Finite element methods for flow problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2004
|
| Ausgabe: | Reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 350 S. Ill., graph. Darst. |
| ISBN: | 0471496669 |
Internformat
MARC
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| 245 | 1 | 0 | |a Finite element methods for flow problems |c Jean Donea and Antonio Huerta |
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| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2004 | |
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Datensatz im Suchindex
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| adam_text | Titel: Finite element methods for flow problems
Autor: Donea, Jean
Jahr: 2004
Contents
Preface xi
1 Introduction and preliminaries 1
1.1 Finite elements in fluid dynamics 1
1.2 Subjects covered 2
1.3 Kinematical descriptions of the flow field 4
1.3.1 Lagrangian and Eulerian descriptions 5
1.3.2 ALE description of motion 8
1.3.3 The fundamental ALE equation 11
1.3.4 Time derivative of integrals over moving
volumes 12
1.4 The basic conservation equations 13
1.4.1 Mass equation 13
1.4.2 Momentum equation 13
1.4.3 Internal energy equation 15
1.4.4 Total energy equation 17
1.4.5 ALE form of the conservation equations 18
1.4.6 Closure of the initial boundary value problem 19
1.5 Basic ingredients of the finite element method 19
1.5.1 Mathematical preliminaries 19
Vi CONTENTS
1.5.2 Trial solutions and weighting functions 21
1.5.3 Compact integral forms 23
1.5.4 Strong and weak forms of a boundary value
problem 23
1.5.5 Finite element spatial discretization 27
2 Steady transport problems 33
2.1 Problem statement 33
2.1.1 Strong form 33
2.1.2 Weakform 35
2.2 Galerkin approximation 36
2.2.1 Piecewise linear approximation in 1D 37
2.2.2 Analysis of the discrete equation 40
2.2.3 Piecewise quadratic approximation in ID 45
2.2.4 Analysis of the discrete equations 47
2.3 Early Petrov-Galerkin methods 50
2.3.1 Upwind approximation of the convective term 50
2.3.2 First finite elements of upwind type 51
2.3.3 The concept of balancing diffusion 53
2.4 Stabilization techniques 59
2.4.1 The SUPG method 60
2.4.2 The Galerkin/Least-squares method 63
2.4.3 The stabilization parameter 64
2.5 Other stabilization techniques and new trends 65
2.5.1 Finite increment calculus 66
2.5.2 Bubble functions and wavelet approximations 67
2.5.3 The variational multiscale method 68
2.5.4 Complements 70
2.6 Applications and solved exercises 70
2.6.1 Construction of a bubble function method 70
2.6.2 One-dimensional transport 72
2.6.3 Convection-diffusion across a source term 74
2.6.4 Convection-diffusion skew to the mesh 75
2.6.5 Convection-diffusion-reaction in 2D 76
2.6.6 The Hemker problem 78
3 Unsteady convective transport 79
3.1 Introduction 79
3.2 Problem statement 81
CONTENTS Vii
3.3 The method of characteristics 82
3.3.1 The concept of characteristic lines 82
3.3.2 Properties of the linear convection equation 84
3.3.3 Methods based on the characteristics 87
3.4 Classical time and space discretization techniques 91
3.4.1 Time discretization 92
3.4.2 Galerkin spatial discretization 94
3.5 Stability and accuracy analysis 98
3.5.1 Analysis of stability by Fourier techniques 99
3.5.2 Analysis of classical time-stepping schemes 101
3.5.3 The modified equation method 105
3.6 Taylor-Galerkin Methods 107
3.6.1 The need for higher-order time schemes 107
3.6.2 Third-order explicit Taylor-Galerkin method 108
3.6.3 Fourth-order explicit leap-frog method 113
3.6.4 Two-step explicit Taylor-Galerkin methods 114
3.7 An introduction to monotonicity-preserving schemes 117
3.8 Least-squares-based spatial discretization 120
3.8.1 Least-squares approach for the 6 family of
methods 121
3.8.2 Taylor least-squares method 122
3.9 The discontinuous Galerkin method 124
3.10 Space-time formulations 126
3.10.1 Time-discontinuous Galerkin formulation 126
3.10.2 Time-discontinuous least-squares formulation 128
3.10.3 Space-timeGalerkin/Least-squaresformulation 128
3.11 Applications and solved exercises 129
3.11.1 Propagation of a cosine profile 129
3.11.2 Travelling wave package 133
3.11.3 The rotating cone problem 135
3.11.4 Propagation of a steep front 137
Compressible Flow Problems 147
4.1 Introduction 147
4.2 Nonlinear hyperbolic equations 149
4.2.1 Scalar equations 149
4.2.2 Weak solutions and entropy condition 152
4.2.3 Time and space discretization 156
4.3 The Euler equations 159
Vtli CONTENTS
4.3.1 Strong form of the conservation equations 159
4.3.2 The quasi-linear form of the Euler equations 161
4.3.3 Basic properties of the Euler equations 163
4.3.4 Boundary conditions 165
4.4 Spatial discretization techniques 166
4.4.1 Galerkin formulation 167
4.4.2 Upwind-type discretizations 168
4.5 Numerical treatment of shocks 176
4.5.1 Introduction 176
4.5.2 Early artificial diffusion methods 178
4.5.3 High-resolution methods 180
4.6 Nearly incompressible flows 186
4.7 Fluid-structure interaction 187
4.7.1 Acoustic approximation 189
4.7.2 Nonlinear transient dynamic problems 191
4.7.3 Illustrative examples 196
4.8 Solved exercises 199
4.8.1 One-step Taylor-Galerkin solution of Burgers
equation 199
4.8.2 The shock tube problem 202
5 Unsteady convection-diffusion problems 209
5.1 Introduction 209
5.2 Problem statement 210
5.3 Time discretization procedures 211
5.3.1 Classical methods 211
5.3.2 Fractional-step methods 213
5.3.3 High-order time-stepping schemes 215
5.4 Spatial discretization procedures 222
5.4.1 Galerkin formulation of the semi-discrete
scheme 222
5.4.2 Galerkin formulation of 0 family methods 224
5.4.3 Galerkin formulation ofexplicit Pade schemes 228
5.4.4 Galerkin formulation of implicit multistage
schemes 229
5.4.5 Stabilization of the semi-discrete scheme 231
5.4.6 Stabilization of multistage schemes 233
5.5 Stabilized space-time formulations 241
5.6 Solved exercises 243
CONTENTS IX
5.6.1 Convection-diffusion of a Gaussian hill 243
5.6.2 Transient rotating pulse 246
5.6.3 Steady rotating pulse problem 250
5.6.4 Nonlinear propagation of a step 250
5.6.5 Burgers equation in ID 251
5.6.6 Two-dimensional Burgers equation 252
Appendix Least-squares in transient/relaxation problems 254
Viscous incompressible flows 265
6.1 Introduction 265
6.2 Basic concepts 267
6.2.1 Strain rate and spin tensors 267
6.2.2 The stress tensor in a Newtonian fluid 268
6.2.3 The Navier-Stokes equations 269
6.3 Main issues in incompressible flow problems 272
6.4 Trial solutions and weighting functions 273
6.5 Stationary Stokes problem 275
6.5.1 Formulation in terms of Cauchy stress 275
6.5.2 Formulation in terms of velocity and pressure 278
6.5.3 Galerkin formulation 279
6.5.4 Matrix problem 281
6.5.5 Solvability condition and solution procedure 283
6.5.6 The LBB compatibility condition 284
6.5.7 Some popular velocity-pressure couples 285
6.5.8 Stabilization of the Stokes problem 287
6.5.9 Penalty method 288
6.6 Steady Navier-Stokes problem 293
6.6.1 Weak form and Galerkin formulation 293
6.6.2 Matrix problem 293
6.7 Unsteady Navier-Stokes equations 294
6.7.1 Weak formulation and spatial discretization 295
6.7.2 Stabilized finite element formulation 296
6.7.3 Time discretization by fractional-step methods 297
6.8 Applications and solved exercices 306
6.8.1 Stokes flow with analytical solution 306
6.8.2 Cavity flow problem 307
6.8.3 Plane jet simulation 313
6.8.4 Natural convection in a square cavity 317
X CONTENTS
References 323
Index 345
|
| adam_txt |
Titel: Finite element methods for flow problems
Autor: Donea, Jean
Jahr: 2004
Contents
Preface xi
1 Introduction and preliminaries 1
1.1 Finite elements in fluid dynamics 1
1.2 Subjects covered 2
1.3 Kinematical descriptions of the flow field 4
1.3.1 Lagrangian and Eulerian descriptions 5
1.3.2 ALE description of motion 8
1.3.3 The fundamental ALE equation 11
1.3.4 Time derivative of integrals over moving
volumes 12
1.4 The basic conservation equations 13
1.4.1 Mass equation 13
1.4.2 Momentum equation 13
1.4.3 Internal energy equation 15
1.4.4 Total energy equation 17
1.4.5 ALE form of the conservation equations 18
1.4.6 Closure of the initial boundary value problem 19
1.5 Basic ingredients of the finite element method 19
1.5.1 Mathematical preliminaries 19
Vi CONTENTS
1.5.2 Trial solutions and weighting functions 21
1.5.3 Compact integral forms 23
1.5.4 Strong and weak forms of a boundary value
problem 23
1.5.5 Finite element spatial discretization 27
2 Steady transport problems 33
2.1 Problem statement 33
2.1.1 Strong form 33
2.1.2 Weakform 35
2.2 Galerkin approximation 36
2.2.1 Piecewise linear approximation in 1D 37
2.2.2 Analysis of the discrete equation 40
2.2.3 Piecewise quadratic approximation in ID 45
2.2.4 Analysis of the discrete equations 47
2.3 Early Petrov-Galerkin methods 50
2.3.1 Upwind approximation of the convective term 50
2.3.2 First finite elements of upwind type 51
2.3.3 The concept of balancing diffusion 53
2.4 Stabilization techniques 59
2.4.1 The SUPG method 60
2.4.2 The Galerkin/Least-squares method 63
2.4.3 The stabilization parameter 64
2.5 Other stabilization techniques and new trends 65
2.5.1 Finite increment calculus 66
2.5.2 Bubble functions and wavelet approximations 67
2.5.3 The variational multiscale method 68
2.5.4 Complements 70
2.6 Applications and solved exercises 70
2.6.1 Construction of a bubble function method 70
2.6.2 One-dimensional transport 72
2.6.3 Convection-diffusion across a source term 74
2.6.4 Convection-diffusion skew to the mesh 75
2.6.5 Convection-diffusion-reaction in 2D 76
2.6.6 The Hemker problem 78
3 Unsteady convective transport 79
3.1 Introduction 79
3.2 Problem statement 81
CONTENTS Vii
3.3 The method of characteristics 82
3.3.1 The concept of characteristic lines 82
3.3.2 Properties of the linear convection equation 84
3.3.3 Methods based on the characteristics 87
3.4 Classical time and space discretization techniques 91
3.4.1 Time discretization 92
3.4.2 Galerkin spatial discretization 94
3.5 Stability and accuracy analysis 98
3.5.1 Analysis of stability by Fourier techniques 99
3.5.2 Analysis of classical time-stepping schemes 101
3.5.3 The modified equation method 105
3.6 Taylor-Galerkin Methods 107
3.6.1 The need for higher-order time schemes 107
3.6.2 Third-order explicit Taylor-Galerkin method 108
3.6.3 Fourth-order explicit leap-frog method 113
3.6.4 Two-step explicit Taylor-Galerkin methods 114
3.7 An introduction to monotonicity-preserving schemes 117
3.8 Least-squares-based spatial discretization 120
3.8.1 Least-squares approach for the 6 family of
methods 121
3.8.2 Taylor least-squares method 122
3.9 The discontinuous Galerkin method 124
3.10 Space-time formulations 126
3.10.1 Time-discontinuous Galerkin formulation 126
3.10.2 Time-discontinuous least-squares formulation 128
3.10.3 Space-timeGalerkin/Least-squaresformulation 128
3.11 Applications and solved exercises 129
3.11.1 Propagation of a cosine profile 129
3.11.2 Travelling wave package 133
3.11.3 The rotating cone problem 135
3.11.4 Propagation of a steep front 137
Compressible Flow Problems 147
4.1 Introduction 147
4.2 Nonlinear hyperbolic equations 149
4.2.1 Scalar equations 149
4.2.2 Weak solutions and entropy condition 152
4.2.3 Time and space discretization 156
4.3 The Euler equations 159
Vtli CONTENTS
4.3.1 Strong form of the conservation equations 159
4.3.2 The quasi-linear form of the Euler equations 161
4.3.3 Basic properties of the Euler equations 163
4.3.4 Boundary conditions 165
4.4 Spatial discretization techniques 166
4.4.1 Galerkin formulation 167
4.4.2 Upwind-type discretizations 168
4.5 Numerical treatment of shocks 176
4.5.1 Introduction 176
4.5.2 Early artificial diffusion methods 178
4.5.3 High-resolution methods 180
4.6 Nearly incompressible flows 186
4.7 Fluid-structure interaction 187
4.7.1 Acoustic approximation 189
4.7.2 Nonlinear transient dynamic problems 191
4.7.3 Illustrative examples 196
4.8 Solved exercises 199
4.8.1 One-step Taylor-Galerkin solution of Burgers'
equation 199
4.8.2 The shock tube problem 202
5 Unsteady convection-diffusion problems 209
5.1 Introduction 209
5.2 Problem statement 210
5.3 Time discretization procedures 211
5.3.1 Classical methods 211
5.3.2 Fractional-step methods 213
5.3.3 High-order time-stepping schemes 215
5.4 Spatial discretization procedures 222
5.4.1 Galerkin formulation of the semi-discrete
scheme 222
5.4.2 Galerkin formulation of 0 family methods 224
5.4.3 Galerkin formulation ofexplicit Pade schemes 228
5.4.4 Galerkin formulation of implicit multistage
schemes 229
5.4.5 Stabilization of the semi-discrete scheme 231
5.4.6 Stabilization of multistage schemes 233
5.5 Stabilized space-time formulations 241
5.6 Solved exercises 243
CONTENTS IX
5.6.1 Convection-diffusion of a Gaussian hill 243
5.6.2 Transient rotating pulse 246
5.6.3 Steady rotating pulse problem 250
5.6.4 Nonlinear propagation of a step 250
5.6.5 Burgers'equation in ID 251
5.6.6 Two-dimensional Burgers' equation 252
Appendix Least-squares in transient/relaxation problems 254
Viscous incompressible flows 265
6.1 Introduction 265
6.2 Basic concepts 267
6.2.1 Strain rate and spin tensors 267
6.2.2 The stress tensor in a Newtonian fluid 268
6.2.3 The Navier-Stokes equations 269
6.3 Main issues in incompressible flow problems 272
6.4 Trial solutions and weighting functions 273
6.5 Stationary Stokes problem 275
6.5.1 Formulation in terms of Cauchy stress 275
6.5.2 Formulation in terms of velocity and pressure 278
6.5.3 Galerkin formulation 279
6.5.4 Matrix problem 281
6.5.5 Solvability condition and solution procedure 283
6.5.6 The LBB compatibility condition 284
6.5.7 Some popular velocity-pressure couples 285
6.5.8 Stabilization of the Stokes problem 287
6.5.9 Penalty method 288
6.6 Steady Navier-Stokes problem 293
6.6.1 Weak form and Galerkin formulation 293
6.6.2 Matrix problem 293
6.7 Unsteady Navier-Stokes equations 294
6.7.1 Weak formulation and spatial discretization 295
6.7.2 Stabilized finite element formulation 296
6.7.3 Time discretization by fractional-step methods 297
6.8 Applications and solved exercices 306
6.8.1 Stokes flow with analytical solution 306
6.8.2 Cavity flow problem 307
6.8.3 Plane jet simulation 313
6.8.4 Natural convection in a square cavity 317
X CONTENTS
References 323
Index 345 |
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| index_date | 2024-07-02T17:14:03Z |
| indexdate | 2024-07-09T20:56:32Z |
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| spelling | Donea, Jean Verfasser aut Finite element methods for flow problems Jean Donea and Antonio Huerta Reprint. Chichester [u.a.] Wiley 2004 XI, 350 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Huerta, Antonio Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015598106&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Donea, Jean Huerta, Antonio Finite element methods for flow problems Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4017233-8 (DE-588)4123623-3 |
| title | Finite element methods for flow problems |
| title_auth | Finite element methods for flow problems |
| title_exact_search | Finite element methods for flow problems |
| title_exact_search_txtP | Finite element methods for flow problems |
| title_full | Finite element methods for flow problems Jean Donea and Antonio Huerta |
| title_fullStr | Finite element methods for flow problems Jean Donea and Antonio Huerta |
| title_full_unstemmed | Finite element methods for flow problems Jean Donea and Antonio Huerta |
| title_short | Finite element methods for flow problems |
| title_sort | finite element methods for flow problems |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Strömungsmechanik Finite-Elemente-Methode Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015598106&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT doneajean finiteelementmethodsforflowproblems AT huertaantonio finiteelementmethodsforflowproblems |