The Least-Squares spectral collocation method for incompressible flows:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Köster
2009
|
| Edition: | 1. Aufl. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 154 S. Ill., graph. Darst. |
| ISBN: | 9783895747281 |
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MARC
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| 245 | 1 | 0 | |a The Least-Squares spectral collocation method for incompressible flows |c von Thorsten Kattelans |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Berlin |b Köster |c 2009 | |
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| 502 | |a Zugl.: Duisburg-Essen, Univ., Diss., 2009 | ||
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 2 THE STOKES AND NAVIER-STOKES EQUATIONS 11
2.1 FIRST-ORDER FORMULATION 11
2.2 THE STOKES EQUATIONS 12
2.3 THE NAVIER-STOKES EQUATIONS 13
2.3.1 IMPLICIT SCHEME 13
2.3.2 EXPLICIT SCHEME 14
3 THE LEAST-SQUARES SPECTRAL ELEMENT METHOD 15
3.1 THE LEAST-SQUARES FORMULATION 15
3.2 SPECTRAL ELEMENTS 16
3.3 LEAST-SQUARES SPECTRAL ELEMENT METHOD BASED ON VARIATIONAL ANALYSIS
18
4 INTRODUCTION TO SPECTRAL COLLOCATION 19
4.1 ORTHOGONAL POLYNOMIALS 19
4.2 GAUSS QUADRATURE AND INTERPOLATION 20
4.3 CHEBYSHEV POLYNOMIALS 21
4.4 DIFFERENTIATION 24
5 LEAST-SQUARES SPECTRAL COLLOCATION METHOD 27
5.1 OVER-COLLOCATION 30
5.2 DIFFERENT POLYNOMIAL DEGREES 31
5.3 THE DISCRETE LINEAR SYSTEM OF EQUATIONS 32
5.3.1 C INTERFACE CONDITIONS 33
5.3.2 C INTERFACE CONDITIONS 33
5.3.3 THE PRESSURE CONDITION 34
5.3.4 RANK OF THE ALGEBRAIC SYSTEM 34
5.4 SOLVING THE LINEAR SYSTEMS OF EQUATIONS 35
6 NUMERICAL RESULTS FOR THE STOKES EQUATIONS 37
6.1 CONDITION NUMBERS: C L VERSUS C INTERFACE CONDITIONS 37
6.2 APPROXIMATIONS, EXAMPLE 1 39
6.3 APPROXIMATIONS, EXAMPIE 2 44
7 NUMERICAL RESULTS FOR THE NAVIER-STOKES EQUATIONS 49
7.1 CONDITION NUMBERS 49
7.2 COLLOCATION CONDITIONS 50
7.3 SMOOTH EXAMPLE 52
7.4 THE REGULARIZED CAVITY FLOW 54
7.4.1 DIFFERENT DECOMPOSITIONS OF THE DOMAIN 54
7.4.2 EXPLICIT SCHEME VERSUS IMPLICIT SCHEME - . 60
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/997987812
DIGITALISIERT DURCH
IMAGE 2
6 CONTENTS
7.4.3 C 1 VERSUS C INTERFACE CONDITIONS 63
7.4.4 OVER-COLLOCATION 64
7.4.5 DIFFERENT POLYNOMIAL DEGREES 66
7.5 THE LID-DRIVEN CAVITY FLOW 68
7.5.1 DIFFERENT DECOMPOSITIONS OF THE DOMAIN 68
7.5.2 C 1 VERSUS C INTERFACE CONDITIONS 74
7.5.3 OVER-COLLOCATION 75
7.5.4 DIFFERENT POLYNOMIAL DEGREES 77
8 CHANNEL FLOW AROUND A CYLINDER 81
8.1 PROBLEM SET-UP 82
8.2 DECOMPOSITION AND DISCRETIZATION OF THE DOMAIN 82
8.3 THE STEADY STOKES EQUATIONS 86
8.3.1 SMOOTH MODEL PROBLEM 86
8.3.2 CONSTANT PRESSURE MODE: CIENSHAW-CURTIS VERSUS CANCELLING . 88
8.3.3 CHANNEL FLOW 90
8.3.4 LSSCM VERSUS LSSEM 103
8.4 UNSTEADY STOKES EQUATIONS 110
8.4.1 SMOOTH MODEL PROBLEM 110
8.4.2 UNSTEADY STOKES FLOW AROUND A CYLINDER 112
8.5 NAVIER-STOKES EQUATIONS 119
8.5.1 STEADY MODEL PROBLEM 119
8.5.2 UNSTEADY MODEL PROBLEM 120
8.5.3 CHANNEL FLOW 121
9 CONCLUSION 139
PUBLICATIONS 141
LIST OF FIGURES 143
LIST OF TABLES 147
BIBLIOGRAPHY 151
|
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| author | Kattelans, Thorsten |
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| ctrlnum | (OCoLC)502405965 (DE-599)DNB997987812 |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| indexdate | 2024-07-09T22:07:54Z |
| institution | BVB |
| isbn | 9783895747281 |
| language | English |
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| physical | 154 S. Ill., graph. Darst. |
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| spelling | Kattelans, Thorsten Verfasser (DE-588)1072384051 aut The Least-Squares spectral collocation method for incompressible flows von Thorsten Kattelans 1. Aufl. Berlin Köster 2009 154 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zugl.: Duisburg-Essen, Univ., Diss., 2009 Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Kollokationsmethode (DE-588)4164696-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Inkompressible Strömung (DE-588)4129759-3 s Kollokationsmethode (DE-588)4164696-4 s Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018803916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kattelans, Thorsten The Least-Squares spectral collocation method for incompressible flows Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Kollokationsmethode (DE-588)4164696-4 gnd |
| subject_GND | (DE-588)4038974-1 (DE-588)4129759-3 (DE-588)4164696-4 (DE-588)4113937-9 |
| title | The Least-Squares spectral collocation method for incompressible flows |
| title_auth | The Least-Squares spectral collocation method for incompressible flows |
| title_exact_search | The Least-Squares spectral collocation method for incompressible flows |
| title_full | The Least-Squares spectral collocation method for incompressible flows von Thorsten Kattelans |
| title_fullStr | The Least-Squares spectral collocation method for incompressible flows von Thorsten Kattelans |
| title_full_unstemmed | The Least-Squares spectral collocation method for incompressible flows von Thorsten Kattelans |
| title_short | The Least-Squares spectral collocation method for incompressible flows |
| title_sort | the least squares spectral collocation method for incompressible flows |
| topic | Methode der kleinsten Quadrate (DE-588)4038974-1 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Kollokationsmethode (DE-588)4164696-4 gnd |
| topic_facet | Methode der kleinsten Quadrate Inkompressible Strömung Kollokationsmethode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018803916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kattelansthorsten theleastsquaresspectralcollocationmethodforincompressibleflows |