Numerical Particle in Cell Methods Theory and Applications 1st Edition by Yu N Grigoryev ,V A Vshivkov ,M P Fedoruk ISBN 9067643688 978-9067643689

Numerical Particle in Cell Methods Theory and Applications 1st Edition by Yu N.Grigoryev ,V.A. Vshivkov ,M.P. Fedoruk – Ebook PDF Instant Download/Delivery:9067643688 ,978-9067643689
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Product details: 

ISBN 10:9067643688

ISBN 13:978-9067643689

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

01/07 This title is now available from Walter de Gruyter. Please see for more information. Algorithms known as “particle” methods, whose characteristic feature is the discretization technique when the set of discrete objects is introduced, which are model “particles” considered as some mesh of moving nodes, are becoming more and more widespread in mathematical modelling. Until recently, particle methods have mainly been developed as an alternative to classical numerical methods for solving problems in some applied domains of physics and mathematics. As a result, no specialized monographs on this subject have been available. The aim of this book is to fill the gap in literature on this subject of numerical methodes and deals with combined Lagrangian-Eulerian schemes of the “particle-in-cell” type, the most widespread among particle methods. The authors describe a universal approach to the construction of such algorithms. The approach is based on splitting the initial problem by which the auxiliary problem with a hyperbolic (divergent) operator is separated. After special discretization of the solution, such a splitting naturally leads to the well-known schemes of “particle-in-cell” methods. Examples of calculations in this book give the reader an idea of the capabilities of particle-in-cell methods, their requirements to computers, and the degree of precision that can be achieved. This book is primarily intended for specialists in calculations, who want to get a general idea of numerical particle-in-cell methods and the sphere of their applications. As a methodological guide, it will be of interest to undergraduate and postgraduate students, mathematicians and physicists specializing in mathematical modelling.

Table of contents: 

Particleincell methods
General scheme
Model particles and their properties
Errors of the particleincell schemes
The continuity equation in the particle method
Particleincell methods on unstructured meshes
Finiteelements bases
The Lagrangian step on unstructured meshes
The Euler step The finitevolume method
The particle methods in gas dynamics
Basic equations
The realization of the method
The combined particle method
The example of application
Vortexincell methods
Vorticity dynamics in twodimensional flows
The vortexincell method in twodimensional case
The dynamics of vortices in threedimensional flows
The vortexincell scheme for threedimensional flows
The examples of applications
Particleincell methods in collisionless plasma dynamics
Collisionless plasma basic equations
General scheme and computation cycle of the method
Conservation laws in model plasma
Examples of applications
Statistical particleincell methods
Kinetic equations of rarefied gas
Some procedures of Monte Carlo methods
Statistical particle methods
Examples of the application

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Tags: Yu N Grigoryev, V A Vshivkov, M P Fedoruk, Numerical, Particle