Introduction to the numerical analysis of incompressible viscous flows:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
2008
|
| Series: | Computational science and engineering
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 213 S. Ill., graph. Darst. 26 cm |
| ISBN: | 9780898716573 |
Staff View
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| 245 | 1 | 0 | |a Introduction to the numerical analysis of incompressible viscous flows |c William Layton |
| 264 | 1 | |a Philadelphia |b Society for Industrial and Applied Mathematics |c 2008 | |
| 300 | |a XIX, 213 S. |b Ill., graph. Darst. |c 26 cm | ||
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| 490 | 1 | |a Computational science and engineering |v 6 | |
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Record in the Search Index
| _version_ | 1804138002411159552 |
|---|---|
| adam_text | Contents
List of
Figures
ix
Foreword
xi
Preface
xiii
I Mathematical Foundations
1
1
Mathematical Preliminaries: Energy and Stress
3
1.1
Finite Kinetic Energy: The Hilbert Space
Ζ,2(Ω)
............. 3
1.1.1
Other norms
............................ 7
1.2
Finite Stress: The Hilbert Space X
:=
//„ (Ω)
............... 8
1.2.1
Weak derivatives and some useful inequalities
.......... 10
1.3
Some Snapshots in the History of the Equations of Fluid Motion
..... 12
1.4
Remarks on Chapter
1........................... 15
1.5
Exercises
.................................. 15
2
Approximating Scalars
17
2.1
Introduction to Finite Element Spaces
................... 17
2.2
An Elliptic Boundary Value Problem
................... 26
2.3
The Galerkin-Finite Element Method
................... 30
2.4
Remarks on Chapter
2........................... 33
2.5
Exercises
.................................. 34
3
Vector and Tensor Analysis
37
3.1
Scalars, Vectors, and Tensors
....................... 37
3.2
Vector and Tensor Calculus
........................ 39
3.3
Conservation Laws
............................. 43
3.4
Remarks on Chapter
3........................... 48
3.5
Exercises
.................................. 49
v¡
Contents
II Steady Fluid Flow Phenomena
51
4
Approximating Vector Functions
53
4.1
Introduction to Mixed Methods for Creeping Row
............ 53
4.2
Variational Formulation of the Stokes Problem
.............. 56
4.3
The Galerkin Approximation
........................ 59
4.4
More About the Discrete Inf-Sup Condition
................ 63
4.4.1
Other div-stable elements
..................... 66
4.5
Remarks on Chapter
4........................... 66
4.6
Exercises
.................................. 68
5
The Equations of Fluid Motion
71
5.1
Conservation of Mass and Momentum
.................. 71
5.2
Stress and Strain in a Newtonian Fluid
.................. 74
5.2.1
More about internal forces
..................... 75
5.2.2
More about V
........................... 76
5.3
Boundary Conditions
............................ 78
5.4
The Reynolds Number
........................... 83
5.5
Boundary Layers
.............................. 87
5.6
An Example of Fluid Motion: The Taylor Experiment
.......... 91
5.7
Remarks on Chapter
5........................... 92
5.8
Exercises
.................................. 95
6
The Steady Navier-Stokes Equations
99
6.1
The Steady Navier-Stokes Equations
................... 99
6.2
Uniqueness for Small Data
......................... 106
6.2.1
The
Oseen
problem
........................ 108
6.3
Existence of Steady Solutions
....................... 110
6.4
The Structure of Steady Solutions
..................... 114
6.5
Remarks on Chapter
6 . . :........................ 117
6.6
Exercises
.................................. 117
7
Approximating Steady Flows
121
7.1
Formulation and Stability of the Approximation
............. 121
7.2
A Simple Example
............................. 124
7.3
Errors in Approximations of Steady Rows
................ 125
7.4
More on the Global Uniqueness Conditions
................131
7.5
Remarks on Chapter
7...........................132
7.6
Exercises
.................. ..... 133
III Time-Dependent Fluid Flow Phenomena
137
8
The Time-Dependent Navier-Stokes Equations
139
8.1
Introduction
................................139
8.2
Weak Solution of the NSE
.....................141
Contents
vii
8.3
Kinetic Energy and Energy Dissipation
..................145
8.4
Remarks on Chapter
8...........................147
8.5
Exercises
..................................148
9
Approximating Time-Dependent Flows
151
9.1
Introduction
................................ 151
9.2
Stability and Convergence of the
Semidiscrete
Approximations
..... 154
9.3
Rates of Convergence
........................... 158
9.4
Time-Stepping Schemes
.......................... 161
9.5
Convergence Analysis of the
Trapezoid
Rule
............... 165
9.5.1
Notation for the discrete time method
............... 165
9.5.2
Error analysis of the
trapezoid
rule
................ 168
9.6
Remarks on Chapter
9........................... 175
9.7
Exercises
.................................. 176
10
Models of Turbulent Flow
179
10.1
Introduction to Turbulence
.........................179
10.2
The K4
1
Theory of Homogeneous,
Isotropie
Turbulence
.........181
10.2.1
Fourier series
............................182
10.2.2
The
inerţial
range
.........................183
10.3
Models in Large Eddy Simulation
.....................186
10.3.1
A first choice of vT
.........................189
10.4
The Smagorinsky Model for vT
......................190
10.5
Near Wall Models: Boundary Conditions for the Large Eddies
......192
10.6
Remarks on Chapter
10..........................194
10.7
Exercises
..................................195
Appendix Nomenclature
197
A.I Vectors and Tensors
............................197
A.2 Fluid Variables
...............................197
A.3 Basic Function Spaces and Norms
.....................198
A.3.1 Other norms
............................198
A.4 Velocity and Pressure Spaces and Norms
.................199
A.5 Finite Element Notation
..........................200
A.6 Turbulence
.................................200
Bibliography
203
Index
211
|
| adam_txt |
Contents
List of
Figures
ix
Foreword
xi
Preface
xiii
I Mathematical Foundations
1
1
Mathematical Preliminaries: Energy and Stress
3
1.1
Finite Kinetic Energy: The Hilbert Space
Ζ,2(Ω)
. 3
1.1.1
Other norms
. 7
1.2
Finite Stress: The Hilbert Space X
:=
//„'(Ω)
. 8
1.2.1
Weak derivatives and some useful inequalities
. 10
1.3
Some Snapshots in the History of the Equations of Fluid Motion
. 12
1.4
Remarks on Chapter
1. 15
1.5
Exercises
. 15
2
Approximating Scalars
17
2.1
Introduction to Finite Element Spaces
. 17
2.2
An Elliptic Boundary Value Problem
. 26
2.3
The Galerkin-Finite Element Method
. 30
2.4
Remarks on Chapter
2. 33
2.5
Exercises
. 34
3
Vector and Tensor Analysis
37
3.1
Scalars, Vectors, and Tensors
. 37
3.2
Vector and Tensor Calculus
. 39
3.3
Conservation Laws
. 43
3.4
Remarks on Chapter
3. 48
3.5
Exercises
. 49
v¡
Contents
II Steady Fluid Flow Phenomena
51
4
Approximating Vector Functions
53
4.1
Introduction to Mixed Methods for Creeping Row
. 53
4.2
Variational Formulation of the Stokes Problem
. 56
4.3
The Galerkin Approximation
. 59
4.4
More About the Discrete Inf-Sup Condition
. 63
4.4.1
Other div-stable elements
. 66
4.5
Remarks on Chapter
4. 66
4.6
Exercises
. 68
5
The Equations of Fluid Motion
71
5.1
Conservation of Mass and Momentum
. 71
5.2
Stress and Strain in a Newtonian Fluid
. 74
5.2.1
More about internal forces
. 75
5.2.2
More about V
. 76
5.3
Boundary Conditions
. 78
5.4
The Reynolds Number
. 83
5.5
Boundary Layers
. 87
5.6
An Example of Fluid Motion: The Taylor Experiment
. 91
5.7
Remarks on Chapter
5. 92
5.8
Exercises
. 95
6
The Steady Navier-Stokes Equations
99
6.1
The Steady Navier-Stokes Equations
. 99
6.2
Uniqueness for Small Data
. 106
6.2.1
The
Oseen
problem
. 108
6.3
Existence of Steady Solutions
. 110
6.4
The Structure of Steady Solutions
. 114
6.5
Remarks on Chapter
6 . . :. 117
6.6
Exercises
. 117
7
Approximating Steady Flows
121
7.1
Formulation and Stability of the Approximation
. 121
7.2
A Simple Example
. 124
7.3
Errors in Approximations of Steady Rows
. 125
7.4
More on the Global Uniqueness Conditions
.131
7.5
Remarks on Chapter
7.132
7.6
Exercises
. . 133
III Time-Dependent Fluid Flow Phenomena
137
8
The Time-Dependent Navier-Stokes Equations
139
8.1
Introduction
.139
8.2
Weak Solution of the NSE
.141
Contents
vii
8.3
Kinetic Energy and Energy Dissipation
.145
8.4
Remarks on Chapter
8.147
8.5
Exercises
.148
9
Approximating Time-Dependent Flows
151
9.1
Introduction
. 151
9.2
Stability and Convergence of the
Semidiscrete
Approximations
. 154
9.3
Rates of Convergence
. 158
9.4
Time-Stepping Schemes
. 161
9.5
Convergence Analysis of the
Trapezoid
Rule
. 165
9.5.1
Notation for the discrete time method
. 165
9.5.2
Error analysis of the
trapezoid
rule
. 168
9.6
Remarks on Chapter
9. 175
9.7
Exercises
. 176
10
Models of Turbulent Flow
179
10.1
Introduction to Turbulence
.179
10.2
The K4
1
Theory of Homogeneous,
Isotropie
Turbulence
.181
10.2.1
Fourier series
.182
10.2.2
The
inerţial
range
.183
10.3
Models in Large Eddy Simulation
.186
10.3.1
A first choice of vT
.189
10.4
The Smagorinsky Model for vT
.190
10.5
Near Wall Models: Boundary Conditions for the Large Eddies
.192
10.6
Remarks on Chapter
10.194
10.7
Exercises
.195
Appendix Nomenclature
197
A.I Vectors and Tensors
.197
A.2 Fluid Variables
.197
A.3 Basic Function Spaces and Norms
.198
A.3.1 Other norms
.198
A.4 Velocity and Pressure Spaces and Norms
.199
A.5 Finite Element Notation
.200
A.6 Turbulence
.200
Bibliography
203
Index
211 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:59:48Z |
| indexdate | 2024-07-09T21:21:16Z |
| institution | BVB |
| isbn | 9780898716573 |
| language | English |
| lccn | 2008018448 |
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| series2 | Computational science and engineering |
| spelling | Layton, William J. Verfasser (DE-588)1020165960 aut Introduction to the numerical analysis of incompressible viscous flows William Layton Philadelphia Society for Industrial and Applied Mathematics 2008 XIX, 213 S. Ill., graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Computational science and engineering 6 Viscous flow / Mathematical models Numerical analysis Fluid mechanics Mathematisches Modell Viscous flow Mathematical models Viskose Strömung (DE-588)4226965-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Viskose Strömung (DE-588)4226965-9 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Computational science and engineering 6 (DE-604)BV022382702 6 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016727542&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Layton, William J. Introduction to the numerical analysis of incompressible viscous flows Computational science and engineering Viscous flow / Mathematical models Numerical analysis Fluid mechanics Mathematisches Modell Viscous flow Mathematical models Viskose Strömung (DE-588)4226965-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4226965-9 (DE-588)4042805-9 (DE-588)4077970-1 |
| title | Introduction to the numerical analysis of incompressible viscous flows |
| title_auth | Introduction to the numerical analysis of incompressible viscous flows |
| title_exact_search | Introduction to the numerical analysis of incompressible viscous flows |
| title_exact_search_txtP | Introduction to the numerical analysis of incompressible viscous flows |
| title_full | Introduction to the numerical analysis of incompressible viscous flows William Layton |
| title_fullStr | Introduction to the numerical analysis of incompressible viscous flows William Layton |
| title_full_unstemmed | Introduction to the numerical analysis of incompressible viscous flows William Layton |
| title_short | Introduction to the numerical analysis of incompressible viscous flows |
| title_sort | introduction to the numerical analysis of incompressible viscous flows |
| topic | Viscous flow / Mathematical models Numerical analysis Fluid mechanics Mathematisches Modell Viscous flow Mathematical models Viskose Strömung (DE-588)4226965-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Viscous flow / Mathematical models Numerical analysis Fluid mechanics Mathematisches Modell Viscous flow Mathematical models Viskose Strömung Numerische Mathematik Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016727542&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022382702 |
| work_keys_str_mv | AT laytonwilliamj introductiontothenumericalanalysisofincompressibleviscousflows |