iso | en | |
dc.title | 在生物體內的傳輸現象. 直接耦合方法求解流固耦合問題. | zh_TW |
dc.title | Transport in biological systems. Monolithic method for fluid–structure interaction | en |
dc.type | Thesis | |
dc.date.schoolyear | 107-1 | |
dc.description.degree | 博士 | |
dc.contributor.coadvisor | Marc Thiriet | |
dc.contributor.oralexamcommittee | 趙修武,洪子倫,馬克沁(Maxim Solovchuk),Olivier Pironneau,Thierry Coupez | |
dc.subject.keyword | 血流,尤拉耦合方法,流固耦合,有限元素法,靜脈瓣膜, | zh_TW |
dc.subject.keyword | blood flow,eulerian monolithic formulation,fluid-structure interaction,hyperelastic model,Mooney-Rivlin model,StVenant-Kirchhoff model,finite element method,FreeFem++ solver,valved veins, | en |
dc.relation.page | 192 | |
dc.identifier.doi | 10.6342/NTU201900210 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2019-01-25 | |
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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