Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart
Teubner
1997
|
| Series: | Advances in numerical mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 293 S. Ill., graph. Darst. |
| ISBN: | 3519027232 |
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MARC
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| 240 | 1 | 0 | |a Projektions- und Quasi-Kompressibilitätsmethoden zur Lösung der inkompressiblen Navier-Stokes-Gleichungen |
| 245 | 1 | 0 | |a Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations |c von Andreas Prohl |
| 264 | 1 | |a Stuttgart |b Teubner |c 1997 | |
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Record in the Search Index
| _version_ | 1804125875772325888 |
|---|---|
| adam_text | Contents
1 Introduction 1
2 Preliminaries 17
2.1 Notation 17
2.2 Summary of Results Concerning the Stationary Incompress¬
ible Stokes Problem 18
2.3 A priori Estimates for the Nonstationary Incompressible Stokes
Equations 20
2.4 A Numerical Test Problem 22
3 Stationary Quasi Compressibility Methods: The Penalty
Method and the Pressure Stabilization Method 25
3.1 Overview and Results 25
3.2 Analysis of the Penalty Method 30
3.2.1 The Stokes Case 30
3.2.2 The Navier Stokes Equations 33
3.3 Analysis of the Pressure Stabilization Method 38
3.3.1 The Stokes Case 38
3.3.2 The Navier Stokes Case 44
4 Nonstationary Quasi Compressibility Methods 49
4.1 Overview and Results 49
4.2 The Artificial Compressibility Scheme and its Modification . . 53
4.2.1 Approximation Results for the Artificial Compressibil¬
ity Scheme and its Modification 53
4.2.2 Analysis of the Original Artificial Compressibility Scheme 56
4.3 The Pressure Correction Scheme and its Modification 61
XI
4.3.1 Approximation Results for the Pressure Correction
Scheme and its Modification 61
4.3.2 Perturbation Analysis for the Pressure Correction
Method 64
4.3.3 A Modified Pressure Correction Ansatz 79
5 Mixed Quasi Compressibility Methods 91
5.1 Overview 91
5.2 Error Analysis for the Case i) 94
6 The Projection Scheme of Chorin 105
6.1 Overview and Results 105
6.2 Analysis for a Pressure Stabilized Stokes Problem 110
6.2.1 Part 1. Consistency Error 110
6.2.2 Part 2. Perturbation Error 112
6.3 Analysis of the Pressure Stabilized Navier Stokes Problem . . 120
6.4 Completion of the Analysis for the Chorin Scheme 129
6.4.1 Interior Super Convergence Results for the Pressure . . 132
6.5 Computational Results 133
7 The Projection Scheme of Van Kan 141
7.1 Overview and Results 141
7.1.1 A priori Bounds for the Crank Nicolson Scheme .... 148
7.1.2 Error Estimates for the Crank Nicolson Scheme .... 149
7.2 Proposal of a Pressure Correction Version of the Stokes Equa¬
tions 154
7.2.1 Proposal and Analysis of an Auxiliary Problem . . . .156
7.2.2 Analysis of the Pressure Correction Method (7.26) ... 160
7.3 Error Estimates for the Van Kan Scheme 166
7.4 Computational Results for the Van Kan Scheme 168
8 Two Modified Chorin Schemes 179
8.1 Overview and Results 179
8.2 An Analysis of the Modified Chorin Scheme of
Timmermans et al 186
8.2.1 Proposal of a Modified Pressure Stabilization Scheme .186
8.2.2 Transfer of the Error Statements of Subsection 8.2.1 to
the Modified Chorin Method 193
XII
8.3 Analysis for the Chorin Uzawa Scheme 196
8.4 Computational Results 200
8.4.1 The Modified Chorin Scheme 200
8.4.2 The Chorin Uzawa Scheme 201
9 Multi Component Schemes 207
9.1 Overview 207
9.2 The Chorin /Van Kan Scheme — Proposal and Analysis . . . 209
9.3 Proposal and Analysis of a Modified Chorin Uzawa Scheme . . 226
10 Time Discretization on Time Grids with Structure —
from Euler to Revised Projection Schemes 233
10.1 Introduction 233
10.2 The Euler and Trapezoidal Method on Stabilizing Time Grids 236
10.2.1 Preliminaries and Notations 239
10.2.2 Time Cascades and Main Results 241
10.2.3 Proof of Theorem 10.1 for the Euler method 245
10.2.4 Proof of Theorem 10.2 for the Trapezoidal Method . . 250
10.2.5 Comments and Outlook 256
10.3 A Revised Chorin Uzawa Scheme on the Time Grid £2(^+1) ¦ 257
10.3.1 Stability Statements for the Euler Scheme on the Time
Grid g2(km+1) 260
10.3.2 Analysis of a nonstationary Quasi Compressibility
Method on the Time Grid 72(fcm+i) 261
10.3.3 Introduction of an Auxiliary Problem on the Time
Grid g2(km+1) 262
10.3.4 Completion of the Proof of Theorem 10.3 267
10.3.5 Analysis of the Semi Explicit System 269
10.4 A Revised Van Kan Scheme on the Time Grid structure
(W) 270
10.4.1 Stability Results for the Incompressible Stokes
Problem 273
10.4.2 Error Statements for an Auxiliary Problem 274
10.4.3 The Propagation of Error Effects 279
10.4.4 The Semi Explicit Quasi Compressibility Method ... 281
11 Summary and Outlook 283
|
| any_adam_object | 1 |
| author | Prohl, Andreas 1968- |
| author_GND | (DE-588)115385843 |
| author_facet | Prohl, Andreas 1968- |
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| isbn | 3519027232 |
| language | English |
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| physical | XII, 293 S. Ill., graph. Darst. |
| publishDate | 1997 |
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| publisher | Teubner |
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| spelling | Prohl, Andreas 1968- Verfasser (DE-588)115385843 aut Projektions- und Quasi-Kompressibilitätsmethoden zur Lösung der inkompressiblen Navier-Stokes-Gleichungen Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations von Andreas Prohl Stuttgart Teubner 1997 XII, 293 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in numerical mathematics Fluid dynamics Fluid mechanics Navier-Stokes equations Numerical solutions Projektionsverfahren (DE-588)4175879-1 gnd rswk-swf Quasi-Kompressibilitätsmethode (DE-588)4482842-1 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Navier-Stokes-Gleichung (DE-588)4041456-5 s DE-604 Projektionsverfahren (DE-588)4175879-1 s Quasi-Kompressibilitätsmethode (DE-588)4482842-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Prohl, Andreas 1968- Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations Fluid dynamics Fluid mechanics Navier-Stokes equations Numerical solutions Projektionsverfahren (DE-588)4175879-1 gnd Quasi-Kompressibilitätsmethode (DE-588)4482842-1 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4175879-1 (DE-588)4482842-1 (DE-588)4041456-5 (DE-588)4113937-9 |
| title | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations |
| title_alt | Projektions- und Quasi-Kompressibilitätsmethoden zur Lösung der inkompressiblen Navier-Stokes-Gleichungen |
| title_auth | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations |
| title_exact_search | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations |
| title_full | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations von Andreas Prohl |
| title_fullStr | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations von Andreas Prohl |
| title_full_unstemmed | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations von Andreas Prohl |
| title_short | Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations |
| title_sort | projection and quasi compressibility methods for solving the incompressible navier stokes equations |
| topic | Fluid dynamics Fluid mechanics Navier-Stokes equations Numerical solutions Projektionsverfahren (DE-588)4175879-1 gnd Quasi-Kompressibilitätsmethode (DE-588)4482842-1 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Fluid dynamics Fluid mechanics Navier-Stokes equations Numerical solutions Projektionsverfahren Quasi-Kompressibilitätsmethode Navier-Stokes-Gleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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