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Computational Computational Methods in Plasma Physics by Stephen Jardin

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  1. Feb 23, 2013 #1

    Astronuc

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    Staff: Mentor


    Table of Contents
    Code (Text):
    Introduction to Magnetohydrodynamic Equations
    Introduction
    Magnetohydrodynamic (MHD) Equations
    Characteristics

    Introduction to Finite Difference Equations
    Introduction
    Implicit and Explicit Methods
    Errors
    Consistency, Convergence, and Stability
    Von Neumann Stability Analysis
    Accuracy and Conservative Differencing

    Finite Difference Methods for Elliptic Equations
    Introduction
    One Dimensional Poisson’s Equation
    Two Dimensional Poisson’s Equation
    Matrix Iterative Approach
    Physical Approach to Deriving Iterative Methods
    Multigrid Methods
    Krylov Space Methods
    Finite Fourier Transform

    Plasma Equilibrium
    Introduction
    Derivation of the Grad–Shafranov Equation
    The Meaning of Ψ
    Exact Solutions
    Variational Forms of the Equilibrium Equation
    Free Boundary Grad–Shafranov Equation
    Experimental Equilibrium Reconstruction

    Magnetic Flux Coordinates in a Torus
    Introduction
    Preliminaries
    Magnetic Field, Current, and Surface Functions
    Constructing Flux Coordinates from Ψ(R, Z)
    Inverse Equilibrium Equation

    Diffusion and Transport in Axisymmetric Geometry
    Introduction
    Basic Equations and Orderings
    Equilibrium Constraint
    Time Scales

    Numerical Methods for Parabolic Equations
    Introduction
    One Dimensional Diffusion Equations
    Multiple Dimensions

    Methods of Ideal MHD Stability Analysis
    Introduction
    Basic Equations
    Variational Forms
    Cylindrical Geometry
    Toroidal Geometry

    Numerical Methods for Hyperbolic Equations
    Introduction
    Explicit Centered-Space Methods
    Explicit Upwind Differencing
    Limiter Methods
    Implicit Methods

    Spectral Methods for Initial Value Problems
    Introduction
    Orthogonal Expansion Functions
    Non-Linear Problems
    Time Discretization
    Implicit Example: Gyrofluid Magnetic Reconnection

    The Finite Element Method
    Introduction
    Ritz Method in One Dimension
    Galerkin Method in One Dimension
    Finite Elements in Two Dimensions
    Eigenvalue Problems

    Bibliography

    Index
    From publisher:
    Publisher's site - http://www.crcpress.com/product/isbn/9781439810217
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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