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Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation [Minkštas viršelis]

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  • Formatas: Paperback / softback, 328 pages, aukštis x plotis: 235x152 mm, weight: 567 g, 16 color illus. 19 halftones. 23 line illus. 2 tables.
  • Serija: Princeton Series in Astrophysics
  • Išleidimo metai: 24-Nov-2013
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691141738
  • ISBN-13: 9780691141732
Kitos knygos pagal šią temą:
Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, RotationDidesnis paveikslėlis
  • Formatas: Paperback / softback, 328 pages, aukštis x plotis: 235x152 mm, weight: 567 g, 16 color illus. 19 halftones. 23 line illus. 2 tables.
  • Serija: Princeton Series in Astrophysics
  • Išleidimo metai: 24-Nov-2013
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691141738
  • ISBN-13: 9780691141732
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780691141732.html
Raktažodžiai:
"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. Describes how to create codes that simulate the internal dynamics of planets and stars Builds on basic concepts and simple methods Shows how to improve the efficiency and accuracy of the numerical methods Describes more relevant geometries and boundary conditions Demonstrates how to incorporate more sophisticated physics "--

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.

  • Describes how to create codes that simulate the internal dynamics of planets and stars
  • Builds on basic concepts and simple methods
  • Shows how to improve the efficiency and accuracy of the numerical methods
  • Describes more relevant geometries and boundary conditions
  • Demonstrates how to incorporate more sophisticated physics

Recenzijos

"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. It is very useful for readers having a basic understanding of classical physics, vector calculus, partial differential equations, and simple computer programming."--Claudia-Veronika Meister, Zentralblatt MATH

Preface xi
PART I THE FUNDAMENTALS
1(82)
Chapter 1 A Model of Rayleigh-Benard Convection
3(14)
1.1 Basic Theory
3(7)
1.2 Boussinesq Equations
10(3)
1.3 Model Description
13(4)
Supplemental Reading
15(1)
Exercises
15(2)
Chapter 2 Numerical Method
17(10)
2.1 Vorticity-Streamfunction Formulation
17(2)
2.2 Horizontal Spectral Decomposition
19(2)
2.3 Vertical Finite-Difference Method
21(1)
2.4 Time Integration Scheme
22(2)
2.5 Poisson Solver
24(3)
Supplemental Reading
25(1)
Exercises
25(2)
Chapter 3 Linear Stability Analysis
27(8)
3.1 Linear Equations
27(2)
3.2 Linear Code
29(1)
3.3 Critical Rayleigh Number
30(1)
3.4 Analytic Solutions
31(4)
Supplemental Reading
34(1)
Exercises
34(1)
Computational Projects
34(1)
Chapter 4 Nonlinear Finite-Amplitude Dynamics
35(16)
4.1 Modifications to the Linear Model
35(1)
4.2 A Galerkin Method
36(2)
4.3 Nonlinear Code
38(5)
4.4 Nonlinear Simulations
43(8)
Supplemental Reading
48(1)
Exercises
49(1)
Computational Projects -
49(2)
Chapter 5 Postprocessing
51(8)
5.1 Computing and Storing Results
51(1)
5.2 Displaying Results
51(3)
5.3 Analyzing Results
54(5)
Supplemental Reading
57(1)
Exercises
57(1)
Computational Projects
57(2)
Chapter 6 Internal Gravity Waves
59(9)
6.1 Linear Dispersion Relation
59(3)
6.2 Code Modifications and Simulations
62(4)
6.3 Wave Energy Analysis
66(2)
Supplemental Reading
66(1)
Exercises
67(1)
Computational Projects
67(1)
Chapter 7 Double-Diffusive Convection
68(15)
7.1 Salt-Fingering Instability
69(3)
7.2 Semiconvection Instability
72(2)
7.3 Oscillating Instabilities
74(2)
7.4 Staircase Profiles
76(3)
7.5 Double-Diffusive Nonlinear Simulations
79(4)
Supplemental Reading
80(1)
Exercises
80(1)
Computational Projects
80(3)
PART II ADDITIONAL NUMERICAL METHODS
83(84)
Chapter 8 Time Integration Schemes
85(10)
8.1 Fourth-Order Runge-Kutta Scheme
85(2)
8.2 Semi-Implicit Scheme
87(2)
8.3 Predictor-Corrector Schemes
89(2)
8.4 Infinite Prandtl Number: Mantle Convection
91(4)
Supplemental Reading
92(1)
Exercises
93(1)
Computational Projects
93(2)
Chapter 9 Spatial Discretizations
95(20)
9.1 Nonuniform Grid
95(2)
9.2 Coordinate Mapping
97(1)
9.3 Fully Finite---Difference
98(4)
9.4 Fully Spectral: Chebyshev-Fourier
102(6)
9.5 Parallel Processing
108(7)
Supplemental Reading
112(1)
Exercises
112(1)
Computational Projects
112(3)
Chapter 10 Boundaries and Geometries
115(52)
10.1 Absorbing Top and Bottom Boundaries
115(2)
10.2 Permeable Periodic Side Boundaries
117(5)
10.3 2D Annulus Geometry
122(8)
10.4 Spectral-Transform Method
130(3)
10.5 3D and 2.5D Cartesian Box Geometry
133(2)
10.6 3D and 2.5D Spherical-Shell Geometry
135(32)
Supplemental Reading
162(1)
Exercises
162(2)
Computational Projects
164(3)
PART III ADDITIONAL PHYSICS
167(116)
Chapter 11 Magnetic Field
169(24)
11.1 Magnetohydrodynamics
170(3)
11.2 Magnetoconvection with a Vertical Background Field
173(6)
11.3 Linear Analyses: Magnetic
179(3)
11.4 Nonlinear Simulations: Magnetic
182(2)
11.5 Magnetoconvection with a Horizontal Background Field
184(3)
11.6 Magnetoconvection with an Arbitrary Background Field
187(6)
Supplemental Reading
189(1)
Exercises
190(1)
Computational Projects
191(2)
Chapter 12 Density Stratification
193(36)
12.1 Anelastic Approximation
194(13)
12.2 Reference State: Polytropes
207(7)
12.3 Numerical Method: Anelastic
214(5)
12.4 Linear Analyses: Anelastic
219(3)
12.5 Nonlinear Simulations: Anelastic
222(7)
Supplemental Reading
227(1)
Exercises
227(1)
Computational Projects
228(1)
Chapter 13 Rotation
229(54)
13.1 Coriolis, Centrifugal, and Poincare Forces
229(4)
13.2 2D Rotating Equatorial Box
233(8)
13.3 2D Rotating Equatorial Annulus: Differential Rotation
241(6)
13.4 2.5D Rotating Spherical Shell: Inertial Oscillations
247(12)
13.5 3D Rotating Spherical Shell: Dynamo Benchmarks
259(5)
13.6 3D Rotating Spherical Shell: Dynamo Simulations
264(11)
13.7 Concluding Remarks
275(8)
Supplemental Reading
277(1)
Exercises
278(1)
Computational Projects
279(4)
Appendix A A Tridiagonal Matrix Solver 283(1)
Appendix B Making Computer-Graphical Movies 284(4)
Appendix C Legendre Functions and Gaussian Quadrature 288(3)
Appendix D Parallel Processing: OpenMP 291(1)
Appendix E Parallel Processing: MPI 292(3)
Bibliography 295(12)
Index 307
Gary A. Glatzmaier is professor of earth and planetary sciences at the University of California, Santa Cruz. He is a fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences.