Numerical "Particle-in-Cell" Methods

Theory and Applications

Yu. N. Grigoryev, V. A. Vshivkov, M. P. Fedoruk

• Publisher: De Gruyter
• Year: 2012
• Print ISBN: 9783110622911
• eBook ISBN: 9783110916706
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

No detailed description available for "Numerical "Particle-in-Cell" Methods".

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