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Mathematical modeling of Earth's dynamical systems 1 edition

Mathematical modeling of Earth's dynamical systems
Rudy Slingerland

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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