Introduction to theoretical and computational fluid dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
1997
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 675 S. Ill., graph. Darst. |
| ISBN: | 0195093208 |
Internformat
MARC
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| 100 | 1 | |a Pozrikidis, Constantine |d 1958- |e Verfasser |0 (DE-588)13868796X |4 aut | |
| 245 | 1 | 0 | |a Introduction to theoretical and computational fluid dynamics |c C. Pozrikidis |
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 1997 | |
| 300 | |a X, 675 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804125748157480960 |
|---|---|
| adam_text | Contents
Preface ix
Note to the Instructor xi
Note to the Reader xii
1
Kinematics of a Flow 1
1.1 Fluid velocity and motion of fluid parcels 1
1.2 Lagrangian labels 6
1.3 Properties of parcels, conservation of mass, and the continuity equation 10
1.4 Material vectors, material lines, and material surfaces 13
1.5 Differential geometry of surfaces 20
1.6 Description of a material surface in Eulerian form 23
1.7 Streamlines, stream tubes, path lines, and streak lines 24
1.8 Vorticity, vortex lines, vortex tubes, and circulation around loops 30
1.9 Line vortices and vortex sheets 33
2
Analysis of Kinematics 39
2.1 Irrotational flows and the velocity potential 40
2.2 The reciprocal relation for harmonic functions and Green s functions of Laplace s
equation 49
2.3 Integral representation and further properties of potential flow 55
2.4 The vector potential for incompressible flow 62
2.5 Representation of an incompressible flow in terms of the vorticity 64
2.6 Representation of a flow in terms of the rate of expansion and the vorticity 70
2.7 Stream functions for incompressible flow 71
2.8 Flow induced by vorticity 76
2.9 Axisymmetric flow induced by vorticity 83
2.10 Two dimensional flow induced by vorticity 88
3
Stresses, the Equation of Motion, and the Vorticity Transport Equation 94
3.1 Forces acting in a fluid, traction, the stress tensor, and the equation of motion 94
3.2 Constitutive relations for the stress tensor 105
3.3 Traction, force, torque, energy dissipation, and the reciprocal theorem for incompressible
Newtonian fluids 109
3.4 The Navier Stokes, Euler, and Bernoulli equations 114
3.5 Equations and boundary conditions governing the motion of an incompressible Newtonian
fluid 120
Vi INTRODUCTION TO THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
3.6 Traction, vorticity, and flow kinematics at rigid boundaries, free surfaces, and fluid
interfaces 128
3.7 Scaling of the Navier Stokes equation and dynamic similitude 135
3.8 Change of circulation around material loops and dynamics of the vorticity field 139
3.9 Computation of exact solutions to the equation of motion in two dimensions on the basis
of the vorticity transport equation 149
4
Hydrostatics 155
4.1 Pressure distribution within a fluid in rigid body motion 155
4.2 The Laplace Young equation 159
4.3 Two dimensional interfaces 166
4.4 Axisymmetric interfaces 171
4.5 Three dimensional interfaces 177
5
Computing Incompressible Flows 179
5.1 Steady unidirectional flows 180
5.2 Unsteady unidirectional flows 192
5.3 Stagnation point flows 203
5.4 Flow due to a rotating disk 211
5.5 Flow in a corner due to a point source 214
5.6 Flow due to a point force 216
6
Flow at Low Reynolds Numbers 222
6.1 Equations and fundamental properties of Stokes flow 222
6.2 Local solutions in corners 227
6.3 Nearly unidirectional flows 243
6.4 Flow due to a point force 253
6.5 Fundamental solutions of Stokes flow 259
6.6 Stokes flow past or due to the motion of rigid bodies and liquid drops 264
6.7 Computation of singularity representations 273
6.8 The Lorentz reciprocal theorem and its applications 276
6.9 Boundary integral representation of Stokes flow 280
6.10 Boundary integral equation methods 287
6.11 Generalized Faxen relations 292
6.12 Formulation of two dimensional Stokes flow in complex variables 296
6.13 Effects of inertia and Oseen flow 298
6.14 Unsteady Stokes flow 301
6.15 Computation of unsteady Stokes flow past or due to the motion of particles 309
7
Irrotational Flow 314
7.1 Equations and computation of irrotational flow 315
7.2 Flow past or due to the motion of three dimensional bodies 318
7.3 Force and torque exerted on a three dimensional body 324
7.4 Flow past or due to the motion of a sphere 332
CONTENTS Vii
7.5 Flow past or due to the motion of nonspherical bodies 337
7.6 Flow past or due to the motion of two dimensional bodies 344
7.7 Computation of two dimensional flow past or due to the motion of a body 349
7.8 Formulation of two dimensional flow in complex variables 357
7.9 Conformal mapping 364
7.10 Applications of conformal mapping to flow past two dimensional bodies 370
7.11 The Schwarz Christoffel transformation and its applications 377
8
Boundary Layers 385
8.1 Boundary layer theory 386
8.2 The boundary layer on a semi infinite flat plate 394
8.3 Boundary layers in accelerating and decelerating flow 401
8.4 Computation of boundary layers around two dimensional bodies 405
8.5 Boundary layers in axisymmetric and three dimensional flows 413
8.6 Unsteady boundary layers 416
9
Hydrodynamic Stability 421
9.1 Evolution equations and formulation of the linear stability problem 422
9.2 Solution of the initial value problem and normal mode analysis 426
9.3 Normal mode analysis of unidirectional flows 430
9.4 General theorems on the temporal stability of inviscid shear flows 439
9.5 Stability of a uniform vortex layer subject to spatially periodic disturbances 441
9.6 Numerical solution of the Orr Sommerfeld and Rayleigh equations 449
9.7 Stability of certain classes of unidirectional flows 455
9.8 Stability of a planar interface in potential flow 458
9.9 Viscous interfacial flows 465
9.10 Capillary instability of a curved interface 473
9.11 Inertial instability of rotating fluids 477
10
Boundary Integral Methods for Potential Flow 482
10.1 The boundary integral equation 482
10.2 Boundary element methods 491
10.3 Generalized boundary integral representations 495
10.4 The single layer potential 496
10.5 The double layer potential 500
10.6 Investigation of integral equations of the second kind 506
10.7 Regularization of integral equations of the second kind 511
10.8 Completed double layer representation for exterior flow 516
10.9 Iterative solution of integral equations of the second kind 517
11
Vortex Motion 520
11.1 Invariants of the motion 521
11.2 Point vortices 523
11.3 Vortex blobs 532
Viii INTRODUCTION TO THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
11.4 Two dimensional vortex sheets 535
11.5 Two dimensional flows with distributed vorticity 545
11.6 Two dimensional vortex patches 548
11.7 Axisymmetric flow 551
11.8 Three dimensional flow 553
12
Finite Difference Methods for the Convection Diffusion Equation 558
12.1 Definitions and procedures 558
12.2 One dimensional diffusion 562
12.3 Diffusion in two and three dimensions 571
12.4 One dimensional convection 577
12.5 Convection in two and three dimensions 587
12.6 Convection diffusion in one dimension 589
12.7 Convection diffusion in two and three dimensions 596
13
Finite Difference Methods for Incompressible Newtonian Flow 599
13.1 Methods based on the vorticity transport equation 600
13.2 Velocity pressure formulation 613
13.3 Implementation of methods in primitive variables 617
13.4 Operator splitting, projection, and pressure correction methods 623
13.5 Methods of modified dynamics or false transients 627
Appendix A
Index Notation, Differential Operators, and Theorems of Vector Calculus 632
A.1 Index notation 632
A.2 Vector and matrix products, differential operators in Cartesian coordinates 633
A.3 Orthogonal curvilinear coordinates 635
A.4 Differential operators in cylindrical and plane polar coordinates 637
A.5 Differential operators in spherical polar coordinates 638
A.6 Integral theorems of vector calculus 640
Appendix B
Primer of Numerical Methods 641
B.1 Linear algebraic equations 641
B.2 Computation of eigenvalues of a matrix 646
B.3 Nonlinear algebraic equations 647
B.4 Function interpolation 649
B.5 Computation of derivatives 652
B.6 Function integration 652
B.7 Function approximation 657
B.8 Integration of ordinary differential equations 659
B.9 Computation of special functions 660
Index 663
|
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| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.05 |
| dewey-search | 532.05 |
| dewey-sort | 3532.05 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| spelling | Pozrikidis, Constantine 1958- Verfasser (DE-588)13868796X aut Introduction to theoretical and computational fluid dynamics C. Pozrikidis New York [u.a.] Oxford Univ. Press 1997 X, 675 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerische Strömungssimulation (DE-588)4690080-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Strömungsmechanik (DE-588)4077970-1 s DE-604 Numerische Strömungssimulation (DE-588)4690080-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007548674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| subject_GND | (DE-588)4690080-9 (DE-588)4077970-1 (DE-588)4123623-3 |
| title | Introduction to theoretical and computational fluid dynamics |
| title_auth | Introduction to theoretical and computational fluid dynamics |
| title_exact_search | Introduction to theoretical and computational fluid dynamics |
| title_full | Introduction to theoretical and computational fluid dynamics C. Pozrikidis |
| title_fullStr | Introduction to theoretical and computational fluid dynamics C. Pozrikidis |
| title_full_unstemmed | Introduction to theoretical and computational fluid dynamics C. Pozrikidis |
| title_short | Introduction to theoretical and computational fluid dynamics |
| title_sort | introduction to theoretical and computational fluid dynamics |
| topic | Numerische Strömungssimulation (DE-588)4690080-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Numerische Strömungssimulation Strömungsmechanik Lehrbuch |
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