Introduction to numerical geodynamic modelling:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Edition: | Reprint. with corr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 326 - 339 |
| Physical Description: | XI, 345 S. Ill., graph. Darst. |
| ISBN: | 9780521887540 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804150423122083840 |
|---|---|
| adam_text | Contents
Acknowledgements page
χ
Introduction
1
What is this book?
1
What this book is not
1
Get started
1
Short history of
geodynamics
and numerical geodynamic
modelling
4
A few words about programming and visualisation
7
How to use this book
8
Programming exercises and homework
9
The continuity equation
11
1.1
Continuum
-
what is it?
11
1.2
Continuity equation
13
1.3
Eulerian and Lagrangian points
-
what is the difference?
14
1.4
Derivation of the Eulerian continuity equation
15
1.5
Derivation of the Lagrangian continuity equation
18
1.6
Comparing Eulerian and Lagrangian continuity equations.
Advective transport term
20
1.7
Incompressible continuity equation
23
Analytical exercise
23
Programming exercise and homework
24
Density and gravity
25
2.1
Density of rocks and minerals. Equations of state
25
2.2
Gravity and gravitational potential
30
Analytical exercise
34
Programming exercises and homework
35
vi
Contents
3
Numerical solutions of partial differential equations
37
3.1
Finite-difference method
37
3.2
Solving linear equations
43
3.3
Geometrical and global indexing of unknowns
47
Programming exercises and homework
48
4
Stress and strain
51
4.1
Stress
51
4.2
Strain and strain rate
56
Analytical exercise
59
Programming exercise and homework
60
5
The momentum equation
61
5.1
Momentum equation
61
5.2
Newtonian law of viscous friction
64
5.3
Navier-Stokes equation
65
5.4
Poisson
equation
68
5.5
Stream function approach
69
Analytical exercise
71
Programming exercise and homework
71
6
Viscous rheology of rocks
73
6.1
Rock rheology
73
6.2
Effective viscosity
74
6.3
Non-Newtonian channel flow
79
Programming exercises and homework
80
7
Numerical solutions of the momentum and continuity equations
83
7.1
Grids
83
7.2
Discretisation of the equations
86
7.3
Conservative finite differences
87
7.4
Boundary conditions
92
7.5
Indexing of unknowns
95
Programming exercises and homework
101
8
The advection equation and marker-in-cell method
105
8.1
Advection equation
105
8.2
Eulerian advection methods
106
8.3
Marker-in-cell techniques
113
Programming exercises and homework
119
9
The heat conservation equation
123
9.1
Fourier s law of heat conduction
123
9.2
Heat conservation equation
124
9.3
Heat generation and consumption
127
Contents
vii
9.4
Simplified
temperature
equations
128
9.5
Heat diffusion timescales
129
Analytical exercises
130
Programming exercises and homework
131
10
Numerical solution of the heat conservation equation
133
10.1
Explicit and implicit formulation of the temperature
equation I33
10.2
Conservative finite differences
135
10.3
Advection of temperature with Eulerian methods
140
10.4
Advection of temperature with markers
141
10.5
Thermal boundary conditions
144
Programming exercises and homework
146
11
2D thermomechanical code structure
149
11.1
What do we expect from geodynamic codes
? 149
11.2
Thermomechanical code structure
150
11.3
Adding self-gravity and free surface
158
Programming exercise and homework
163
12
Elasticity and plasticity
165
12.1
Why care about elasticity and plasticity?
165
12.2
Elastic rheology
165
12.3
Rotation of elastic stresses
168
12.4
Maxwell visco-elastic rheology
172
12.5
Plastic rheology
173
12.6
Visco-elasto-plastic rheology
175
Analytical exercise
177
Programming exercises and homework
177
13
2D implementation of visco-elasto-plastic rheology
179
13.1
Viscous-like reformulation of visco-elasto-plasticity
179
13.2
Structure of visco-elasto-plastic thermomechanical
code
180
13.3
Visco-elasto-plastic iterations
189
Programming exercises and homework
191
14
The multigrid method
193
14.1
Multigrid
-
what is it?
193
14.2
Solving the
Poisson
equation with multigrid
200
14.3
Solving Stokes and continuity equations with multigrid
205
Programming exercises and homework
217
15
Programming of
3D
problems
221
15.1
Why simply not always
3D? 221
viii Contents
15.2 3D
staggered grid and discretisation of momentum,
continuity, temperature and
Poisson
equations
222
15.3
Solving discretised
3D
equations
231
Programming exercises and homework
239
16
Numerical benchmarks
241
16.1
Code benchmarking: why should we spend time on it?
241
16.2
Test
1.
Rayleigh-Taylor instability benchmark
242
16.3
Test
2.
Falling block benchmark
244
16.4
Test
3.
Channel flow with a non-Newtonian rheology
246
16.5
Test
4.
Non-steady temperature distribution in a
Newtonian channel
247
16.6
Test
5.
Couette
flow with viscous heating
250
16.7
Test
6.
Advection of sharp temperature fronts
253
16.8
Test
7.
Channel flow with variable thermal conductivity
253
16.9
Test
8.
Thermal convection with constant and variable
viscosity
255
16.10
Test
9.
Stress build-up in a visco-elastic Maxwell body
260
16.11
Test
10.
Recovery of the original shape of an elastic slab
261
16.12
Test
11.
Numerical sandbox benchmark
263
16.13
Possible further benchmarks
267
Programming exercises and homework
267
17
Design of 2D numerical geodynamic models
269
17.1
Warning message!
269
17.2
What is numerical modelling all about?
269
17.3
Material properties
270
17.4
Visco-elasto-plastic slab bending
271
17.5
Retreating oceanic
subduction
276
17.6
Lithospheric extension
279
17.7
Continental collision
282
17.8
Slab breakoff
287
17.9
Intrusion emplacement into the crust
291
17.10
Mantle convection with phase changes
296
17.11
Deformation of self-gravitating planetary body
301
Programming exercise and homework
306
Epilogue: outlook
307
Where are we now?
307
Where to go further?
307
State-of-the-art overview
311
Efficient direct solvers
312
Parallelisation of numerical codes
ЗІЗ
moments
IX
Mesh refinement algorithms
313
Including complex realistic physics in numerical
geodynamic models
314
3D
visualisation challenges
317
Conceptual warning
318
Conclusion
318
Appendix:
MATLAB
program examples
319
References
326
Index
340
until now, numerical modelling of geodynamic
processes has been the domain of highly trained
mathematicians with long experience of numerical
and computational techniques. Now, for the first
time, students and new researchers in the Earth
sciences can learn the basic theory and applications
from a single, accessible reference text.
Assumingonly minimal prerequisite
mathematical training (simple linear algebra and
derivatives), the author provides a solid grounding
in the basic mathematical theory and techniques,
including continuum mechanics and partial
differential equations, before introducing key
numerical and modelling methods. Eight well-
documented and state-of-the-art visco-elasto-
plastic, 2-D models are then presented, which allow
robust modelling of key dynamic processes, such
as
subduction, Nthospheric
extension, collision,
slab break-off, intrusion emplacement, mantle
convection and planetary core formation.
incorporating
47
practical exercises and
67
matlab
examples (for which codes are available
online at www.cambridge.org/gerya), this textbook
provides a user-friendly introduction for graduate
courses or for self-study, and encourages readers to
experiment with geodynamic models, first hand.
|
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| dewey-ones | 550 - Earth sciences |
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| discipline | Geologie / Paläontologie Geographie |
| edition | Reprint. with corr. |
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| id | DE-604.BV041059715 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:38:41Z |
| institution | BVB |
| isbn | 9780521887540 |
| language | English |
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| physical | XI, 345 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| spelling | Gerya, Taras V. 1962- Verfasser (DE-588)135825660 aut Introduction to numerical geodynamic modelling Taras V. Gerya Reprint. with corr. Cambridge [u.a.] Cambridge Univ. Press 2011 XI, 345 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 326 - 339 Geophysik (DE-588)4020252-5 gnd rswk-swf Geodynamik (DE-588)4020212-4 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Numerisches Modell (DE-588)4338132-7 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Geodynamik (DE-588)4020212-4 s Numerisches Modell (DE-588)4338132-7 s Geophysik (DE-588)4020252-5 s Mathematische Modellierung (DE-588)7651795-0 s 1\p DE-604 Modellierung (DE-588)4170297-9 s 2\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026036873&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026036873&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gerya, Taras V. 1962- Introduction to numerical geodynamic modelling Geophysik (DE-588)4020252-5 gnd Geodynamik (DE-588)4020212-4 gnd Modellierung (DE-588)4170297-9 gnd Numerisches Modell (DE-588)4338132-7 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4020252-5 (DE-588)4020212-4 (DE-588)4170297-9 (DE-588)4338132-7 (DE-588)7651795-0 |
| title | Introduction to numerical geodynamic modelling |
| title_auth | Introduction to numerical geodynamic modelling |
| title_exact_search | Introduction to numerical geodynamic modelling |
| title_full | Introduction to numerical geodynamic modelling Taras V. Gerya |
| title_fullStr | Introduction to numerical geodynamic modelling Taras V. Gerya |
| title_full_unstemmed | Introduction to numerical geodynamic modelling Taras V. Gerya |
| title_short | Introduction to numerical geodynamic modelling |
| title_sort | introduction to numerical geodynamic modelling |
| topic | Geophysik (DE-588)4020252-5 gnd Geodynamik (DE-588)4020212-4 gnd Modellierung (DE-588)4170297-9 gnd Numerisches Modell (DE-588)4338132-7 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Geophysik Geodynamik Modellierung Numerisches Modell Mathematische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026036873&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026036873&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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