| Preface | 5 |
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| I Elements of the theory of numerical modeling of gas-discharge phenomena | 13 |
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| 1 Models of gas-discharge physical mechanics | 15 |
| 1.1 Models of homogeneous chemically equilibrium plasma | 17 |
| 1.1.1 Mathematical model of radio-frequency (RF) plasma generator | 26 |
| 1.1.2 Mathematical model of electric-arc (EA) plasma generator | 31 |
| 1.1.3 Models of micro-wave (MW) plasma generators | 34 |
| 1.1.4 Models of laser supported plasma generators (LSPG) | 37 |
| 1.1.5 Numerical simulation models of steady-state radiative gas dynamics of RF-, EA-, MW-, and LSW-plasma generators | 45 |
| 1.1.6 Method of numerical simulation of non-stationary radiative gas-dynamic processes in subsonic plasma flows. The method of unsteady dynamic variables | 59 |
| 1.2 Models of nonuniform chemically equilibrium and nonequilibrium plasma | 61 |
| 1.2.1 Model of the five-component RF plasma generator | 66 |
| 1.2.2 Model of the three-component RF plasma generator | 69 |
| 1.2.3 Two-temperature model of RF plasma under ionization equilibrium | 71 |
| 1.2.4 One-liquid two-temperature model of laser supported plasma | 73 |
| 2 Application of numerical simulation models for the investigation of laser supported waves | 76 |
| 2.1 Air laser supported plasma generator | 76 |
| 2.2 Hydrogen laser supported plasma generator | 86 |
| 2.3 Bifurcation of subsonic gas flows in the vicinity of localized heat release regions | 93 |
| 2.3.1 Statement of the problem | 95 |
| 2.3.2 Qualitative analysis of the phenomenon | 96 |
| 2.3.3 Quantitative results of numerical simulation | 97 |
| 2.4 Laser supported waves in the field of gravity | 103 |
| 3 Computational models of magnetohydrodynamic processes | 116 |
| 3.1 General relations | 117 |
| 3.2 Vector form of Navier-Stokes equations | 118 |
| 3.3 System of equations of magnetic induction | 119 |
| 3.4 Force acting on ionized gas from electric and magnetic fields | 123 |
| 3.5 A heat emission caused by action of electromagnetic forces | 124 |
| 3.6 Complete set of the MHD equations in a flux form | 126 |
| 3.6.1 The MHD equations in projections | 127 |
| 3.6.2 Completely conservative form of the MHD equations | 129 |
| 3.7 The flux form of MHD equations in a dimensionless form | 132 |
| 3.7.1 Definition of the normalizing parameters | 132 |
| 3.7.2 Nondimension system of the MHD equations in flux form | 134 |
| 3.8 The MHD equations in the flux form. The use of pressure instead of specific internal energy | 138 |
| 3.9 Eigenvectors and eigenvalues of Jacobian matrixes for transformation of the MHD equations from conservative to the quasilinear form. Statement of nonstationary boundary conditions | 141 |
| 3.9.1 Jacobian matrixes of passage from conservative to the quasilinear form of the equations | 141 |
| 3.10 A singularity of Jacobian matrixes for transformation of the equations formulated in the conservative form | 145 |
| 3.11 System of the MHD equations without singular transfer matrixes | 152 |
| 3.12 Eigenvalues and eigenvectors of nonsingular matrixes of quasilinear system of the MHD equations | 156 |
| 3.12.1 Matrix Ãx | 156 |
| 3.12.2 Matrix Ãy | 160 |
| 3.12.3 Matrix Ãz | 163 |
| 3.13 A method of splitting for three-dimensional (3D) MHD equations | 165 |
| 3.14 Application of a splitting method for nonstationary 3D MHD flow field, generated by plasma plume in the ionosphere | 173 |
| II Numerical simulation models of glow discharge | 181 |
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| 4 The physical mechanics of direct current glow discharge | 183 |
| 4.1 Fundamentals of the physics of direct current glow discharge. The Engel-Steenbeck theory of a cathode layer | 184 |
| 4.2 Drift-diffusion model of glow discharge | 190 |
| 4.2.1 Governing equations | 190 |
| 4.2.2 Reduction of governing equations to a form convenient for numerical solution | 193 |
| 4.2.3 Initial conditions of the boundary value problem for the glow discharge | 196 |
| 4.2.4 Glow discharge with heat of gas | 198 |
| 4.2.5 Estimation of typical time scales of the solved problem | 199 |
| 4.3 Finite-difference methods for the drift-diffusion model | 206 |
| 4.3.1 Finite-difference scheme for the Poisson equation | 206 |
| 4.3.2 Finite-difference scheme for the equation of charge motion | 209 |
| 4.3.3 Conservative properties of the finite-difference scheme for the motion equation | 212 |
| 4.3.4 The order of accuracy of the finite-difference approximation used. The mesh diffusion | 215 |
| 4.3.5 The finite-difference grids | 219 |
| 4.3.6 Iterative methods for solving systems of linear algebraic equations in canonical form | 222 |
| 4.3.7 An iterative algorithm for the solution of a self-consistent problem | 233 |
| 4.3.8 Characteristic properties of a solution of a two-dimensional problem about glow discharge in a nonstationary statement | 234 |
| 4.4 Numerical simulation of the one-dimensional glow discharge | 237 |
| 4.4.1 Governing equations and boundary conditions | 238 |
| 4.4.2 The elementary implicit finite-difference scheme | 240 |
| 4.5 Diffusion of charges along a current line and effective method of grid diffusion elimination in calculations of glow discharges | 241 |
| 4.5.1 Governing equations for the one-dimensional case | 242 |
| 4.5.2 Boundary conditions | 242 |
| 4.5.3 Numerical methods for the one-dimensional calculation case | 243 |
| 4.5.4 Results of 1D numerical simulation | 244 |
| 4.5.5 Method of fourth order accuracy for the solution of the drift-diffusion model equations | 247 |
| 4.6 Two-dimensional structure of glow discharge regarding neutral gas heating | 253 |
| 4.6.1 Statement of two-dimensional axially symmetric problem | 254 |
| 4.6.2 Numerical simulation results | 256 |
| 5 Drift-diffusion model of glow discharge in an external magnetic field | 273 |
| 5.1 Derivation of the equations for calculation model | 273 |
| 5.2 Numerical simulation results | 278 |
| 5.3 Glow discharge in a cross magnetic field in view of heating of neutral gas | 291 |
| 5.3.1 Problem formulation | 292 |
| 5.3.2 Constitutive thermophysic and electrophysic parameters | 293 |
| 5.3.3 The method of numerical integration
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