Title Computational methods for geodynamics / Alik Ismail-Zadeh, Paul J. Tackley

Published Cambridge ; New York : Cambridge University Press, 2010

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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 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 fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online"-- Provided by publisher Bibliography Includes bibliographical references and index Notes Print version record Subject Geodynamics -- Data processing SCIENCE -- Earth Sciences -- Geography. SCIENCE -- Earth Sciences -- Geology. Geodynamics -- Data processing Geodynamik Datenverarbeitung Form Electronic book Author Tackley, Paul J., author ISBN 9780511776632 0511776632 0511774052 9780511774058 9780511780820 0511780826 9786612724886 6612724889 1107210275 9781107210271 1282724886 9781282724884 0511775873 9780511775871 0511775113 9780511775116

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