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Basic Equations | p. 1 |
The Boltzmann Equation | p. 1 |
Conservation Laws of Hydrodynamics | p. 6 |
The Validity of the Continuous Medium Approximation | p. 10 |
Eulerian and Lagrangian Formulation of Hydrodynamics | p. 12 |
Viscosity and Navier-Stokes Equations | p. 14 |
Radiation Transfer | p. 19 |
Absorption, Emission, and Scattering | p. 21 |
Moments of the Boltzmann Equation for Photons | p. 22 |
Optically Thick and Optically Thin Limits | p. 25 |
Flux-Limited Diffusion | p. 26 |
Energy Equation in the Optically Thick Limit | p. 27 |
Conducting and Magnetized Media | p. 29 |
Maxwell's Equations | p. 29 |
Equations of Magnetohydrodynamics | p. 32 |
Limits of the MHD Approximation | p. 33 |
Field Freezing | p. 34 |
Summary | p. 36 |
References | p. 36 |
Numerical Approximations to Partial Differential Equations | p. 39 |
Numerical Modeling with Finite-Difference Equations | p. 39 |
Difference Quotient | p. 41 |
Discrete Representation of Variables, Functions, and Derivatives | p. 43 |
Stability of Finite-Difference Methods | p. 49 |
Physical Meaning of Stability Criterion | p. 52 |
A Useful Implicit Scheme | p. 58 |
Diffusion, Dispersion, and Grid Resolution Limit | p. 62 |
Alternative Methods | p. 65 |
References | p. 70 |
N-Body Particle Methods | p. 73 |
Introduction to the N-Body Problem | p. 73 |
Euler and Runge-Kutta Methods | p. 74 |
The Description of Orbital Motion in Terms of Orbital Elements | p. 79 |
The Few-Body Problem: Bulirsch-Stoer Integration | p. 85 |
Lyapunov Time Estimation | p. 87 |
Symplectic Integration | p. 90 |
N-Body Codes for Large N | p. 94 |
Close Encounters and Regularization | p. 99 |
Force Calculation: The Tree Method | p. 104 |
Force Calculation: Fast Fourier Transforms | p. 107 |
References | p. 113 |
Smoothed Particle Hydrodynamics | p. 115 |
Rudimentary SPH | p. 115 |
Colliding Planets: An SPH Test Problem | p. 118 |
Necessary Improvements to Rudimentary SPH | p. 120 |
Initial Conditions | p. 122 |
Kernels with Compact Support | p. 122 |
Combining SPH with a Tree Code | p. 123 |
Variable Smoothing Lengths | p. 124 |
A Resolution Requirement | p. 126 |
Introducing an Energy Equation into SPH | p. 127 |
Heat Transfer in SPH | p. 128 |
Shocks in SPH | p. 129 |
Time Integration | p. 133 |
Summary | p. 134 |
References | p. 137 |
Stellar Evolution | p. 139 |
Equations for Equilibrium of a Star | p. 140 |
Radiative, Conductive, and Convective Energy Transfer | p. 141 |
Change in Chemical Composition | p. 143 |
Boundary Conditions | p. 144 |
An Implicit Lagrangian Technique: Henyey Method | p. 147 |
Physics Packages | p. 155 |
Equation of State | p. 156 |
Opacity | p. 158 |
Nuclear Reactions | p. 160 |
Examples | p. 164 |
Evolution of the Sun | p. 164 |
Age Determination for a Star Cluster | p. 166 |
References | p. 168 |
Grid-Based Hydrodynamics | p. 169 |
Flow Discontinuities and How to Handle Them | p. 170 |
Steepening of Sound Waves | p. 170 |
Rankine-Hugoniot Conditions | p. 173 |
Shock Tube and Riemann Problem | p. 175 |
Artificial Viscosity | p. 178 |
A Simple Lagrangian Hydrocode | p. 181 |
Basic Eulerian Techniques | p. 185 |
Conservation of Physical Quantities | p. 185 |
Advection | p. 186 |
Godunov Method for Calculating Fluxes | p. 188 |
Operator Splitting | p. 189 |
Accuracy, Convergence, and Efficiency | p. 191 |
Adaptive Mesh Refinement | p. 193 |
A Multidimensional Eulerian Hydrocode | p. 197 |
Source Terms | p. 200 |
Advection Terms | p. 201 |
Boundary Conditions | p. 204 |
Time Step Control | p. 204 |
2 1/2-Dimensional Simulations | p. 206 |
Axial Symmetry | p. 206 |
Radiation Transport | p. 208 |
Thin Circumstellar Disk | p. 213 |
Examples | p. 214 |
Rayleigh-Taylor Instability | p. 214 |
Supernova Explosion | p. 216 |
Protostar Collapse and Disk Formation | p. 217 |
Spiral Waves in a Thin Self-Gravitating Disk | p. 219 |
References | p. 221 |
Poisson Equation | p. 223 |
Poisson Solutions: I | p. 224 |
Direct Summation | p. 224 |
Fourier Methods for Solving Equation (7.4) | p. 225 |
Self-Consistent Field | p. 230 |
Poisson Solutions: II | p. 235 |
Boundary Conditions | p. 236 |
Alternating Direction Implicit Method | p. 239 |
Successive Overrelaxation | p. 241 |
Multigrid Method | p. 243 |
Fourier Techniques | p. 243 |
Cyclic Reduction | p. 247 |
Polynomial Expansions in Three Dimensions | p. 248 |
Test of the Potential | p. 249 |
References | p. 251 |
Magnetohydrodynamics | p. 253 |
Basic Assumptions and Definitions | p. 253 |
MHD Source Terms | p. 256 |
Solving the Induction Equation | p. 259 |
Initial and Boundary Conditions | p. 264 |
Examples and Exercises | p. 265 |
Contraction of a Magnetized Ring | p. 265 |
Propagation of a Jet with a Helical Field | p. 265 |
Magnetic Buoyancy Instability | p. 267 |
Magnetorotational Instability | p. 270 |
Concluding Remarks | p. 274 |
References | p. 274 |
Radiation Transport | p. 277 |
Solving the Ray Equation for the Continuum | p. 277 |
Solution for Frequency-Dependent Radiation Transfer in Spherical Symmetry | p. 279 |
Frequency-Dependent Stellar Atmospheres | p. 285 |
Technique for Flux-Limited Diffusion in Two Space Dimensions | p. 290 |
Example: Spectrum of a Rotating, Collapsing Object | p. 300 |
Example: 3-D Calculations of the Solar Photosphere | p. 305 |
References | p. 308 |
Numerical Codes | p. 309 |
Radiation Transfer | p. 309 |
Stellar Evolution | p. 311 |
One-Dimensional Lagrangian Hydro | p. 316 |
ZEUS: 3-D Hydrodynamics | p. 317 |
N-Body Codes | p. 318 |
Smoothed Particle Hydrodynamics | p. 322 |
References | p. 323 |
Index | p. 325 |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.