Chapter
1.4. Errors of the particle-in-cell schemes
pp.：
30 – 43
1.5. The continuity equation in the particle method
pp.：
43 – 56
2. Particle-in-cell methods on unstructured meshes
pp.：
56 – 64
2.1. Introduction
pp.：
64 – 64
2.2. Finite-elements bases
pp.：
64 – 66
2.3. The Lagrangian step on unstructured meshes
pp.：
66 – 70
2.4. The Euler step. The finite-volume method
pp.：
70 – 86
3. The particle methods in gas dynamics
pp.：
86 – 93
3.2. Basic equations
pp.：
93 – 94
3.1. Introduction
pp.：
93 – 93
3.3. The realization of the method
pp.：
94 – 96
3.4. The combined particle method
pp.：
96 – 105
3.5. The example of application
pp.：
105 – 107
4. Vortex-in-cell methods
pp.：
107 – 110
4.2. Vorticity dynamics in two-dimensional flows
pp.：
110 – 111
4.1. Introduction
pp.：
110 – 110
4.3. The vortex-in-cell method in two-dimensional case
pp.：
111 – 112
4.4. The dynamics of vortices in three-dimensional flows
pp.：
112 – 119
4.5. The vortex-in-cell scheme for three-dimensional flows
pp.：
119 – 122
4.6. The examples of applications
pp.：
122 – 127
5. Particle-in-cell methods in collisionless plasma dynamics
pp.：
127 – 132
5.1. Introduction
pp.：
132 – 132
5.2. Collisionless plasma basic equations
pp.：
132 – 134
5.3. General scheme and computation cycle of the method
pp.：
134 – 137
5.4. Conservation laws in model plasma
pp.：
137 – 146
5.5. Examples of applications
pp.：
146 – 151
6. Statistical particle-in-cell methods
pp.：
151 – 181
6.2. Kinetic equations of rarefied gas
pp.：
181 – 182
6.1. Introduction
pp.：
181 – 181
6.3. Some procedures of Monte Carlo methods
pp.：
182 – 190
6.4. Statistical particle methods
pp.：
190 – 195
6.5. Examples of the application
pp.：
195 – 211
Supplements
pp.：
211 – 216
B. Subroutines of interpolation between the Lagrangian and Eulerian meshes
pp.：
216 – 218
A. Subroutine of initial data preparation
pp.：
216 – 216
B1. Interpolation of the mesh vector-function to the Lagrangian mesh of particles
pp.：
218 – 218
B2. Interpolation of the scalar function from the Lagrangian mesh of particles to nodes of the Eulerian mesh
pp.：
218 – 219
B3. The subroutine of interpolation of generalized fields to the particle location on unstructured grids
pp.：
219 – 222
B4. The subroutine for assignment of the particle charge on unstructured grids
pp.：
222 – 223
B5. The subroutine for the determination of the scalar density in the nodes of unstructured grids
pp.：
223 – 224
C. Subroutine for the particle dynamics
pp.：
224 – 225
C2. The subroutine for relativistic particle pusher according to Boris
pp.：
225 – 228
C1. Subroutine for calculation of the particles dynamics in fields of mass forces
pp.：
225 – 225
D. The subroutines of a localization of particles on the unstructured grid
pp.：
228 – 229
D1. The subroutines of particle localization on two-dimensional triangular grid (Löhner’s algorithm)
pp.：
229 – 230
D2. The subroutines of particle localization on three-dimensional tetrahedrons grid (Assous algorithm)
pp.：
230 – 231
E. The subroutines for calculation of linear shape-functions on unstructured grids
pp.：
231 – 235
E2. The subroutine of calculation of the shape-functions with respect to the particle locations for three-dimensional case
pp.：
235 – 236
E1. The subroutine for calculation shape-functions with respect to the particle locations in two-dimensional case
pp.：
235 – 235
F. The auxiliary subroutines
pp.：
236 – 237
F3. The subroutine used in subroutine ploc3
pp.：
237 – 238
F1. The subroutine of determination of the local coordinates of point r (r-vector)
pp.：
237 – 237
F2. The subroutine for determination of auxiliary vectors of tetrahedrons with nodes (k1,k2,k3,k4)
pp.：
237 – 237
F4. The subroutine for Gauss elimination
pp.：
238 – 239
G. Subroutines for the solution of the Poisson equation (Poisson solvers)
pp.：
239 – 240
G2. Combined iteration method
pp.：
240 – 243
G1. Direct method
pp.：
240 – 240
H. Subroutine of numerical integration of the full system of Maxwell equations
pp.：
243 – 245
Bibliography
pp.：
245 – 249
Numerical "Particle-in-Cell" Methods
：Theory and Applications
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