Numerical "Particle-in-Cell" Methods: Theory and Applications

✍ Scribed by Yu. N. Grigoryev; V. A. Vshivkov; M. P. Fedoruk

• Publisher: De Gruyter
• Year: 2012
• Tongue: English
• Leaves: 260
• Edition: Reprint 2012
• Category: Library

✦ Table of Contents

Introduction. Computational particle methods
General characteristics
Some applications
1. Particle-in-cell methods
1.1. Introduction
1.2. General scheme
1.3. Model particles and their properties
1.4. Errors of the particle-in-cell schemes
1.5. The continuity equation in the particle method
2. Particle-in-cell methods on unstructured meshes
2.1. Introduction
2.2. Finite-elements bases
2.3. The Lagrangian step on unstructured meshes
2.4. The Euler step. The finite-volume method
3. The particle methods in gas dynamics
3.1. Introduction
3.2. Basic equations
3.3. The realization of the method
3.4. The combined particle method
3.5. The example of application
4. Vortex-in-cell methods
4.1. Introduction
4.2. Vorticity dynamics in two-dimensional flows
4.3. The vortex-in-cell method in two-dimensional case
4.4. The dynamics of vortices in three-dimensional flows
4.5. The vortex-in-cell scheme for three-dimensional flows
4.6. The examples of applications
5. Particle-in-cell methods in collisionless plasma dynamics
5.1. Introduction
5.2. Collisionless plasma basic equations
5.3. General scheme and computation cycle of the method
5.4. Conservation laws in model plasma
5.5. Examples of applications
6. Statistical particle-in-cell methods
6.1. Introduction
6.2. Kinetic equations of rarefied gas
6.3. Some procedures of Monte Carlo methods
6.4. Statistical particle methods
6.5. Examples of the application
Supplements
A. Subroutine of initial data preparation
B. Subroutines of interpolation between the Lagrangian and Eulerian meshes
B1. Interpolation of the mesh vector-function to the Lagrangian mesh of particles
B2. Interpolation of the scalar function from the Lagrangian mesh of particles to nodes of the Eulerian mesh
B3. The subroutine of interpolation of generalized fields to the particle location on unstructured grids
B4. The subroutine for assignment of the particle charge on unstructured grids
B5. The subroutine for the determination of the scalar density in the nodes of unstructured grids
C. Subroutine for the particle dynamics
C1. Subroutine for calculation of the particles dynamics in fields of mass forces
C2. The subroutine for relativistic particle pusher according to Boris
D. The subroutines of a localization of particles on the unstructured grid
D1. The subroutines of particle localization on two-dimensional triangular grid (Löhner’s algorithm)
D2. The subroutines of particle localization on three-dimensional tetrahedrons grid (Assous algorithm)
E. The subroutines for calculation of linear shape-functions on unstructured grids
E1. The subroutine for calculation shape-functions with respect to the particle locations in two-dimensional case
E2. The subroutine of calculation of the shape-functions with respect to the particle locations for three-dimensional case
F. The auxiliary subroutines
F1. The subroutine of determination of the local coordinates of point r (r-vector)
F2. The subroutine for determination of auxiliary vectors of tetrahedrons with nodes (k1,k2,k3,k4)
F3. The subroutine used in subroutine ploc3
F4. The subroutine for Gauss elimination
G. Subroutines for the solution of the Poisson equation (Poisson solvers)
G1. Direct method
G2. Combined iteration method
H. Subroutine of numerical integration of the full system of Maxwell equations
Bibliography