# Mathematical modeling of Earth's dynamical systems 1 edition

Mathematical modeling of Earth's dynamical systems

Rudy Slingerland

Mathematical modeling of Earth's dynamical systems
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##
**Mathematical modeling of Earth's dynamical systems**

*a primer*

Rudy Slingerland and Lee Kump

####
Published
**2011**
by
Princeton University Press
in
Princeton, N.J
.

Written in English.

### Table of 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 | ||

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 | ||

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) | ||

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. |

### Edition Notes

Includes bibliographical references (p. 211-215) and index.

### Classifications

## Dewey Decimal Class |
550.1/5118 |

## Library of Congress |
QH331 .S55 2011 |

### The Physical Object

## Pagination |
xii, 231 p. : |

## Number of pages |
231 |

### ID Numbers

## Open Library |
OL25566191M |

## Internet Archive |
mathematicalmode00slin |

## ISBN 10 |
069114513X, 0691145148 |

## ISBN 13 |
9780691145136, 9780691145143 |

## LC Control Number |
2010041656 |

## OCLC/WorldCat |
671916625 |

## History Created July 30, 2014 · 1 revision Download catalog record: RDF / JSON

July 30, 2014 | Created by ImportBot | import new book |