| Preface | p. x |
| Review of Relevant Continuum Mechanics | p. 1 |
| Kinematics | p. 3 |
| Description of motion of material points in a body | p. 3 |
| Referential and spatial descriptions | p. 4 |
| Deformation gradient and measures of stretch and strain | p. 5 |
| Velocity gradient and the rate of deformation tensor | p. 7 |
| Special motions | p. 8 |
| Governing equations | p. 9 |
| The transport theorem | p. 9 |
| Conservation of mass | p. 10 |
| Balance of linear momentum | p. 11 |
| Balance of angular momentum | p. 13 |
| Mechanical energy equation | p. 14 |
| Balance of energy | p. 14 |
| Restrictions on constitutive equations | p. 15 |
| Nonlinear viscous fluids | p. 18 |
| Restrictions due to invariance requirements | p. 19 |
| Restrictions on the Reiner-Rivlin equation due to behavior of real fluids | p. 19 |
| Restrictions on generalized Newtonian fluids due to thermodynamic considerations | p. 20 |
| Examples of generalized Newtonian fluids | p. 20 |
| Yield stress "fluids" | p. 21 |
| Bingham model | p. 22 |
| Modified Bingham model | p. 24 |
| Herschel-Bulkley model | p. 24 |
| Casson model | p. 25 |
| Viscoelastic fluids | p. 25 |
| Simple fluids | p. 26 |
| Approximations for simple fluids with fading memory | p. 31 |
| Finite viscoelastic models | p. 34 |
| Thixotropic fluids | p. 36 |
| Rheometrical flows | p. 38 |
| Viscometric flows | p. 38 |
| Periodic flows | p. 45 |
| Non-periodic unsteady flows | p. 51 |
| Rheometers | p. 53 |
| Couette rheometer | p. 54 |
| Cone and plate rheometer | p. 54 |
| Capillary rheometer | p. 55 |
| Nonlinear elastic solids | p. 55 |
| Introduction to hyperelastic materials | p. 56 |
| Invariance restrictions | p. 57 |
| Example: incompressible, isotropic hyperelastic materials | p. 58 |
| References | p. 59 |
| Hemorheology | p. 63 |
| Blood components | p. 66 |
| Plasma | p. 67 |
| Red blood cells (Erythrocytes) | p. 67 |
| White blood cells (Leukocytes) | p. 68 |
| Platelets (Thrombocytes) | p. 69 |
| Relevant parameters for flow in the human cardiovascular system | p. 69 |
| Multiphase behavior of blood in shear flows | p. 72 |
| Low shear behavior: aggregation and disaggregation of erythrocytes | p. 73 |
| High shear rate behavior: deformation, tumbling and realignment of erythrocytes | p. 75 |
| Spatial distribution of erythrocytes in shear flows | p. 76 |
| Outcomes of non-homogeneous distribution of erythrocytes | p. 77 |
| Platelet activation and blood coagulation | p. 78 |
| Vasoconstriction | p. 78 |
| Primary hemostasis | p. 78 |
| Secondary hemostasis or clot formation | p. 79 |
| Wall repair and clot dissolution | p. 79 |
| Models of activation and blood coagulation | p. 79 |
| Special considerations in rheometry of blood | p. 80 |
| Inhomogeneous distribution of particles | p. 80 |
| Thixotropy | p. 82 |
| Biochemical effects | p. 82 |
| Other considerations | p. 82 |
| Viscosity of whole blood | p. 83 |
| Nomenclature for blood viscosity | p. 83 |
| Experimental data for whole blood viscosity | p. 84 |
| Significance of shear thinning in the circulatory system | p. 86 |
| Viscosity models for blood | p. 89 |
| Dependence of blood viscosity on factors other than shear rate | p. 90 |
| Yield stress behavior of blood | p. 96 |
| Yield stress data for blood | p. 97 |
| Yield stress constitutive models for blood | p. 99 |
| Viscoelasticity of blood | p. 100 |
| Measurements of blood viscoelasticity | p. 100 |
| Dependence of viscoelasticity on other factors | p. 105 |
| Significance of viscoelasticity in the circulatory system | p. 107 |
| Viscoelastic constitutive models | p. 107 |
| Disease states and mechanical properties of blood | p. 108 |
| Increased hematocrit | p. 108 |
| Plasma hyperviscosity | p. 109 |
| Hyperaggregation of red blood cells | p. 109 |
| Decreased RBC deformability | p. 109 |
| Gender and the mechanical properties of blood | p. 110 |
| References | p. 112 |
| Mathematical Problems in Classical and Non-Newtonian Fluid Mechanics | p. 121 |
| Problems in the pipe flow of a Navier-Stokes liquid | p. 125 |
| Fully developed flows | p. 125 |
| The entry flow problem | p. 142 |
| Mathematical modeling of a piping system. Unbounded domain approach | p. 148 |
| Mathematical modeling of a piping system. Bounded domain approach with "do-nothing" boundary conditions | p. 171 |
| Problems in non-Newtonian fluid mechanics | p. 193 |
| Why non-Newtonian models? | p. 193 |
| Problems related to generalized Newtonian models | p. 196 |
| Problems related to viscoelastic liquid models | p. 220 |
| Some results in the mathematical theory of second-order fluids 226 | |
| Some results in the mathematical theory of Oldroyd-B fluids and related models | p. 232 |
| Problems in liquid-particle interaction | p. 236 |
| Sedimentation of symmetric particles in viscoelastic liquid | p. 238 |
| Shape-tilting phenomenon | p. 245 |
| Motion of a disk in the shear flow of a liquid in a horizontal channel | p. 247 |
| References | p. 266 |
| Methods for Numerical Flow Simulation | p. 275 |
| Finite-element methods for the simulation of viscous flow | p. 276 |
| The Navier-Stokes equations | p. 276 |
| Discretization of space | p. 278 |
| The stationary algebraic problems | p. 284 |
| Discretization of time | p. 284 |
| The quasi-stationary algebraic problems | p. 288 |
| Numerical simulation of pipe flow | p. 289 |
| Variational `open' boundary conditions | p. 289 |
| Problems with the `do-nothing' boundary condition | p. 292 |
| The problem of well-posedness | p. 293 |
| The closure problem | p. 294 |
| Mesh adaptation and model calibration | p. 295 |
| Principles of a-posteriori error estimation | p. 296 |
| The dual weighted residual (DWR) method | p. 298 |
| Model problems and practical aspects | p. 304 |
| Hyperbolic model case: transport problem | p. 310 |
| Application to flow models | p. 315 |
| Application in optimal flow control | p. 320 |
| Application in hydrodynamic stability analysis | p. 321 |
| Calibration of flow models | p. 323 |
| Current work and further development | p. 328 |
| References | p. 328 |
| Numerics of Fluid-Structure Interaction | p. 333 |
| Fluid-`single rigid body' interaction | p. 334 |
| Model setup in the body frame | p. 335 |
| The stationary free-fall problem | p. 337 |
| Numerical approximation | p. 339 |
| The issue of domain truncation | p. 343 |
| Toward economical meshes | p. 344 |
| Hydrodynamic stability | p. 350 |
| Dynamics of non-stationary free fall | p. 350 |
| Open problems and further development | p. 351 |
| Fluid-`many rigid bodies-wall' interaction | p. 352 |
| The stress-DLM method | p. 352 |
| The fractional-step scheme | p. 353 |
| Open problems and further development | p. 356 |
| Fluid-`elastic structure' interaction | p. 357 |
| Solution methods for FSI problems | p. 357 |
| Variational formulation | p. 358 |
| Numerical approximation | p. 363 |
| Mesh adaptation | p. 365 |
| Stationary test case `Elastic Flow Cavity' | p. 369 |
| Non-stationary test case `Vibrating Thin Plate' | p. 371 |
| Open problems and further development | p. 373 |
| References | p. 375 |
| Numerical Techniques for Multiphase Flow with Liquid-Solid Interaction | p. 379 |
| Numerical methods for incompressible flow | p. 380 |
| Introduction | p. 380 |
| Discretization of the Navier-Stokes equations in time | p. 382 |
| Discretization of the Navier-Stokes equations in space | p. 387 |
| Pressure Schur complement solvers | p. 394 |
| Global MPSC approach | p. 397 |
| Local MPSC approach | p. 401 |
| Multilevel solution strategy | p. 403 |
| Coupling with scalar equations | p. 405 |
| Coupling with k - ¿ turbulence model | p. 408 |
| Adaptive time-step control | p. 413 |
| Some numerical examples | p. 415 |
| Application to more complex flow models | p. 418 |
| Conclusions | p. 429 |
| FSI for fluid - elastic solid configurations | p. 431 |
| Overview | p. 431 |
| Continuum description | p. 433 |
| Fluid structure interaction problem formulation | p. 438 |
| Applications | p. 447 |
| FSI benchmark | p. 451 |
| Conclusion | p. 454 |
| Numerical techniques for fluid-rigid solid configurations | p. 457 |
| Introduction | p. 457 |
| Description of the physical models | p. 460 |
| Moving-mesh method | p. 462 |
| Numerical method | p. 464 |
| Numerical results | p. 471 |
| Conclusions | p. 485 |
| References | p. 492 |
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