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

<p><b>Geoffrey Pert, PhD,</b> is Emeritus Professor, Department of Physics, University of York, UK. He has continuously been involved in research in plasma physics, primarily the interaction of high-power lasers with materials, since first studying the subject as a research student in the 1960's. Professor Pert is also a Fellow of the Royal Society.

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