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Computational methods for geodynamics /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2010.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.