Numerical Methods in Astrophysics: An Introduction, 1st Edition (Hardback) book cover

Numerical Methods in Astrophysics

An Introduction, 1st Edition

By Peter Bodenheimer, Peter Bodenheimer, Gregory P. Laughlin, Gregory P. Laughlin, Michal Rozyczka, Tomasz Plewa, Harold. W Yorke, Michal Rozyczka, Harold W. Yorke

CRC Press

346 pages | 10 Color Illus. | 79 B/W Illus.

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pub: 2006-12-13
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Description

Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations. This resource indicates which methods are most suitable for particular problems, demonstrates what the accuracy requirements are in numerical simulations, and suggests ways to test for and reduce the inevitable negative effects.

After an introduction to the basic equations and derivations, the book focuses on practical applications of the numerical methods. It explores hydrodynamic problems in one dimension, N-body particle dynamics, smoothed particle hydrodynamics, and stellar structure and evolution. The authors also examine advanced techniques in grid-based hydrodynamics, evaluate the methods for calculating the gravitational forces in an astrophysical system, and discuss specific problems in grid-based methods for radiation transfer. The book incorporates brief user instructions and a CD-ROM of the numerical codes, allowing readers to experiment with the codes to suit their own needs.

With numerous examples and sample problems that cover a wide range of current research topics, this highly practical guide illustrates how to solve key astrophysics problems, providing a clear introduction for graduate and undergraduate students as well as researchers and professionals.

Reviews

… a very thorough introduction … the book is ideal for a postgraduate student just beginning a Ph.D. in numerical astrophysics or for an undergraduate with a numerical project. However, it also offers more advanced researchers and professionals [with] a clear and useful reminder of the important issues involved in numerical algorithms. … The codes make an interesting addition to the book in that they allow the reader to actually try out … some of the numerical algorithms discussed in the book. …

—Matthew Bate, Geophysical and Astrophysical Fluid Dynamics

The sweep of the book is impressive given its size. Even with the space constraint, room has been found for excellent discussions of code stability, starting with very simple examples, and including nice comparative discussions for various techniques . . . This is a most welcome and carefully thought out book that should help in the search for deeper subterranean seams.

—James Collett, Physical Sciences Educational Review, 2007, Vol. 8, No. 1

Table of Contents

Basic Equations

The Boltzmann Equation

Conservation Laws of Hydrodynamics

The Validity of the Continuous Medium Approximation

Eulerian and Lagrangian Formulation of Hydrodynamics

Viscosity and Navier–Stokes Equations

Radiation Transfer

Conducting and Magnetized Media

Numerical Approximations to Partial Differential Equations

Numerical Modeling with Finite-Difference Equations

Difference Quotient

Discrete Representation of Variables, Functions, and Derivatives

Stability of Finite-Difference Methods

Physical Meaning of Stability Criterion

A Useful Implicit Scheme

Diffusion, Dispersion, and Grid Resolution Limit

Alternative Methods

N-Body Particle Methods

Introduction to the N-Body Problem

Euler and Runge–Kutta Methods

The Description of Orbital Motion in Terms of Orbital Elements

The Few-Body Problem: Bulirsch–Stoer Integration

Lyapunov Time Estimation

Symplectic Integration

N-Body Codes for Large N

Close Encounters and Regularization

Force Calculation: The Tree Method

Force Calculation: Fast Fourier Transforms

Smoothed Particle Hydrodynamics

Rudimentary SPH

Colliding Planets: An SPH Test Problem

Necessary Improvements to Rudimentary SPH

Summary

Stellar Evolution

Equations for Equilibrium of a Star

Radiative, Conductive, and Convective Energy Transfer

Change in Chemical Composition

Boundary Conditions

An Implicit Lagrangian Technique: Henyey Method

Physics Packages

Examples

Grid-Based Hydrodynamics

Flow Discontinuities and How to Handle Them

A Simple Lagrangian Hydrocode

Basic Eulerian Techniques

Adaptive Mesh Refinement

A Multidimensional Eulerian Hydrocode

2 1/2-Dimensional Simulations

Examples

Poisson Equation

Poisson Solutions: I

Poisson Solutions: II

Test of the Potential

Magnetohydrodynamics

Basic Assumptions and Definitions

MHD Source Terms

Solving the Induction Equation

Initial and Boundary Conditions

Examples and Exercises

Concluding Remarks

Radiation Transport

Solving the Ray Equation for the Continuum

Solution for Frequency-Dependent Radiation Transfer in Spherical Symmetry

Frequency-Dependent Stellar Atmospheres

Technique for Flux-Limited Diffusion in Two Space Dimensions

Example: Spectrum of a Rotating, Collapsing Object

Example: 3-D Calculations of the Solar Photosphere

Numerical Codes

Radiation Transfer

Stellar Evolution

One-Dimensional Lagrangian Hydro

ZEUS: 3-D Hydrodynamics

N-Body Codes

Smoothed Particle Hydrodynamics

INDEX

References appear in each chapter.

About the Series

Series in Astronomy and Astrophysics

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Subject Categories

BISAC Subject Codes/Headings:
SCI005000
SCIENCE / Astrophysics & Space Science
SCI040000
SCIENCE / Mathematical Physics