Essentials of computational fluid dynamics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2016
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xi, 225 Seiten Illustrationen, Diagramme |
| ISBN: | 9781482227307 |
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| 245 | 1 | 0 | |a Essentials of computational fluid dynamics |c Jens-Dominik Müller |
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| adam_text | Contents
Foreword xi
1 Introduction 1
LI CFD, the virtual wind tunnel.................................... 1
1.2 Examples of CFD applications .................................. 2
1.3 Prerequisites ................................................. 8
1.4 Literature.................................................... 11
1.5 Ingredients................................................... 11
1.6 Organisation of the chapters ................................. 13
1.7 Exercises .................................................... 13
2 Physical and mathematical principles of modern CFD 15
2.1 The physical model ........................................... 15
2.1.1 Continuum assumption .................................. 15
2.1.2 Lagrangian vs. Eulerian description ................... 15
2.1.3 Conservation principles.............................. 16
2.2 The mathematical model: the equations of fluid flow........... 16
2.2.1 Mass conservation in 1-D............................... 17
2.2.2 Mass conservation in 3-D............................. 19
2.2.3 Divergence and gradient operators, total derivative . . 21
2.2.4 The total or material derivative....................... 21
2.2.5 The divergence form of the total derivative ...... 23
2.2.6 Reynolds’ transport theorem........................... 23
2.2.7 Transport of a passive scalar........................ 25
2.3 The momentum equations ....................................... 25
2.3.1 Examples of momentum balance......................... 26
2.3.2 The inviscid momentum equation — the Euler equation 26
2.3.3 The viscous momentum equations — Navier-Stokes . . 29
2.3.4 The incompressible Navier-Stokes equations........... 31
2.3.5 Energy balance....................................... 32
2.3.6 Summary of properties for the Navier-Stokes equations 33
2.4 Simplified model equations ................................... 34
2.4.1 Linear advection equation............................ 34
2.4.2 Inviscid Burgers’ equation........................... 35
2.4.3 Heat equation........................................ 37
2.5 Excercises ................................................... 38
v
VI
Contents
3 Discretisation of the equations 41
3.1 Discretisation of the linear advection equation ............. 42
3.1.1 Finite difference discretisation of linear advection ... 42
3.1.2 Solving the finite difference approximation........... 44
3.1.3 Mesh refinement....................................... 46
3.1.4 Finite volume discretisation of the 1-D advection ... 47
3.1.5 Solving the finite volume approximation............... 51
3.1.6 Finite difference vs. finite volume formulations .... 51
3.2 Burgers’ equation: non-linear advection and conservation . . 54
3.3 Heat equation in 1-D ...................................... 55
3.3.1 Discretising second derivatives....................... 55
3.3.2 1-D Heat equation, differential form.................. 56
3.3.3 Solving the 1-D heat equation.......................... 56
3.4 Advection equation in 2-D 57
3.4.1 Discretisation on a structured grid................... 58
3.5 Solving the Navier-Stokes equations ......................... 52
3.6 The main steps in the finite volume method ..................... 52
3.6.1 Discretisation on arbitrary grids........................ 53
3.6.2 Transport through an arbitrary face...................... 54
3.6.3 The concept of pseudotime-stepping....................... 55
3.6.4 Time-stepping for compressible flows..................... 57
3.6.5 Iterative methods for incompressible flows............... 58
3.6.6 The SIMPLE scheme........................................ 70
3.7 Exercises ...................................................... 7^
4 Analysis of discretisations
4.1 Forward, backward and central differences ...................... 7^
4.2 Taylor analysis: consistency, first- and second-order accuracy 74
4.2.1 Round-off errors......................................... 75
4.2.2 Order of accuracy and mesh refinement.................... 77
4.3 Stability, artificial viscosity and second-order accuracy .... 7^
4.3.1 Artificial viscosity .................................... 80
4.3.2 Artificial viscosity and finite volume methods........... ^1
4.3.3 Stable second-order accurate discretisations for CFD . 84
4.3.4 Monotonicity and second-order accuracy: limiters ... 86
4.4 Summary of spatial discretisation approaches..................... ^
4.5 Convergence of the time-stepping iterations..................... 91
4.5.1 Explicit methods......................................... 92
4.5.2 Implicit methods......................................... 93
4.5.3 Increasing mesh resolution ........................ • • 95
4.5.4 Multigrid................................................ 97
. nc
4.6 Excercises ..................................................
Contents vii
5 Boundary conditions and flow physics 99
5.1 Selection of boundary conditions.............................. 99
5.1.1 Some simple examples............................. 99
5.1.2 Selecting boundary conditions to satisfy the equations 101
5.2 Characterisation of partial differential equations .......... 102
5.2.1 Wave-like solutions: hyperbolic equations ............ 103
5.2.2 Smoothing-type solutions: elliptic equations.... 105
5.2.3 The borderline case — parabolic equations....... 105
5.2.4 The domain of dependence, the domain of influence . 106
5.2.5 Example of characterisation: surface waves ........... 107
5.2.6 Compressible and incompressible flows........... 109
5.2.7 Characterisation of the Navier-Stokes equations .... 110
5.3 Choice of boundary conditions ............................... Ill
5.3.1 Boundary conditions for incompressible flow..... Ill
5.3.2 Boundary conditions for hyperbolic equations.... 113
5.4 Exercises ................................................... 114
6 Turbulence modelling 115
6.1 The challenges of turbulent flow for CFD ................... 115
6.2 Description of turbulent flow................................ 117
6.3 Self-similar profiles through scaling ....................... 120
6.3.1 Laminar velocity profiles............................. 120
6.3.2 Turbulent velocity profile............................ 120
6.4 Velocity profiles of turbulent boundary layers............... 121
6.4.1 Outer scaling: friction velocity ..................... 122
6.4.2 Inner scaling: non-dimensional wall distance y+ ... 124
6.5 Levels of turbulence modelling ............................ 127
6.5.1 Direct Numerical Simulation (DNS) .................... 127
6.5.2 Reynolds-Averaged Navier-Stokes (RANS) ....... 128
6.5.3 Large Eddy (LES) Detached Eddy Simulation (DES) 130
6.5.4 Summary of approaches to turbulence modelling . . . 132
6.6 Eddy viscosity models........................................ 133
6.6.1 Mixing length model............................. 133
6.6.2 The Spalart-Allmaras model ........................... 134
6.6.3 The k — e model................................. 135
6.7 Near-wall mesh requirements.................................. 137
6.7.1 Estimating the wall distance of the first point. 138
6.8 Exercises ................................................. 142 7
7 Mesh quality and grid generation 143
7.1 Influence of mesh quality on the accuracy.................... 143
7.1.1 Maximum angle condition......................... 143
7.1.2 Regularity.......................................... 145
7.1.3 Size variation...................................... 147
7.2 Requirements for the ideal mesh generator ................... 147
Contents
viii
7.3 Structured grids .......................................
7.3.1 Algebraic grids using transfinite interpolation . . .
7.4 Unstructured grids....................................
7.4.1 The Advancing Front Method....................
7.4.2 Delaunay triangulation........................
7.4.3 Hierarchical grid Methods.....................
7.4.4 Hexahedral unstructured mesh generation ....
7.4.5 Hybrid mesh generation for viscous flow.......
7.5 Mesh adaptation.......................................
7.5.1 Mesh movement: r-refinement...................
7.5.2 Mesh refinement: refinement...................
7.6 Exercises ............................................
148
149
153
155
156
157
159
161
162
164
165
167
8 Analysis of the results
8.1 Types of errors..............................
8.1.1 Incorrect choice of boundary conditions
8.1.2 Insufficient convergence..............
8.1.3 Artificial viscosity..................
8.1.4 Modelling errors......................
8.2 Mesh convergence ............................
8.2.1 Cost of error reduction...............
8.3 Validation ..................................
8.4 Summary......................................
8.5 Exercises ...................................
169
169
169
171
173
174
175
175
176
177
178
9 Case studies
9.1 Aerofoil in 2-D, inviscid flow ..............
9.1.1 Case description......................
9.1.2 Flow physics..........................
9.1.3 Meshes ...............................
9.1.4 Simulation results for the C-mesh . . .
9.1.5 Comparison of C- vs O-mesh............
9.1-6 Analysis of lift and drag values . . . .
9.2 Blood vessel bifurcation in 2-D..............
9.2.1 Geometry and flow parameters . . . .
9.2.2 Flow physics and boundary conditions
9.2.3 Velocity and pressure fields..........
9.2.4 Velocity profile in the neck .........
9.2.5 Effect of outlet boundary condition . .
9.3 Aerofoil in 2-D, viscous flow ...............
9.3.1 Flow physics..........................
9.3.2 Turbulence modelling .................
9.3.3 Flow results..........................
9.3.4 Lift and drag.........................
179
179
179
180
182
182
189
192
194
194
196
198
200
200
202
203
205
206
206
Contents
IX
10 Appendix 211
10.1 Finite-volume implementation of 2-D advection...... 211
Bibliography 221
Index 223
Mechanical Engineering
ESSENTIALS OF
COMPUTATIONAL
fluid dynamics
• t of a user of a commercial flow package, Essentials
Covered from the vantage P° vides the information needed to compe-
of Computational Fluia uy This book provides a physical description
tently operate a commerce weaknesses of computational fluid dynamics
of fluid flow, outhnes the s V* of the equations, focuses on the un-
(CFD). presents the basics jnteract with a typical finite-volume discretisa-
derstanding of how the f ° j* * nature of CFD. It emphasizes how the physical
tion, and highlights the app momentum balance) are reflected in the CFD solu-
concepts (mass conserva . A mathematical/numerical background. In addition,
tions while minimismg t and biomedical engineering and includes
it uses cases studies codes and exercise questions. The book also
MATLAB and spreads e ^ core princip|es and key behaviors and incor-
provides practical demon examples of CFD simulations in various fields of
porates a wide range of colorful examp
engineering.
; * *££££ ^;scr«isa«onS. Bn»r action equation, and forward. j
backward (flrsl.order upwind) implemented in a
. Prop«*IP ^ m higWigb„ the diffusive character
spreadsheet rriincation error, and order of accuracy
I l Analyzes the tr^ation error of the forward, backward, central differences j
I . *7*^1*^ upwinding produces ArtificialViscosity (AV) and its j
importance f°r S“^yboondary conditions based on physical considerations
. Explains how number of carefully discussed case studies.
. Illustrates these concepts
rational Fluid Dynamics provides a solid introduction to the
Essentials of Compu and serves as a resource for students in mechanical
basic principles of practica CFq
course as well as practicing professionals
|
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| language | English |
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| spelling | Müller, Jens-Dominik Verfasser aut Essentials of computational fluid dynamics Jens-Dominik Müller Boca Raton ; London ; New York CRC Press 2016 xi, 225 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Numerische Strömungssimulation (DE-588)4690080-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Numerische Strömungssimulation (DE-588)4690080-9 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028436984&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028436984&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Müller, Jens-Dominik Essentials of computational fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4690080-9 |
| title | Essentials of computational fluid dynamics |
| title_auth | Essentials of computational fluid dynamics |
| title_exact_search | Essentials of computational fluid dynamics |
| title_full | Essentials of computational fluid dynamics Jens-Dominik Müller |
| title_fullStr | Essentials of computational fluid dynamics Jens-Dominik Müller |
| title_full_unstemmed | Essentials of computational fluid dynamics Jens-Dominik Müller |
| title_short | Essentials of computational fluid dynamics |
| title_sort | essentials of computational fluid dynamics |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Numerische Strömungssimulation (DE-588)4690080-9 gnd |
| topic_facet | Strömungsmechanik Numerische Strömungssimulation |
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