Mathematical modeling of Earth's dynamical systems : a primer / Rudy Slingerland and Lee Kump.

Includes bibliographical references and index.

1 Modeling and Mathematical Concepts -- Pros and Cons of Dynamical Models -- An Important Modeling Assumption -- Some Examples -- Example I: Simulation of Chicxulub Impact and Its Consequences -- Example II: Storm Surge of Hurricane Ivan in Escambia Bay -- Steps in Model Building -- Basic Definitions and Concepts -- Nondimensionalization -- A Brief Mathematical Review 2 Basics of Numerical Solutions by Finite Difference -- First Some Matrix Algebra -- Solution of Linear Systems of Algebraic Equations -- General Finite Difference Approach -- Discretization -- Obtaining Difference Operators by Taylor Series -- Explicit Schemes -- Implicit Schemes -- How Good Is My Finite Difference Scheme? -- Stability Is Not Accuracy 3 Box Modeling: Unsteady, Uniform Conservation of Mass -- Translations -- Example I: Radiocarbon Content of the Biosphere as a One-Box Model -- Example II: The Carbon Cycle as a Multibox Model -- Example III: One-Dimensional Energy Balance Climate Model -- Finite Difference Solutions of Box Models -- The Forward Euler Method -- Predictor-Corrector Methods -- Stiff Systems -- Example IV: Rothman Ocean -- Backward Euler Method -- Model Enhancements 4 One-Dimensional Diffusion Problems -- Translations -- Example I: Dissolved Species in a Homogeneous Aquifer -- Example II: Evolution of a Sandy Coastline -- Example III: Diffusion of Momentum -- Finite Difference Solutions to 1-D Diffusion Problems 5 Multidimensional Diffusion Problems -- Translations -- Example I: Landscape Evolution as a 2-D Diffusion Problem -- Example II: Pollutant Transport in a Confined Aquifer -- Example III: Thermal Considerations in Radioactive Waste Disposal -- Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems -- An Explicit Scheme -- Implicit Schemes -- Case of Variable Coefficients 6 Advection-Dominated Problems -- Translations -- Example I: A Dissolved Species in a River -- Example II: Lahars Flowing along Simple Channels -- Finite Difference Solution Schemes to the Linear Advection Equation 7 Advection and Diffusion (Transport) Problems -- Translations -- Example I: A Generic 1-DCase -- Example II: Transport of Suspended Sediment in a Stream -- Example III: Sedimentary Diagenesis -- Finite Difference Solutions to the Transport Equation -- QUICK Scheme -- QUICKEST Scheme 8 Transport Problems with a Twist: The Transport of Momentum -- Translations -- Example I: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation) -- An Analytic Solution to Burgers' Equation -- Finite Difference Scheme for Burgers' Equation -- Solution Scheme Accuracy -- Diffusive Momentum Transport in turbulent Flows -- Adding Sources and Sinks of Momentum:The General Law of Motion 9 Systems of One-Dimensional Non linear Partial Differential Equations -- Translations -- Example I: Gradually Varied Flow in an Open Channel -- Finite Difference Solution Schemes for Equation Sets -- Explicit FTCS Scheme on a Staggered Mesh -- Four-Point Implicit Scheme -- The Dam-Break Problem: An Example 10. Two-Dimensional Nonlinear Hyperbolic Systems -- Translations -- Example I The Circulation of Lakes, Estuaries, and the Coastal Ocean -- An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows -- Lake Ontario Wind-Driven Circulation: An Example.

Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of d.

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