Adaptive finite element solution algorithm for the Euler equations
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Braunschweig
Vieweg
1991
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| Schriftenreihe: | Notes on numerical fluid mechanics
32 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Shapiro, Richard A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Adaptive finite element solution algorithm for the Euler equations |c by Richard A. Shapiro |
| 264 | 1 | |a Braunschweig |b Vieweg |c 1991 | |
| 300 | |a XII, 168 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Notes on numerical fluid mechanics |v 32 | |
| 650 | 7 | |a Eléments finis, méthode des |2 ram | |
| 650 | 7 | |a Fluides, dynamique des |2 ram | |
| 650 | 7 | |a Lagrange, équations de - Solutions numériques |2 ram | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Lagrange equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Eulersche Bewegungsgleichungen |0 (DE-588)4219070-8 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Notes on numerical fluid mechanics |v 32 |w (DE-604)BV000898664 |9 32 | |
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Datensatz im Suchindex
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|---|---|
| DE-BY-TUM_katkey | 527362 |
| DE-BY-TUM_media_number | 040000929022 TEMP2967722 |
| _version_ | 1816711570223267840 |
| adam_text | Contents
1 Introduction 1
1.1 Research Goals 1
1.2 Overview of Thesis 2
1.3 Survey of Finite Element Methods for the Euler Equations 3
2 Governing Equations 5
2.1 Euler Equations 5
2.2 Non Dimensionalization of the Equations 7
2.3 Auxiliary Quantities 8
2.4 Boundary Conditions 8
2.4.1 Solid Surface Boundary Conditions 9
2.4.2 Open Boundary Conditions 9
3 Finite Element Fundamentals 11
3.1 Basic Definitions 11
3.2 Finite Elements and Natural Coordinates 13
3.2.1 Properties of Interpolation Functions 14
3.2.2 Natural Coordinates and Derivative Calculation . 15
VII
3.3 Typical Elements 17
3.3.1 Bilinear Element 17
3.3.2 Biquadratic Element 19
3.3.3 Trilinear Element 20
4 Solution Algorithm 22
4.1 Overview of Algorithm 22
4.2 Spatial Discretization 23
4.3 Choice of Test Functions 25
4.3.1 Test Functions for Galerkin Method 26
4.3.2 Test Functions for Cell Vertex Method 27
4.3.3 Test Functions for Central Difference Method ... 29
4.4 Boundary Conditions 31
4.4.1 Solid Surface Boundary Condition 31
4.4.2 Open Boundary Condition 32
4.5 Smoothing 34
4.5.1 Conservative, Low Accuracy Second Difference . . 34
4.5.2 Non Conservative, High Accuracy Second Difference 35
4.5.3 Combined Smoothing 37
4.5.4 Smoothing on Biquadratic Elements 38
4.6 Time Integration 38
4.7 Consistency and Conservation 39
4.7.1 Making Artificial Viscosity Conservative 40
VIII
5 Algorithm Verification and Comparisons 42
5.1 Introduction 42
5.2 Verification and Comparison of Methods 43
5.2.1 5° Converging Channel 43
5.2.2 15° Converging Channel 45
5.2.3 4% Circular Arc Bump 46
5.2.4 10% Circular Arc Bump 47
5.2.5 10% Cosine Bump 47
5.2.6 CPU Comparison and Recommendations 48
5.2.7 Verification of Conservation 48
5.3 Effects of Added Dissipation 49
5.4 Biquadratic vs. Bilinear 51
5.4.1 5° Channel Flow 51
5.4.2 4% Circular Arc Bump 52
5.4.3 10% Cosine Bump 52
5.5 Three Dimensional Verification 53
5.6 Summary 54
6 Adaptation 76
6.1 Introduction 76
6.2 Adaptation Procedure 77
6.2.1 Placement of Boundary Nodes 79
6.2.2 How Much Adaptation? 80
IX
6.3 Adaptation Criteria 80
6.3.1 First Difference Indicator 81
6.3.2 Second Difference Indicator 82
6.3.3 Two Dimensional Directional Adaptation 83
6.4 Embedded Interface Treatment 84
6.4.1 Two Dimensional Interface 84
6.4.2 Three Dimensional Interface 87
6.5 Examples of Adaptation 88
6.5.1 Multiple Shock Reflections 88
6.5.2 4% Circular Arc Bump 89
6.5.3 10% Circular Arc Bump 90
6.5.4 3 D Channel 90
6.5.5 Distorted Grid 91
6.6 CPU Time Comparisons 91
7 Dispersion Phenomena and the Euler Equations 103
7.1 Introduction 103
7.2 Difference Stencils 103
7.2.1 Some Properties of the Galerkin Stencil 104
7.2.2 Some Properties of the Cell Vertex Stencil 105
7.3 Linearization of the Equations 106
7.4 Fourier Analysis of the Linearized Equations 107
7.5 Numerical Verification Ill
X
7.6 Conclusions 113
8 Scramjet Inlets 120
8.1 Introduction 120
8.2 Two Dimensional Test Cases 121
8.2.1 Moo = 5, 0° Yaw 122
8.2.2 Moo = 5, 5° Yaw 123
8.2.3 Moo = 2, 0° Yaw 123
8.2.4 Moo = 3, 0° Yaw 124
8.2.5 Moo = 3, 7° Yaw 125
8.2.6 Inlet Performance and Total Pressure Loss .... 125
8.3 Three Dimensional Results 126
9 Summary and Conclusions 138
9.1 Summary 138
9.2 Contributions of the Thesis 139
9.3 Conclusions 141
9.4 Areas for Further Exploration 142
A Computational Issues 144
A.I Introduction 144
A.2 Vectorization and Parallelization Issues 144
A.3 Computer Memory Requirements 146
A.3.1 Two Dimensional Memory Requirements 147
XI
A.3.2 Three Dimensional Memory Requirements 147
A.4 Data Structures for Adaptation 148
A.4.1 Finding the Children of an Element 149
A.4.2 Finding The Adjacent Element 150
B Scramjet Geometry Definition 152
References 154
List of Symbols 162
Index 164
XII
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| id | DE-604.BV004449641 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:10:36Z |
| institution | BVB |
| isbn | 3528076321 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002760099 |
| oclc_num | 24583683 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-20 DE-210 DE-706 DE-634 DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-20 DE-210 DE-706 DE-634 DE-83 |
| physical | XII, 168 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Vieweg |
| record_format | marc |
| series | Notes on numerical fluid mechanics |
| series2 | Notes on numerical fluid mechanics |
| spellingShingle | Shapiro, Richard A. Adaptive finite element solution algorithm for the Euler equations Notes on numerical fluid mechanics Eléments finis, méthode des ram Fluides, dynamique des ram Lagrange, équations de - Solutions numériques ram Finite element method Fluid dynamics Lagrange equations Numerical solutions Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4219070-8 (DE-588)4017233-8 |
| title | Adaptive finite element solution algorithm for the Euler equations |
| title_auth | Adaptive finite element solution algorithm for the Euler equations |
| title_exact_search | Adaptive finite element solution algorithm for the Euler equations |
| title_full | Adaptive finite element solution algorithm for the Euler equations by Richard A. Shapiro |
| title_fullStr | Adaptive finite element solution algorithm for the Euler equations by Richard A. Shapiro |
| title_full_unstemmed | Adaptive finite element solution algorithm for the Euler equations by Richard A. Shapiro |
| title_short | Adaptive finite element solution algorithm for the Euler equations |
| title_sort | adaptive finite element solution algorithm for the euler equations |
| topic | Eléments finis, méthode des ram Fluides, dynamique des ram Lagrange, équations de - Solutions numériques ram Finite element method Fluid dynamics Lagrange equations Numerical solutions Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Eléments finis, méthode des Fluides, dynamique des Lagrange, équations de - Solutions numériques Finite element method Fluid dynamics Lagrange equations Numerical solutions Eulersche Bewegungsgleichungen Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002760099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000898664 |
| work_keys_str_mv | AT shapiroricharda adaptivefiniteelementsolutionalgorithmfortheeulerequations |