A Numerical Method For Solving The Vlasov Equation
DOWNLOAD
Download A Numerical Method For Solving The Vlasov Equation PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Numerical Method For Solving The Vlasov Equation book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
A Numerical Method For Solving The Vlasov Equation
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1982
A Numerical Method For Solving The Vlasov Equation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Study Of The Coupling Of Numerical Methods For The Solving Of The Vlasov Maxwell Equations
DOWNLOAD
Author : Thomas Respaud
language : en
Publisher:
Release Date : 2010
Study Of The Coupling Of Numerical Methods For The Solving Of The Vlasov Maxwell Equations written by Thomas Respaud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
A new method for studying the evolution of plasmas is proposed, using the kinetic model coupling the Vlasov equation for the particles distribution, and the Maxwell's ones which rule the evolution of the electromagnetic fields. This is a semi-Lagrangian method, based on a grid of the phase space, and a resolution of the characteristics of the Vlasov equation. These characteristics are followed forwardly in time, which enables a few advantages comparing to the classical method. First, this method is explicit, and implementing high order algorithms is easier, which allows to get more stability. Moreover, this method has similarities with the classical PIC method, which will be used in order to build charge preserving algorithms, which is very important in order to ensure that the computed solutions are physical.
A Spectral Algorithm For Solving The Relativistic Vlasov Maxwell Equations
DOWNLOAD
Author : John V. Shebalin
language : en
Publisher:
Release Date : 2001
A Spectral Algorithm For Solving The Relativistic Vlasov Maxwell Equations written by John V. Shebalin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Algorithms categories.
A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron ditribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.
Numerical Solution Of Hyperbolic Differential Equations
DOWNLOAD
Author : M. Shoucri
language : en
Publisher:
Release Date : 2008
Numerical Solution Of Hyperbolic Differential Equations written by M. Shoucri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The application of the method of characteristics for the numerical solution of hyperbolic type partial differential equations will be presented. Especial attention will be given to the numerical solution of the Vlasov equation, which is of fundamental importance in the study of the kinetic theory of plasmas, and to other equations pertinent to plasma physics. Examples will be presented with possible combination with fractional step methods in the case of several dimensions. The methods are quite general and can be applied to different equations of hyperbolic type in the field of mathematical physics. Examples for the application of the method of characteristics to fluid equations will be presented, for the numerical solution of the shallow water equations and for the numerical solution of the equations of the incompressible ideal magnetohydrodynamic (MHD) flows in plasmas.
Fourth Order Conservative Vlasov Maxwell Solver For Cartesian And Cylindrical Phase Space Coordinates
DOWNLOAD
Author : Genia Vogman
language : en
Publisher:
Release Date : 2016
Fourth Order Conservative Vlasov Maxwell Solver For Cartesian And Cylindrical Phase Space Coordinates written by Genia Vogman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D (x,v_x,v_y) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.
Numerical Solution Of The Non Linear Vlasov Equation
DOWNLOAD
Author : Danuta Mąkosa
language : en
Publisher:
Release Date : 1972
Numerical Solution Of The Non Linear Vlasov Equation written by Danuta Mąkosa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Numerical Methods For Hyperbolic And Kinetic Problems
DOWNLOAD
Author : Stéphane Cordier
language : en
Publisher: European Mathematical Society
Release Date : 2005
Numerical Methods For Hyperbolic And Kinetic Problems written by Stéphane Cordier and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Differential equations, Hyperbolic categories.
Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the Summer Mathematical Research Center on Scientific Computing and its Applications (CEMRACS), held at the Center of International Research in Mathematics (CIRM) in Luminy, was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the present book reflects these results. The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative transfer, sprays, and aeroacoustics. The text is aimed at researchers and engineers interested in applications arising from modelling and numerical simulation of hyperbolic and kinetic problems.
Numerical Integration Methods Of The Vlasov Equation
DOWNLOAD
Author : Homer K. Meier
language : en
Publisher:
Release Date : 1970
Numerical Integration Methods Of The Vlasov Equation written by Homer K. Meier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Numerical integration categories.
Numerical Mathematics And Advanced Applications
DOWNLOAD
Author : F. Brezzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Mathematics And Advanced Applications written by F. Brezzi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
An invaluable instrument for gaining a wide-ranging perspective on the latest developments in mathematical aspects of scientific computing, discovering new applications and the most recent developments in long-standing applications. Provides an insight into the state of the art of Numerical Mathematics and, more generally, into the field of Advanced Applications.
Parallel Computing Technologies
DOWNLOAD
Author : Victor Malyshkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-07
Parallel Computing Technologies written by Victor Malyshkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-07 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Parallel Computing Technologies, PaCT 2007, held in conjunction with the Russian-Taiwan symposium on Methods and Tools of Parallel Programming of Multicomputers. It covers models and languages, applications, techniques for parallel programming supporting, cellular automata, as well as methods and tools of parallel programming of multicomputers.