Hemodynamical flows: modeling, analysis and simulation
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Series: | Oberwolfach seminars
37 |
| Subjects: | |
| Online Access: | Inhaltstext Hemodynamical flows Inhaltsverzeichnis |
| Physical Description: | XII, 501 S. Ill., graph. Darst. |
| ISBN: | 9783764378059 3764378050 |
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| 245 | 1 | 0 | |a Hemodynamical flows |b modeling, analysis and simulation |c Giovanni P. Galdi ... |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XII, 501 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Oberwolfach seminars |v 37 | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Biomechanics | |
| 650 | 4 | |a Blood Circulation |x physiology | |
| 650 | 4 | |a Blood |x Circulation |x Mathematical models | |
| 650 | 4 | |a Blood |x Circulation |x Mathematics | |
| 650 | 4 | |a Blood |x Circulation |x Models | |
| 650 | 4 | |a Computer Simulation | |
| 650 | 4 | |a Hemodynamics |x physiology | |
| 650 | 4 | |a Hemorheology | |
| 650 | 4 | |a Models, Cardiovascular | |
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Contents
Preface x
I. Review of Relevant Continuum Mechanics 1
Anne M. Robertson
1. Kinematics 3
1.1. Description of motion of material points in a body 3
1.2. Referential and spatial descriptions 4
1.3. Deformation gradient and measures of stretch and strain 5
1.4. Velocity gradient and the rate of deformation tensor 7
1.5. Special motions 8
2. Governing equations 9
2.1. The transport theorem 9
2.2. Conservation of mass 10
2.3. Balance of linear momentum 11
2.4. Balance of angular momentum 13
2.5. Mechanical energy equation 14
2.6. Balance of energy 14
2.7. Restrictions on constitutive equations 15
3. Nonlinear viscous fluids 18
3.1. Restrictions due to invariance requirements 19
3.2. Restrictions on the Reiner-Rivlin equation due to behavior of
real fluids 19
3.3. Restrictions on generalized Newtonian fluids due to
thermodynamic considerations 20
3.4. Examples of generalized Newtonian fluids 20
4. Yield stress "fluids" 21
4.1. Bingham model 22
4.2. Modified Bingham model 24
4.3. Herschel-Bulkley model 24
4.4. Casson model 25
5. Viscoelastic fluids 25
5.1. Simple fluids 26
5.2. Approximations for simple fluids with fading memory 31
5.3. Finite viscoelastic models 34
6. Thixotropic fluids 36
7. Rheometrical flows 38
7.1. Viscometric flows 38
7.2. Periodic flows 45
7.3. Non-periodic unsteady flows 51
8. Rheometers 53
8.1. Couette rheometer 54
8.2. Cone and plate rheometer 54
vi Contents
8.3. Capillary rheometer 55
9. Nonlinear elastic solids 55
9.1. Introduction to hyperelastic materials 56
9.2. Invariance restrictions 57
9.3. Example: incompressible, isotropic hyperelastic materials 58
References 59
II. Hemorheology 63
Anne M. Robertson, Ade'lia Sequeira and Marina V. Kameneva
1. Blood components 66
1.1. Plasma 67
1.2. Red blood cells (Erythrocytes) 67
1.3. White blood cells (Leukocytes) 68
1.4. Platelets (Thrombocytes) 69
2. Relevant parameters for flow in the human cardiovascular system 69
3. Multiphase behavior of blood in shear flows 72
3.1. Low shear behavior: aggregation and disaggregation of
erythrocytes 73
3.2. High shear rate behavior: deformation, tumbling and realignment
of erythrocytes 75
3.3. Spatial distribution of erythrocytes in shear flows 76
3.4. Outcomes of non-homogeneous distribution of erythrocytes 77
4. Platelet activation and blood coagulation 78
4.1. Vasoconstriction 78
4.2. Primary hemostasis 78
4.3. Secondary hemostasis or clot formation 79
4.4. Wall repair and clot dissolution 79
4.5. Models of activation and blood coagulation 79
5. Special considerations in rheometry of blood 80
5.1. Inhomogeneous distribution of particles 80
5.2. Thixotropy 82
5.3. Biochemical effects 82
5.4. Other considerations 82
6. Viscosity of whole blood 83
6.1. Nomenclature for blood viscosity 83
6.2. Experimental data for whole blood viscosity 84
6.3. Significance of shear thinning in the circulatory system 86
6.4. Viscosity models for blood 89
6.5. Dependence of blood viscosity on factors other than shear rate 90
7. Yield stress behavior of blood 96
7.1. Yield stress data for blood 97
7.2. Yield stress constitutive models for blood 99
Contents vii
8. Viscoelasticity of blood 100
8.1. Measurements of blood viscoelasticity 100
8.2. Dependence of viscoelasticity on other factors 105
8.3. Significance of viscoelasticity in the circulatory system 107
8.4. Viscoelastic constitutive models 107
9. Disease states and mechanical properties of blood 108
9.1. Increased hematocrit 108
9.2. Plasma hyperviscosity 109
9.3. Hyperaggregation of red blood cells 109
9.4. Decreased RBC deformability 109
10. Gender and the mechanical properties of blood 110
References 112
III. Mathematical Problems in Classical and Non-Newtonian
Fluid Mechanics 121
Giovanni P. Galdi
1. Problems in the pipe flow of a Navier Stokes liquid 125
1.1. Fully developed flows 125
1.2. The entry flow problem 142
1.3. Mathematical modeling of a piping system. Unbounded
domain approach 148
1.4. Mathematical modeling of a piping system. Bounded
domain approach with "do-nothing" boundary conditions 171
2. Problems in non-Newtonian fluid mechanics 193
2.1. Why non-Newtonian models? 193
2.2. Problems related to generalized Newtonian models 196
2.3. Problems related to viscoelastic liquid models 220
2.4. Some results in the mathematical theory of second-order fluids 226
2.5. Some results in the mathematical theory of Oldroyd-B fluids
and related models 232
3. Problems in liquid-particle interaction 236
3.1. Sedimentation of symmetric particles in viscoelastic liquid 238
3.2. Shape-tilting phenomenon 245
3.3. Motion of a disk in the shear flow of a liquid in a horizontal
channel 247
References 266
IV. Methods for Numerical Flow Simulation 275
Rolf Rannacher
1. Finite-element methods for the simulation of viscous flow 276
1.1. The Navier-Stokes equations 276
1.2. Discretization of space 278
1.3. The stationary algebraic problems 284
1.4. Discretization of time 284
viii Contents
1.5. The quasi-stationary algebraic problems 288
2. Numerical simulation of pipe flow 289
2.1. Variational 'open' boundary conditions 289
2.2. Problems with the 'do-nothing' boundary condition 292
2.3. The problem of well-posedness 293
2.4. The closure problem 294
3. Mesh adaptation and model calibration 295
3.1. Principles of a-posteriori error estimation 296
3.2. The dual weighted residual (DWR) method 298
3.3. Model problems and practical aspects 304
3.4. Hyperbolic model case: transport problem 310
3.5. Application to flow models 315
3.6. Application in optimal flow control 320
3.7. Application in hydrodynamic stability analysis 321
3.8. Calibration of flow models 323
3.9. Current work and further development 328
References 328
V. Numerics of Fluid-Structure Interaction 333
Sebastian Bonisch, Thomas Dunne and Rolf Rannacher
1. Fluid-'single rigid body' interaction 334
1.1. Model setup in the body frame 335
1.2. The stationary free-fall problem 337
1.3. Numerical approximation 339
1.4. The issue of domain truncation 343
1.5. Toward economical meshes 344
1.6. Hydrodynamic stability 350
1.7. Dynamics of non-stationary free fall 350
1.8. Open problems and further development 351
2. Fluid-'many rigid bodies-wall' interaction 352
2.1. The stress-DLM method 352
2.2. The fractional-step scheme 353
2.3. Open problems and further development 356
3. Fluid-'elastic structure' interaction 357
3.1. Solution methods for FSI problems 357
3.2. Variational formulation 358
3.3. Numerical approximation 363
3.4. Mesh adaptation 365
3.5. Stationary test case 'Elastic Flow Cavity' 369
3.6. Non-stationary test case 'Vibrating Thin Plate' 371
3.7. Open problems and further development 373
References 375
Contents ix
VI. Numerical Techniques for Multiphase Flow with
Liquid-Solid Interaction 379
Stefan Turek and Jaroslav Horn
1. Numerical methods for incompressible flow 380
1.1. Introduction 380
1.2. Discretization of the Navier-Stokes equations in time 382
1.3. Discretization of the Navier-Stokes equations in space 387
1.4. Pressure Schur complement solvers 394
1.5. Global MPSC approach 397
1.6. Local MPSC approach 401
1.7. Multilevel solution strategy 403
1.8. Coupling with scalar equations 405
1.9. Coupling with k — e turbulence model 408
1.10. Adaptive time-step control 413
1.11. Some numerical examples 415
1.12. Application to more complex flow models 418
1.13. Conclusions 429
2. FSI for fluid - elastic solid configurations 431
2.1. Overview 431
2.2. Continuum description 433
2.3. Fluid structure interaction problem formulation 438
2.4. Applications 447
2.5. FSI benchmark 451
2.6. Conclusion 454
3. Numerical techniques for fluid-rigid solid configurations 457
3.1. Introduction 457
3.2. Description of the physical models 460
3.3. Moving-mesh method 462
3.4. Numerical method 464
3.5. Numerical results 471
3.6. Conclusions 485
References 492 |
| adam_txt |
Contents
Preface x
I. Review of Relevant Continuum Mechanics 1
Anne M. Robertson
1. Kinematics 3
1.1. Description of motion of material points in a body 3
1.2. Referential and spatial descriptions 4
1.3. Deformation gradient and measures of stretch and strain 5
1.4. Velocity gradient and the rate of deformation tensor 7
1.5. Special motions 8
2. Governing equations 9
2.1. The transport theorem 9
2.2. Conservation of mass 10
2.3. Balance of linear momentum 11
2.4. Balance of angular momentum 13
2.5. Mechanical energy equation 14
2.6. Balance of energy 14
2.7. Restrictions on constitutive equations 15
3. Nonlinear viscous fluids 18
3.1. Restrictions due to invariance requirements 19
3.2. Restrictions on the Reiner-Rivlin equation due to behavior of
real fluids 19
3.3. Restrictions on generalized Newtonian fluids due to
thermodynamic considerations 20
3.4. Examples of generalized Newtonian fluids 20
4. Yield stress "fluids" 21
4.1. Bingham model 22
4.2. Modified Bingham model 24
4.3. Herschel-Bulkley model 24
4.4. Casson model 25
5. Viscoelastic fluids 25
5.1. Simple fluids 26
5.2. Approximations for simple fluids with fading memory 31
5.3. Finite viscoelastic models 34
6. Thixotropic fluids 36
7. Rheometrical flows 38
7.1. Viscometric flows 38
7.2. Periodic flows 45
7.3. Non-periodic unsteady flows 51
8. Rheometers 53
8.1. Couette rheometer 54
8.2. Cone and plate rheometer 54
vi Contents
8.3. Capillary rheometer 55
9. Nonlinear elastic solids 55
9.1. Introduction to hyperelastic materials 56
9.2. Invariance restrictions 57
9.3. Example: incompressible, isotropic hyperelastic materials 58
References 59
II. Hemorheology 63
Anne M. Robertson, Ade'lia Sequeira and Marina V. Kameneva
1. Blood components 66
1.1. Plasma 67
1.2. Red blood cells (Erythrocytes) 67
1.3. White blood cells (Leukocytes) 68
1.4. Platelets (Thrombocytes) 69
2. Relevant parameters for flow in the human cardiovascular system 69
3. Multiphase behavior of blood in shear flows 72
3.1. Low shear behavior: aggregation and disaggregation of
erythrocytes 73
3.2. High shear rate behavior: deformation, tumbling and realignment
of erythrocytes 75
3.3. Spatial distribution of erythrocytes in shear flows 76
3.4. Outcomes of non-homogeneous distribution of erythrocytes 77
4. Platelet activation and blood coagulation 78
4.1. Vasoconstriction 78
4.2. Primary hemostasis 78
4.3. Secondary hemostasis or clot formation 79
4.4. Wall repair and clot dissolution 79
4.5. Models of activation and blood coagulation 79
5. Special considerations in rheometry of blood 80
5.1. Inhomogeneous distribution of particles 80
5.2. Thixotropy 82
5.3. Biochemical effects 82
5.4. Other considerations 82
6. Viscosity of whole blood 83
6.1. Nomenclature for blood viscosity 83
6.2. Experimental data for whole blood viscosity 84
6.3. Significance of shear thinning in the circulatory system 86
6.4. Viscosity models for blood 89
6.5. Dependence of blood viscosity on factors other than shear rate 90
7. Yield stress behavior of blood 96
7.1. Yield stress data for blood 97
7.2. Yield stress constitutive models for blood 99
Contents vii
8. Viscoelasticity of blood 100
8.1. Measurements of blood viscoelasticity 100
8.2. Dependence of viscoelasticity on other factors 105
8.3. Significance of viscoelasticity in the circulatory system 107
8.4. Viscoelastic constitutive models 107
9. Disease states and mechanical properties of blood 108
9.1. Increased hematocrit 108
9.2. Plasma hyperviscosity 109
9.3. Hyperaggregation of red blood cells 109
9.4. Decreased RBC deformability 109
10. Gender and the mechanical properties of blood 110
References 112
III. Mathematical Problems in Classical and Non-Newtonian
Fluid Mechanics 121
Giovanni P. Galdi
1. Problems in the pipe flow of a Navier Stokes liquid 125
1.1. Fully developed flows 125
1.2. The entry flow problem 142
1.3. Mathematical modeling of a piping system. Unbounded
domain approach 148
1.4. Mathematical modeling of a piping system. Bounded
domain approach with "do-nothing" boundary conditions 171
2. Problems in non-Newtonian fluid mechanics 193
2.1. Why non-Newtonian models? 193
2.2. Problems related to generalized Newtonian models 196
2.3. Problems related to viscoelastic liquid models 220
2.4. Some results in the mathematical theory of second-order fluids 226
2.5. Some results in the mathematical theory of Oldroyd-B fluids
and related models 232
3. Problems in liquid-particle interaction 236
3.1. Sedimentation of symmetric particles in viscoelastic liquid 238
3.2. Shape-tilting phenomenon 245
3.3. Motion of a disk in the shear flow of a liquid in a horizontal
channel 247
References 266
IV. Methods for Numerical Flow Simulation 275
Rolf Rannacher
1. Finite-element methods for the simulation of viscous flow 276
1.1. The Navier-Stokes equations 276
1.2. Discretization of space 278
1.3. The stationary algebraic problems 284
1.4. Discretization of time 284
viii Contents
1.5. The quasi-stationary algebraic problems 288
2. Numerical simulation of pipe flow 289
2.1. Variational 'open' boundary conditions 289
2.2. Problems with the 'do-nothing' boundary condition 292
2.3. The problem of well-posedness 293
2.4. The closure problem 294
3. Mesh adaptation and model calibration 295
3.1. Principles of a-posteriori error estimation 296
3.2. The dual weighted residual (DWR) method 298
3.3. Model problems and practical aspects 304
3.4. Hyperbolic model case: transport problem 310
3.5. Application to flow models 315
3.6. Application in optimal flow control 320
3.7. Application in hydrodynamic stability analysis 321
3.8. Calibration of flow models 323
3.9. Current work and further development 328
References 328
V. Numerics of Fluid-Structure Interaction 333
Sebastian Bonisch, Thomas Dunne and Rolf Rannacher
1. Fluid-'single rigid body' interaction 334
1.1. Model setup in the body frame 335
1.2. The stationary free-fall problem 337
1.3. Numerical approximation 339
1.4. The issue of domain truncation 343
1.5. Toward economical meshes 344
1.6. Hydrodynamic stability 350
1.7. Dynamics of non-stationary free fall 350
1.8. Open problems and further development 351
2. Fluid-'many rigid bodies-wall' interaction 352
2.1. The stress-DLM method 352
2.2. The fractional-step scheme 353
2.3. Open problems and further development 356
3. Fluid-'elastic structure' interaction 357
3.1. Solution methods for FSI problems 357
3.2. Variational formulation 358
3.3. Numerical approximation 363
3.4. Mesh adaptation 365
3.5. Stationary test case 'Elastic Flow Cavity' 369
3.6. Non-stationary test case 'Vibrating Thin Plate' 371
3.7. Open problems and further development 373
References 375
Contents ix
VI. Numerical Techniques for Multiphase Flow with
Liquid-Solid Interaction 379
Stefan Turek and Jaroslav Horn
1. Numerical methods for incompressible flow 380
1.1. Introduction 380
1.2. Discretization of the Navier-Stokes equations in time 382
1.3. Discretization of the Navier-Stokes equations in space 387
1.4. Pressure Schur complement solvers 394
1.5. Global MPSC approach 397
1.6. Local MPSC approach 401
1.7. Multilevel solution strategy 403
1.8. Coupling with scalar equations 405
1.9. Coupling with k — e turbulence model 408
1.10. Adaptive time-step control 413
1.11. Some numerical examples 415
1.12. Application to more complex flow models 418
1.13. Conclusions 429
2. FSI for fluid - elastic solid configurations 431
2.1. Overview 431
2.2. Continuum description 433
2.3. Fluid structure interaction problem formulation 438
2.4. Applications 447
2.5. FSI benchmark 451
2.6. Conclusion 454
3. Numerical techniques for fluid-rigid solid configurations 457
3.1. Introduction 457
3.2. Description of the physical models 460
3.3. Moving-mesh method 462
3.4. Numerical method 464
3.5. Numerical results 471
3.6. Conclusions 485
References 492 |
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| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV023285101 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:41:17Z |
| indexdate | 2024-07-20T09:39:00Z |
| institution | BVB |
| isbn | 9783764378059 3764378050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016469858 |
| oclc_num | 225390049 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-188 |
| physical | XII, 501 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Oberwolfach seminars |
| series2 | Oberwolfach seminars |
| spelling | Hemodynamical flows modeling, analysis and simulation Giovanni P. Galdi ... Basel [u.a.] Birkhäuser 2008 XII, 501 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oberwolfach seminars 37 Mathematik Mathematisches Modell Biomechanics Blood Circulation physiology Blood Circulation Mathematical models Blood Circulation Mathematics Blood Circulation Models Computer Simulation Hemodynamics physiology Hemorheology Models, Cardiovascular Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Hämodynamik (DE-588)4022810-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Hämodynamik (DE-588)4022810-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Galdi, Giovanni P. 1947- Sonstige (DE-588)11089152X oth Oberwolfach seminars 37 (DE-604)BV019806550 37 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2837973&prov=M&dok_var=1&dok_ext=htm Inhaltstext http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2346776&custom_att_2=simple_viewer Verlagsdaten Springer Hemodynamical flows HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016469858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hemodynamical flows modeling, analysis and simulation Oberwolfach seminars Mathematik Mathematisches Modell Biomechanics Blood Circulation physiology Blood Circulation Mathematical models Blood Circulation Mathematics Blood Circulation Models Computer Simulation Hemodynamics physiology Hemorheology Models, Cardiovascular Mathematisches Modell (DE-588)4114528-8 gnd Hämodynamik (DE-588)4022810-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4022810-1 (DE-588)1071861417 |
| title | Hemodynamical flows modeling, analysis and simulation |
| title_auth | Hemodynamical flows modeling, analysis and simulation |
| title_exact_search | Hemodynamical flows modeling, analysis and simulation |
| title_exact_search_txtP | Hemodynamical flows modeling, analysis and simulation |
| title_full | Hemodynamical flows modeling, analysis and simulation Giovanni P. Galdi ... |
| title_fullStr | Hemodynamical flows modeling, analysis and simulation Giovanni P. Galdi ... |
| title_full_unstemmed | Hemodynamical flows modeling, analysis and simulation Giovanni P. Galdi ... |
| title_short | Hemodynamical flows |
| title_sort | hemodynamical flows modeling analysis and simulation |
| title_sub | modeling, analysis and simulation |
| topic | Mathematik Mathematisches Modell Biomechanics Blood Circulation physiology Blood Circulation Mathematical models Blood Circulation Mathematics Blood Circulation Models Computer Simulation Hemodynamics physiology Hemorheology Models, Cardiovascular Mathematisches Modell (DE-588)4114528-8 gnd Hämodynamik (DE-588)4022810-1 gnd |
| topic_facet | Mathematik Mathematisches Modell Biomechanics Blood Circulation physiology Blood Circulation Mathematical models Blood Circulation Mathematics Blood Circulation Models Computer Simulation Hemodynamics physiology Hemorheology Models, Cardiovascular Hämodynamik Konferenzschrift |
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| volume_link | (DE-604)BV019806550 |
| work_keys_str_mv | AT galdigiovannip hemodynamicalflowsmodelinganalysisandsimulation |