Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods: Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English German |
| Published: |
Düren
Shaker Verlag
2019
|
| Series: | Berichte aus der Mathematik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 187 Seiten Illustrationen 24 cm x 17 cm, 281 g |
| ISBN: | 9783844068016 |
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MARC
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| 245 | 1 | 0 | |a Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods |b Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren |c Andreas Rupp |
| 264 | 1 | |a Düren |b Shaker Verlag |c 2019 | |
| 300 | |a 187 Seiten |b Illustrationen |c 24 cm x 17 cm, 281 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Mathematik | |
| 502 | |b Dissertation |c Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) |d 2019 | ||
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| 653 | |a Darcy’s equation | ||
| 653 | |a diffusion | ||
| 653 | |a discontinuous Galerkin | ||
| 653 | |a homogenization | ||
| 653 | |a microaggregate development | ||
| 653 | |a upscaling | ||
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Record in the Search Index
| _version_ | 1811720470072918016 |
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| adam_text |
CONTENTS
ACKNOWLEDGEMENT
13
ZUSAMMENFASSUNG
(GERMAN)
15
1
INTRODUCTION
21
1.1
OBJECTIVE
OF
THIS
WORK
.
22
1.2
OUTLINE
OF
THE
THESIS
.
23
1.3
PREVIOUSLY
PUBLISHED
ARTICLES
.
24
2
MODEL
FOR
MICROAGGREGATE
DEVELOPMENT
27
2.1
INTRODUCTION
AND
MOTIVATION
.
28
2.2
GEOMETRIC
SETTING
AND
MATHEMATICAL
MODEL
.
31
2.2.1
MODEL
PARTS
.
34
2.2.2
CONTINUUM
MODEL
PARTS
.
35
2.2.3
CELLULAR
AUTOMATON
METHOD
.
45
2.2.4
UPSCALING
RULES
AND
MODEL
CHARACTERISTICS
.
51
2.3
ALGORITHM
AND
IMPLEMENTATION
.
53
2.4
SIMULATION
SCENARIOS
AND
MODEL
EVALUATION
.
55
2.4.1
EFFECTS
OF
BIOMASS
DEVELOPMENT
ON
EFFECTIVE
DIFFUSION
.
56
2.4.2
EFFECTS
OF
GLUING
AGENT
DOMINATED
SOLID
RESTRUCTURING
ON
THE
EFFECTIVE
DIFFUSION
TENSOR
.
57
2.4.3
COMBINED
EFFECTS
OF
BIOMASS
DEVELOPMENT,
GLUING
AGENT,
AND
SOLID
RESTRUCTURING
ON
THE
DIFFUSION
TENSOR
.
61
2.4.4
EFFECTS
OF
THE
RANGE
OF
ATTRACTION
.
63
2.4.5
EFFECTS
OF
THE
SHAPE
OF
BUILDING
UNITS
.
65
2.4.6
EFFECTS
OF
CHARGES
.
66
2.4.7
EFFECTS
OF
THE
ELECTROSTATIC
FIELD
IN
THE
SOLUTION
.
67
2.4.8
EFFECTS
OF
HENRY'S
LAW
AND
GAS
PHASE
.
69
2.4.9
HYBRID
MULTISCALE
MODEL
.
69
2.5
CONCLUSIONS
AND
FUTURE
PROSPECTS
.
71
2.
A
APPENDIX:
LONG
FORMULAS
.
74
3
CONTENTS
2.B
APPENDIX:
A
LOCAL
DISCONTINUOUS
GALERKIN
SCHEME
FOR
DIFFERENT
VERSIONS
OF
THE
NERNST-PLANCK-POISSON
EQUATION
.
76
2.C
APPENDIX:
NOMENCLATURE
FOR
MODELING
.
79
3
PREDICTING
THE
DIFFUSION
IN
POROUS
MEDIA
83
3.1
INTRODUCTION
AND
MOTIVATION
.
84
3.2
WELL-ESTABLISHED
FUNCTIONAL
RELATIONS
BETWEEN
HYDRODYNAMIC
PA
RAMETERS
AND
POROSITY
.
85
3.3
MATHEMATICAL
MODELS
AND
BOUNDS
.
87
3.3.1
STANDARD
UPSCALING
RESULTS
.
88
3.3.2
SPECIAL
CASES
AND
ANALYTICAL
BOUNDS
.
88
3.4
SETTING
AND
NUMERICAL
METHODS
.
91
3.5
EVALUATION
.
96
3.5.1
EVALUATION
OF
EFFECTIVE
TENSORS
OVER
POROSITY
.
96
3.5.2
EVALUATION
OF
EFFECTIVE
TENSORS
OVER
SURFACE
AREA
.
101
3.5.3
REMARK
ON
TORTUOSITY
.
106
3.6
CONCLUSIONS
AND
FUTURE
PROSPECTS
.
107
4
ANALYSIS
OF
HOMOGENIZATION
FOR
DISCONTINUOUS
TENSORS
109
4.1
MOTIVATION
AND
FORMULATION
OF
THE
PROBLEM
.
109
4.2
ANALYSIS
OF
THE
PROBLEM
WITH
COUNTABLE
JUMPS
.
ILL
4.3
TEMPORAL
HOMOGENIZATION
BY
ASYMPTOTIC
EXPANSION
.
113
4.4
CONCLUSIONS
AND
FUTURE
PROSPECTS
.
114
5
ANALYSIS
OF
THE
DISCONTINUOUS
GALERKIN
METHOD
FOR
DARCY
*
S
EQUATION
115
5.1
INTRODUCTION
AND
MOTIVATION
.
116
5.2
A
LOCAL
DISCONTINUOUS
GALERKIN
SCHEME
FOR
DARCY'S
EQUATION
IN
CLUDING
JUMP
CONDITIONS
AND
USING
DIFFERENT
APPROXIMATION
SPACES
119
5.2.1
PROBLEM
FORMULATION
.
120
5.2.2
BASIC
DEFINITIONS
.
122
5.2.3
SPATIAL
DISCRETIZATION
.
123
5.2.4
A
COLLECTION
OF
AUXILIARY
DEFINITIONS
AND
RESULTS
.
125
5.2.5
STABILITY
OF
THE
METHOD
.
128
5.2.6
CONVERGENCE
ORDER
ESTIMATES
.
131
5.2.7
NUMERICAL
RESULTS
.
136
5.3
AN
APPLICATION
OF
THE
LDG
METHOD
WITH
DIFFERENT
APPROXIMATION
SPACES
ON
NON-LINEAR ADVECTION-DIFFUSION
EQUATIONS
.
138
5.3.1
FORMULATION
OF
THE
LDG
SCHEME
.
139
5.3.2
STABILITY
AND
ERROR
ANALYSIS
.
140
5.3.3
NUMERICAL
RESULTS
.
142
4
CONTENTS
5.4
A
HYBRIDIZABLE
LDG
SCHEME
FOR
DARCY'S
EQUATION
INCLUDING
JUMP
CONDITIONS
AND
USING
DIFFERENT
APPROXIMATION
SPACES
.
143
5.4.1
SPATIAL
DISCRETIZATION
.
144
5.4.2
STABILITY
ESTIMATE
.
146
5.4.3
CONVERGENCE
ORDER
ESTIMATES
.
149
5.4.4
NUMERICAL
RESULTS
.
153
5.5
CONCLUSIONS
AND
FUTURE
PROSPECTS
.
156
6
CONCLUSIONS
AND
FUTURE
PROSPECTS
159
BIBLIOGRAPHY
161
INDEX
177
5 |
| any_adam_object | 1 |
| author | Rupp, Andreas 1992- |
| author_GND | (DE-588)1191198812 |
| author_facet | Rupp, Andreas 1992- |
| author_role | aut |
| author_sort | Rupp, Andreas 1992- |
| author_variant | a r ar |
| building | Verbundindex |
| bvnumber | BV046082660 |
| ctrlnum | (OCoLC)1105127122 (DE-599)DNB1188424041 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-10-01T14:01:20Z |
| institution | BVB |
| institution_GND | (DE-588)1064118135 |
| isbn | 9783844068016 |
| language | English German |
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| physical | 187 Seiten Illustrationen 24 cm x 17 cm, 281 g |
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| spelling | Rupp, Andreas 1992- (DE-588)1191198812 aut Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren Andreas Rupp Düren Shaker Verlag 2019 187 Seiten Illustrationen 24 cm x 17 cm, 281 g txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Dissertation Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) 2019 Bodengefüge (DE-588)4112798-5 gnd rswk-swf Diskontinuierliche Galerkin-Methode (DE-588)4588309-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Darcy’s equation diffusion discontinuous Galerkin homogenization microaggregate development upscaling (DE-588)4113937-9 Hochschulschrift gnd-content Bodengefüge (DE-588)4112798-5 s Mathematisches Modell (DE-588)4114528-8 s Diskontinuierliche Galerkin-Methode (DE-588)4588309-9 s DE-604 Shaker Verlag (DE-588)1064118135 pbl DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031463725&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rupp, Andreas 1992- Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren Bodengefüge (DE-588)4112798-5 gnd Diskontinuierliche Galerkin-Methode (DE-588)4588309-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4112798-5 (DE-588)4588309-9 (DE-588)4114528-8 (DE-588)4113937-9 |
| title | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren |
| title_auth | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren |
| title_exact_search | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren |
| title_full | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren Andreas Rupp |
| title_fullStr | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren Andreas Rupp |
| title_full_unstemmed | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren Andreas Rupp |
| title_short | Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods |
| title_sort | simulating structure formation in soils across scales using discontinuous galerkin methods simulation von strukturbildung im boden auf unterschiedlichen skalen mithilfe unstetiger galerkin verfahren |
| title_sub | Simulation von Strukturbildung im Boden auf unterschiedlichen Skalen mithilfe unstetiger Galerkin–Verfahren |
| topic | Bodengefüge (DE-588)4112798-5 gnd Diskontinuierliche Galerkin-Methode (DE-588)4588309-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Bodengefüge Diskontinuierliche Galerkin-Methode Mathematisches Modell Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031463725&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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