作者: Gary A. Glatzmaier | 出版社: Princeton University Press |

ISBN: 9780691141725 | 分类号: P144 /G549 |

出版时间: 2013-12-03 | 有434人浏览 |

**[BOOK DESCRIPTION]**

This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, Gary Glatzmaier begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a two-dimensional box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. He then describes how to implement more efficient and accurate numerical methods and more realistic geometries in two and three dimensions. In the third part of the book, Glatzmaier demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. Featuring numerous exercises throughout, this is an ideal textbook for students and an essential resource for researchers. It describes how to create codes that simulate the internal dynamics of planets and stars. It builds on basic concepts and simple methods. It shows how to improve the efficiency and accuracy of the numerical methods. It describes more relevant geometries and boundary conditions. It demonstrates how to incorporate more sophisticated physics.

Preface xi PART I. THE FUNDAMENTALS

Chapter

A Model of Rayleigh-Benard Convection

1.1 Basic Theory

1.2 Boussinesq Equations

1.3 Model Description

Supplemental Reading

Exercises

Chapter

Numerical Method

2.1 Vorticity-Streamfunction Formulation

2.2 Horizontal Spectral Decomposition

2.3 Vertical Finite-Difference Method

2.4 Time Integration Scheme

2.5 Poisson Solver

Supplemental Reading

Exercises

Chapter

Linear Stability Analysis

3.1 Linear Equations

3.2 Linear Code

3.3 Critical Rayleigh Number

3.4 Analytic Solutions

Supplemental Reading

Exercises

Computational Projects

Chapter

Nonlinear Finite-Amplitude Dynamics

4.1 Modifications to the Linear Model

4.2 A Galerkin Method

4.3 Nonlinear Code

4.4 Nonlinear Simulations

Supplemental Reading

Exercises

Computational Projects

Chapter

Postprocessing

5.1 Computing and Storing Results

5.2 Displaying Results

5.3 Analyzing Results

Supplemental Reading

Exercises

Computational Projects

Chapter

Internal Gravity Waves

6.1 Linear Dispersion Relation

6.2 Code Modifications and Simulations

6.3 Wave Energy Analysis

Supplemental Reading

Exercises

Computational Projects

Chapter

Double-Diffusive Convection

7.1 Salt-Fingering Instability

7.2 Semiconvection Instability

7.3 Oscillating Instabilities

7.4 Staircase Profiles

7.5 Double-Diffusive Nonlinear Simulations

Supplemental Reading

Exercises

Computational Projects

PART II. ADDITIONAL NUMERICAL METHODS

Chapter

Time Integration Schemes

8.1 Fourth-Order Runge-Kutta Scheme

8.2 Semi-Implicit Scheme

8.3 Predictor-Corrector Schemes

8.4 Infinite Prandtl Number: Mantle Convection

Supplemental Reading

Exercises

Computational Projects

Chapter

Spatial Discretizations

9.1 Nonuniform Grid

9.2 Coordinate Mapping

9.3 Fully Finite Difference

9.4 Fully Spectral: Chebyshev-Fourier

9.5 Parallel Processing

Supplemental Reading

Exercises

Computational Projects

Chapter

Boundaries and Geometries

10.1 Absorbing Top and Bottom Boundaries

10.2 Permeable Periodic Side Boundaries

10.3 Annulus Geometry

10.4 Spectral-Transform Method

10.5 and5D Cartesian Box Geometry

10.6 and 5D Spherical-Shell Geometry

Supplemental Reading

Exercises

Computational Projects

PART III. ADDITIONAL PHYSICS

Chapter

Magnetic Field

11.1 Magnetohydrodynamics

11.2 Magnetoconvection with a Vertical Background Field

11.3 Linear Analyses: Magnetic

11.4 Nonlinear Simulations: Magnetic

11.5 Magnetoconvection with a Horizontal Background Field

11.6 Magnetoconvection with an Arbitrary Background Field

Supplemental Reading

Exercises

Computational Projects

Chapter

Density Stratification

12.1 Anelastic Approximation

12.2 Reference State: Polytropes

12.3 Numerical Method: Anelastic

12.4 Linear Analyses: Anelastic

12.5 Nonlinear Simulations: Anelastic

Supplemental Reading

Exercises

Computational Projects

Chapter

Rotation

13.1 Coriolis, Centrifugal, and Poincare Forces

13.2 Rotating Equatorial Box

13.3 Rotating Equatorial Annulus: Differential Rotation

13.4 5D Rotating Spherical Shell: Inertial Oscillations

13.5 Rotating Spherical Shell: Dynamo Benchmarks

13.6 Rotating Spherical Shell: Dynamo Simulations

13.7 Concluding Remarks

Supplemental Reading

Exercises

Computational Projects

Appendix A A Tridiagonal Matrix Solver

Appendix B Making Computer-Graphical Movies

Appendix C Legendre Functions and Gaussian Quadrature

Appendix D Parallel Processing: OpenMP

Appendix E Parallel Processing: MPI

Bibliography

Index