Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems:
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| Format: | Thesis Book |
| Language: | English |
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2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 147 S. graph. Darst. |
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| 001 | BV041279573 | ||
| 003 | DE-604 | ||
| 005 | 20131021 | ||
| 007 | t | ||
| 008 | 130919s2012 d||| m||| 00||| eng d | ||
| 035 | |a (OCoLC)859416663 | ||
| 035 | |a (DE-599)HBZHT017412667 | ||
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| 049 | |a DE-739 | ||
| 084 | |a SK 920 |0 (DE-625)143272: |2 rvk | ||
| 100 | 1 | |a Hussain, Shafqat |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |c vorgelegt von Shafqat Hussain |
| 264 | 1 | |c 2012 | |
| 300 | |a X, 147 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Dortmund, Techn. Univ., Diss., 2012 | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026253038&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026253038 | ||
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| _version_ | 1804150750019846144 |
|---|---|
| adam_text | VII
Contents
1
Introduction
1
1.1
Introduction and Motivation
............................ 1
1.2
Thesis
Contributions
................................ 3
1.3
Publications
..................................... 4
1.4
Thesis Outline....................................
5
2
Basics of the time stepping schemes
7
2.1
Introduction
..................................... 7
2.1.1
Method of lines
............................... 7
2.1.2
Rothe s method
............................... 7
2.1.3
Explicit
Euler
(ЕЕ)
method
......................... 8
2.1.4
Implicit
Euler
(IE) method
......................... 8
2.1.5
Crank-Nicolson (CN) method
....................... 9
2.1.6
Fractional-step-G
(FS
-Θ)
method
...................... 9
2.2
Stability concepts for time discretization schemes
................. 10
2.2.1
Stability of explicit/implicit
Euler
and Crank-Nicolson method
...... 10
3
Fundamentals of the finite element method
13
3.1
Introduction
..................................... 13
3.2
Weighted residual formulation
........................... 13
3.3
Construction of
FEM
basis functions
........................ 15
3.4
Quadrilateral elements
............................... 16
3.5
The conforming Stokes element Q2/Pfisc
..................... 18
3.6
Edge oriented jump stabilization
.......................... 19
4
Solution of nonlinear and linear systems
21
4.1
Basic iterative solvers for sparse linear systems
.................. 22
4.1.1
Stationary iterative solvers
......................... 22
4.1.2
Nonstationary iterative solvers
....................... 22
4.2
Preconditioning
................................... 24
4.3
Multigrid solvers for linear equations
........................ 24
4.3.1
Geometric Multigrid Methods (GMG)
................... 25
4.3.2
Local pressure
Schur
complement (LPSC) type Smoothers
........ 26
4.3.3
Restriction and prolongation
........................ 29
viii
____________________________________________________________________Contents
5
Galerkin
time discretizations for the heat equation using
Gauß-points 31
5.1
The cGP-method for the heat equation
....................... 31
5.1.1
cGPW-method
............................... 34
5.1.2
cGP(2)-method
............................... 34
5.2
Discontinuous Galerkin methods
.......................... 35
5.3
Space Discretization by
FEM
............................ 36
5.3.1
cGPœ-method...............................
37
5.3.2
cGP(2)-meťhod
............................... 38
5.3.3
dG(l)-method
................................ 38
5.4
Solution of the linear systems
............................ 38
5.5
Numerical results
.................................. 39
5.6
Summary
...................................... 44
6
Galerkin time discretizations for the heat equation using
Gauß-Lobatto
points
45
6.1
The cGP-method for the heat equation
....................... 45
6.1.1
cGP(l)-GL(2)-method
........................... 47
6.1.2
cGP(2)-GL(3)-method
........................... 47
6.2
Space Discretization by
FEM
............................ 47
6.2.1
cGP(l)-GL(2)-method
........................... 48
6.2.2
cGP(2)-GL(3)-method
........................... 48
6.3
Numerical results
.................................. 48
6.4
Summary
...................................... 50
7
Analysis of the continuous Galerkin-Petrov methods
53
7.1
Stability of the cGPC^-method
.......................... . 53
7.2
Optimal error estimate of the
cGP(Ä:)-method
................... 54
7.3
Stability of the dGC^-method
............................ 57
8
Galerkin time discretizations for the Stokes equations
61
8.1
The cGP- and dG-methods for the Stokes equations
................ 61
8.1.1
cGPC^-method
............................... 63
8.1.2
cGP(2)-method
............................... 63
8.1.3
dG(l)-method
................................ 64
8.2
Space Discretization by
FEM
............................ 64
8.2.1
cGPW-method
............................... 66
8.2.2
cGP(2)-method
............................... 66
8.2.3
dGC^-method
................................ 67
8.3
Postprocessing for high order pressure
....................... 67
8.3.1
cGPC^-method
............................... 68
8.3.2
cGP(2) and dG(l)-method
......................... 68
8.4
Solution of the linear systems
............................ 68
8.5
Numerical results
.................................. 68
8.6
Summary
...................................... 73
9
Galerkin time discretizations for the Navier-Stokes equations
75
9.1
The cGP- and dG-methods for the Navier-Stokes equation
............ 75
9.1.1
cGPW-method
................................ 77
9.1.2
cGP(2)-method
................................ 77
9.1.3
dGC^-method
................................ 78
9.2
Space Discretization by
FEM
............................ 79
____________________________________________________________
IX
9.2.1
cGPCO-method
............................... 80
9.2.2
cGP(2)-method
............................... 81
9.2.3
dGC^-method
................................ 81
9.3
Nonlinear
Solver..................................
82
9.3.1
General
nonlinear outer iteration
...................... 82
9.3.2
Fixed-point iteration
............................ 83
9.3.3
Newton method
............................... 83
10
Numerical Results
85
10.1
Nonstationary flow around cylinder benchmark
.................. 85
10.2
Nonstationary flow through
a Venturi pipe
..................... 106
10.3
Solver analysis
................................... 124
10.3.1
Nonstationary flow around cylinder benchmark
.............. 124
10.3.2
Nonstationary flow through
a Venturi
pipe
................. 127
10.4
Summary
...................................... 129
11
Conclusions and Outlook
131
11.1
Conclusions
..................................... 131
11.2
Outlook
....................................... 134
A The cGP(l)-method and Crank-Nicolson scheme
137
В
The dG-CO^-method
139
B.I The dG-COC^-method for the heat equation
.................... 139
B.I.I dG-C0(2)-method
.............................. 141
B.2 Numerical results
.................................. 141
Bibliography
143
|
| any_adam_object | 1 |
| author | Hussain, Shafqat |
| author_facet | Hussain, Shafqat |
| author_role | aut |
| author_sort | Hussain, Shafqat |
| author_variant | s h sh |
| building | Verbundindex |
| bvnumber | BV041279573 |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)859416663 (DE-599)HBZHT017412667 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:43:53Z |
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| language | English |
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| physical | X, 147 S. graph. Darst. |
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| spelling | Hussain, Shafqat Verfasser aut Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems vorgelegt von Shafqat Hussain 2012 X, 147 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dortmund, Techn. Univ., Diss., 2012 (DE-588)4113937-9 Hochschulschrift gnd-content Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026253038&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hussain, Shafqat Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |
| subject_GND | (DE-588)4113937-9 |
| title | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |
| title_auth | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |
| title_exact_search | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |
| title_full | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems vorgelegt von Shafqat Hussain |
| title_fullStr | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems vorgelegt von Shafqat Hussain |
| title_full_unstemmed | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems vorgelegt von Shafqat Hussain |
| title_short | Numerical analysis of new class of higher order Galerkin time discretization schemes for nonstationary incompressible flow problems |
| title_sort | numerical analysis of new class of higher order galerkin time discretization schemes for nonstationary incompressible flow problems |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026253038&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hussainshafqat numericalanalysisofnewclassofhigherordergalerkintimediscretizationschemesfornonstationaryincompressibleflowproblems |