Numerical methods in astrophysics : an introduction
Numerical methods in astrophysics : an introduction
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DOI：
10.1201/9781420011869
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发表时间：
2006-12
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影响因子：
--
通讯作者：
P. Bodenheimer
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文献类型：
--
作者：
P. Bodenheimer
基本方程Boltzmann方程流体力学守恒律连续介质近似的有效性流体力学的欧拉和拉格朗日公式粘性和Navier-Stokes方程辐射传输传导和磁化介质偏微分方程的数值近似用微分方程的数值建模差商变量、函数、稳定性判据的物理意义一种实用的隐式格式扩散，色散，和网格分辨率限制替代方法N体粒子方法介绍N体问题Euler和Runge-用轨道要素描述轨道运动少体问题：Bulirsch-Stoer积分李雅普诺夫时间估计辛积分大N次近距离接触的N体代码和正则化力计算：树方法力计算：快速傅立叶变换光滑粒子流体动力学基本SPH碰撞行星：SPH测试问题基本SPH概要星星平衡的恒星演化方程的必要改进辐射、传导和对流能量转移化学成分边界条件的变化隐式拉格朗日方法：Henyey方法物理包示例基于网格的流体力学流动不连续性以及如何处理它们一个简单的拉格朗日水动力学程序基本欧拉技术自适应网格细化一个多维欧拉水动力学程序2 1/2-尺寸模拟示例泊松方程泊松解：I泊松解：二位磁流体力学基本假设和定义的检验磁流体源项求解感应方程初始和边界条件示例和练习总结备注辐射输运求解射线方程的连续解球对称中频率相关的辐射传输两个空间维度中通量限制扩散的频率相关的恒星大气技术示例：旋转、坍缩物体的光谱示例：太阳光球层的3-D计算数值代码辐射传输恒星演化一维拉格朗日流体ZEUS：3-D流体动力学N体代码光滑粒子流体动力学索引参考文献出现在每一章。
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.