Description
Taylor & Francis Ltd Numerical Methods In Astrophysics 2006 Edition by Peter Bodenheimer, Gregory P. Laughlin
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. 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.