Modelling and Simulation in Plasma Physics for Physicists and Mathematicians
Auteur : Pert G. J.
Preface 1 Foundations of Computational Fluid Mechanics 1.1 Basic Concepts of Finite Difference Integration 1.2 Basic Concepts of Fluid Mechanics 1.3 The Basic Equations of Fluid Mechanics 1.4 Ideal (Dissipationless) Flow - Hyperbolic Equations 1.5 Formal Solution 1.6 Discontinuities 1.7 Plasma Fluid Dynamics 1.8 Basic Principles of Finite Differencing 1.9 Numerical Fluid Approximations 1.10 Grid Geometry 1.11 Control Volume Differencing 1.12 Mesh types
2 Analytic and Quasi-Analytic Approximations 2.1 Analytic and Quasi-Analytic Methods Appendix 2.A The Nemchinov conjecture Appendix 2.B The energy integral
3 Numerical Fluid Dynamics 3.1 Eulerian Schemes 3.2 Steady State Problems 3.3 Spatial Differencing 3.4 Generalised Euler Schemes
4 Lagrangian Systems 4.1 Lagrangian Fluid Dynamics 4.2 One Dimensional von Neumann-Richtmyer Algorithm 4.3 Multi-Dimensional Lagrangian Schemes 4.4 Choice of Method
5 Arbitrary Lagrangian-Eulerian Schemes 5.1 Introduction 5.2 Step 1: The Lagrangian Stage 5.3 Step 2: The Iteration Stage 5.4 Step 3: Mesh generation 5.5 Step 4: Rezoning
6 Hybrid or 1 1/2 d Schemes 6.1 Introduction
7 Magneto-hydrodynamics 7.1 Introduction 7.2 The MHD Equations 7.3 Self-generated Fields
8 Monte Carlo Schemes 8.1 Monte-Carlo methods 8.2 Monte Carlo Integration 8.3 Random Walks 8.4 Nuclear Reactor Criticality 8.5 Thermodynamic Properties and Equation of State Appendix 8.A Kinematics of Elastic Scattering
9 Particle transport 9.1 Particle transport 10 Numerical Diffusion Schemes 10.1 Introduction 10.2 Split time step and ADI Methods for Solving Diffusion Problems in Orthogonal Cartesian Grid Systems 10.3 The Diffusion Matrix Appendix 10.A Thomas algorithm -Tri-diagonal matrix equation solver
11 Particle path tracking 11.1 Introduction Appendix 11.A Bunemann-Boris algorithm Appendix 11.B Stability of the 1d electrostatic model 11.B.1 Time step limitation 11.B.2 Space step limitation 11.B.3 Stability of the 1D electro-magnetic model
12 Ion-electron equilibration 13 Ionisation-recombination Models 13.1 Introduction 13.2 Collisional-radiative model 13.3 Two stage model Appendix 13.A Solution of the Collisional radiative equations Appendix 13.B A theorem on determinants Appendix 13.C An algorithm using the exact solution
Supplement M.1 Partial Differential Equations M.1.i General Form of First-Order Partial Differential Equations M.1.ii Linear second order partial differential equations M.1.iii Separation of variables M.1.iv Boundary conditions
Supplement M.2 Stiff Equations
Supplement M.3 Weak solutions
Supplement M.4 Operator Splitting M.4.i Split time step
Supplement M.5 Statistics Primer M.5.i Basic stochastic nomenclature and results M.5.ii Moments M.5.iii Covariance, Correlation and Regression M.5.iv Elementary Statistical Results M.5.v Variance of a Sum of Samples M.5.vi Variance of the mean M.5.vii Weighted averaging
Supplement M.6 Numerical Solution of Poisson’s Equation M.6.i One dimension M.6 .ii Two dimensions 223
Supplement M.7 Compressible Gas Potential Flow M.7.i Compressible Gas Potential Flow M.7.ii Perturbation Flow M.7.iii The General Solution
Supplement M.8 Viscous Incompressible Flow M.8.i Introduction M.8.ii Marker-in-Cell
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Date de parution : 08-2024
