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

Author/creator Slingerland, Rudy
Other author Kump, Lee R.
Format Book
Publication InfoPrinceton, N.J. : Princeton University Press, ©2011.
Descriptionxii, 231 pages : illustrations, maps ; 21 cm
Subjects
Gaia hypothesis--Mathematical models.

Contents Machine generated contents note: 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 -- Summary -- 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 -- Summary -- Modeling Exercises -- 3. Box Modeling: Unsteady, Uniform Conservation of Mass -- Translations
Contents 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 -- Summary -- Modeling Exercises -- 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 -- Summary -- Modeling Exercises -- 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
Contents Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems -- An Explicit Scheme -- Implicit Schemes -- Case of Variable Coefficients -- Summary -- Modeling Exercises -- 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 -- Summary -- Modeling Exercises -- 7. Advection and Diffusion (Transport) Problems -- Translations -- Example I A Generic 1-D Case -- Example II Transport of Suspended Sediment in a Stream -- Example III Sedimentary Diagenesis: Influence of Burrows -- Finite Difference Solutions to the Transport Equation -- QUICK Scheme -- QUICKEST Scheme -- Summary -- Modeling Exercises -- 8. Transport Problems with a Twist: The Transport of Momentum -- Translations -- Example I One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation)
Contents 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 -- Summary -- Modeling Exercises -- 9. Systems of One-Dimensional Nonlinear 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 -- Summary -- Modeling Exercises -- 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 -- Summary -- Modeling Exercises.
Bibliography noteIncludes bibliographical references and index.
LCCN 2010041656
ISBN9780691145136 (hardcover : alk. paper)
ISBN069114513X (hardcover : alk. paper)
ISBN9780691145143 (pbk. : alk. paper)
ISBN0691145148 (pbk. : alk. paper)

Availability

Library Location Call Number Status Item Actions
Joyner General Stacks QH331 .S55 2011 ✔ Available Place Hold