Numerical methods for steady viscous free surface flows:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
CWI
2003
|
| Series: | CWI Tract
134 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 110 S. graph. Darst. |
| ISBN: | 9061965187 |
Staff View
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| 245 | 1 | 0 | |a Numerical methods for steady viscous free surface flows |c E. H. von Brummelen |
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Record in the Search Index
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| adam_text | Contents
Preface iii
1 Introduction 1
1.1 Motivation 1
1.2 Outline 3
2 Mathematical Description of Free Surface Flow 5
2.1 Introduction 5
2.2 Governing Equations for Fluid Flow 5
2.2.1 Conservation Laws 5
2.2.2 Dimensionless Equations 7
2.2.3 Additional Conditions and Well Posedness .... 8
2.3 Interface Conditions 8
2.3.1 Two Fluid Flow Interface Conditions 8
2.3.2 Free Surface Conditions 10
2.4 Problem Statement 12
3 Analysis of Viscous Free Surface Flow 13
3.1 Introduction 13
3.2 Statement of Objectives 14
3.3 Infinitesimal Solutions 15
3.3.1 Generating Solution 15
3.3.2 Infinitesimal Conditions 16
3.3.3 Generic Modes 19
3.3.4 Surface Gravity Waves 21
3.3.5 Constant Perturbations 23
3.3.6 Compatibility of Initial Conditions 23
3.3.7 General Infinitesimal Perturbations 25
3.4 Solution Behavior 26
3.4.1 Evolution of Local Disturbances 26
3.4.2 Steady Waves 27
3.4.3 Asymptotic Temporal Behavior of Wave Groups . 29
3.4.4 Free Surface Boundary Layer 30
v
vi Contents
4 Efficient Numerical Solution of Steady Free Surface Flows 33
4.1 Introduction 33
4.2 Governing Equations 35
4.2.1 Incompressible Viscous Flow 35
4.2.2 Free Surface Conditions 36
4.2.3 Quasi Free Surface Condition 37
4.3 Time Integration Methods 40
4.3.1 Surface Gravity Waves 40
4.3.2 Asymptotic Temporal Behavior 41
4.3.3 Computational Complexity 42
4.4 Efficient Solution of Steady Free Surface Flows 44
4.4.1 Iterative Solution Method 44
4.4.2 Convergence 45
4.4.3 Computational Complexity 47
4.5 Numerical Experiments and Results 48
4.6 Conclusion 51
5 Adjoint Shape Optimization for Steady Free Surface Flows 53
5.1 Introduction 53
5.2 Problem Statement 54
5.2.1 Governing Equations 54
5.2.2 Optimal Shape Design Formulation 55
5.3 Adjoint Optimization Method 56
5.3.1 Induced Disturbance 56
5.3.2 Adjoint Operators and Duality 58
5.3.3 Optimization Method 60
5.4 Fourier Analysis of the Optimization Problem 61
5.4.1 Hessian of the Functional 61
5.4.2 Fourier Analysis of the Hessian 62
5.4.3 Properties of the Optimization Problem 64
5.4.4 Stability of the Adjoint Method 66
5.4.5 Convergence of the Adjoint Method 67
5.5 Preconditioning 69
5.5.1 Reconsideration of Objectives 70
5.5.2 General Outline 70
5.5.3 A Preconditioner for 2D Free Surface Flows .... 71
5.6 Numerical Experiments 72
5.7 Conclusions and Discussion 74
6 Interface Capturing 77
6.1 Introduction 77
6.2 Two Fluid Flows 78
6.2.1 Conservation Laws 78
6.2.2 Interface Conditions 79
Contents vii
6.2.3 Two Fluid Euler Equations 80
6.3 Pressure Oscillations 82
6.3.1 Exemplification 82
6.3.2 Pressure Invariance Condition 84
6.3.3 A Non Oscillatory Conservative Scheme 85
6.4 A Modified Osher Scheme for Two Fluids 86
6.4.1 The Two Fluid Riemann Problem 86
6.4.2 Riemann Invariants 88
6.4.3 Rarefaction Waves Only Approximation 90
6.4.4 The Modified Osher Scheme 92
6.5 Numerical Experiments and Results 93
6.5.1 Test Case I 94
6.5.2 Test Case II 95
6.6 Conclusions 97
Bibliography 99
Author Index 105
Subject Index 107
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:18:23Z |
| institution | BVB |
| isbn | 9061965187 |
| language | English |
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| physical | VII, 110 S. graph. Darst. |
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| series2 | CWI Tract |
| spelling | Brummelen, E. Harald van Verfasser aut Numerical methods for steady viscous free surface flows E. H. von Brummelen Amsterdam CWI 2003 VII, 110 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CWI Tract 134 Numerieke methoden gtt Reologie gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Navier-Stokes equations Numerical solutions Surfaces (Technology) Mathematical models Viskose Strömung (DE-588)4226965-9 gnd rswk-swf Oberflächenströmung (DE-588)4172260-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Viskose Strömung (DE-588)4226965-9 s Oberflächenströmung (DE-588)4172260-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 CWI Tract 134 (DE-604)BV001902011 134 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010524254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brummelen, E. Harald van Numerical methods for steady viscous free surface flows CWI Tract Numerieke methoden gtt Reologie gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Navier-Stokes equations Numerical solutions Surfaces (Technology) Mathematical models Viskose Strömung (DE-588)4226965-9 gnd Oberflächenströmung (DE-588)4172260-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4226965-9 (DE-588)4172260-7 (DE-588)4128130-5 |
| title | Numerical methods for steady viscous free surface flows |
| title_auth | Numerical methods for steady viscous free surface flows |
| title_exact_search | Numerical methods for steady viscous free surface flows |
| title_full | Numerical methods for steady viscous free surface flows E. H. von Brummelen |
| title_fullStr | Numerical methods for steady viscous free surface flows E. H. von Brummelen |
| title_full_unstemmed | Numerical methods for steady viscous free surface flows E. H. von Brummelen |
| title_short | Numerical methods for steady viscous free surface flows |
| title_sort | numerical methods for steady viscous free surface flows |
| topic | Numerieke methoden gtt Reologie gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Navier-Stokes equations Numerical solutions Surfaces (Technology) Mathematical models Viskose Strömung (DE-588)4226965-9 gnd Oberflächenströmung (DE-588)4172260-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Numerieke methoden Reologie Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Navier-Stokes equations Numerical solutions Surfaces (Technology) Mathematical models Viskose Strömung Oberflächenströmung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010524254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT brummeleneharaldvan numericalmethodsforsteadyviscousfreesurfaceflows |