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Computational methods for geodynamics

Author: Alik Ismail-Zadeh; Paul J Tackley
Publisher: Cambridge ; New York : Cambridge University Press, 2010.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ismail-Zadeh, Alik.
Computational methods for geodynamics.
Cambridge ; New York : Cambridge University Press, 2010
(DLC) 2010017823
(OCoLC)567130604
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alik Ismail-Zadeh; Paul J Tackley
ISBN: 9780511776632 0511776632 0511774052 9780511774058 9780521867672 0521867673 9780511780820 0511780826 9786612724886 6612724889
OCLC Number: 659563267
Description: 1 online resource (xv, 313 pages, [16] pages of color plates) : illustrations
Contents: Cover --
Half-title --
Title --
Copyright --
Contents --
Foreword --
Preface --
Acknowledgements --
1 Basic concepts of computational geodynamics --
1.1 Introduction to scienti.c computing and computational geodynamics --
1.2 Mathematical models of geodynamic problems --
1.3 Governing equations --
1.3.1 The equation of continuity --
1.3.2 The equation of motion --
1.3.3 The heat equation --
1.3.4 The rheological law --
1.3.5 Other equations --
1.3.6 Boussinesq approximation --
1.3.7 Stream function formulation --
1.3.8 Poloidal and toroidal decomposition --
1.4 Boundary and initial conditions --
1.5 Analytical and numerical solutions --
1.6 Rationale of numerical modelling --
1.7 Numerical methods: possibilities and limitations --
1.8 Components of numerical modelling --
1.9 Properties of numerical methods --
1.10 Concluding remarks --
2 Finite difference method --
2.1 Introduction: basic concepts --
2.2 Convergence, accuracy and stability --
2.3 Finite difference sweep method --
2.4 Principle of the maximum --
2.5 Application of a .nite difference method to a two-dimensional heat equation --
2.5.1 Statement of the problem --
2.5.2 Finite difference discretisation --
2.5.3 Monotonic 8220;nite difference scheme --
2.5.4 Solution method --
2.5.5 Veri8220;cation of the 8220;nite difference scheme --
3 Finite volume method --
3.1 Introduction --
3.2 Grids and control volumes: structured and unstructured grids --
3.3 Comparison to .nite difference and .nite element methods --
3.4 Treatment of advection8211;diffusion problems --
3.4.1 Diffusion --
3.4.2 Advection --
3.5 Treatment of momentum8211;continuity equations --
3.5.1 Discretisation --
3.5.2 Solution methods --
3.5.3 Multigrid --
3.6 Modelling convection and model extensions --
3.6.1 Overall solution strategy --
3.6.2 Extension to compressible equations --
3.6.3 Extension to spherical geometry --
4 Finite element method --
4.1 Introduction --
4.2 Lagrangian versus Eulerian description of motion --
4.3 Mathematical preliminaries --
4.4 Weighted residual methods: variational problem --
4.5 Simple FE problem --
4.6 The Petrov8211;Galerkin method for advection-dominated problems --
4.7 Penalty-function formulation of Stokes .ow --
4.8 FE discretisation --
4.9 High-order interpolation functions: cubic splines --
4.10 Twoand three-dimensional FE problems --
4.10.1 Two-dimensional problem of gravitational advection --
4.10.2 Three-dimensional problem of gravitational advection --
4.11 FE solution re.nements --
4.12 Concluding remarks --
Step 1. Pre-processing phase --
Step 2. Solution phase --
Step 3. Post-processing phase --
5 Spectral methods --
5.1 Introduction --
5.2 Basis functions and transforms --
5.2.1 Overview --
5.2.2 Trigonometric --
5.2.3 Chebyshev polynomials --
5.2.4 Spherical harmonics --
5.3 Solution methods --
5.3.1 Poisson s equation --
5.3.2 Galerkin, Tau and pseudo-spectral methods --
5.4 Modelling mantle convection --
5.4.1 Constant viscosity, three-dimensional Cartesian geometry --
5.4.2 Constant viscosity, spherical geometry --
5.4.3 Compressibility --
5.4.4 Self-gravitation and geoid --
5.4.5 Tectonic plates and laterally varying viscosity --
6 Numerical methods for solving linear algebraic equations --
6.1 Introduction --
6.2 Direct met.
Responsibility: Alik Ismail-Zadeh, Paul J. Tackley.
More information:

Abstract:

Both a textbook and a handy reference, this book brings together key numerical techniques for geodynamic modeling - providing a foundation in the basic principles and practical demonstrations of the  Read more...

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'An outstanding synthesis of contemporary issues in geodynamics with a rigorous but highly accessible treatment of modern methods in numerical modeling. I have no doubt that this book will be an Read more...

 
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