Numerical "particle-in-cell" Methods

Theory and Applications

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

Publisher: Walter de Gruyter

ISBN: 9789067643689

Category: Science

Page: 249

View: 3266

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.
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Plasma Physics via Computer Simulation

Author: C.K. Birdsall,A.B Langdon

Publisher: CRC Press

ISBN: 9780750310253

Category: Science

Page: 504

View: 9039

Divided into three main parts, the book guides the reader to an understanding of the basic concepts in this fascinating field of research. Part 1 introduces you to the fundamental concepts of simulation. It examines one-dimensional electrostatic codes and electromagnetic codes, and describes the numerical methods and analysis. Part 2 explores the mathematics and physics behind the algorithms used in Part 1. In Part 3, the authors address some of the more complicated simulations in two and three dimensions. The book introduces projects to encourage practical work Readers can download plasma modeling and simulation software — the ES1 program — with implementations for PCs and Unix systems along with the original FORTRAN source code. p-BodyText2Now available in paperback, Plasma Physics via Computer Simulation is an ideal complement to plasma physics courses and for self-study.
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Computer Simulation Using Particles

Author: R.W Hockney,J.W Eastwood

Publisher: CRC Press

ISBN: 9781439822050

Category: Science

Page: 540

View: 3800

Computer simulation of systems has become an important tool in scientific research and engineering design, including the simulation of systems through the motion of their constituent particles. Important examples of this are the motion of stars in galaxies, ions in hot gas plasmas, electrons in semiconductor devices, and atoms in solids and liquids. The behavior of the system is studied by programming into the computer a model of the system and then performing experiments with this model. New scientific insight is obtained by observing such computer experiments, often for controlled conditions that are not accessible in the laboratory. Computer Simulation using Particles deals with the simulation of systems by following the motion of their constituent particles. This book provides an introduction to simulation using particles based on the NGP, CIC, and P3M algorithms and the programming principles that assist with the preparations of large simulation programs based on the OLYMPUS methodology. It also includes case study examples in the fields of astrophysics, plasmas, semiconductors, and ionic solids as well as more detailed mathematical treatment of the models, such as their errors, dispersion, and optimization. This resource will help you understand how engineering design can be assisted by the ability to predict performance using the computer model before embarking on costly and time-consuming manufacture.
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Numerical Simulation in Molecular Dynamics

Numerics, Algorithms, Parallelization, Applications

Author: Michael Griebel,Stephan Knapek,Gerhard Zumbusch

Publisher: Springer Science & Business Media

ISBN: 3540680950

Category: Science

Page: 476

View: 304

This book details the necessary numerical methods, the theoretical background and foundations and the techniques involved in creating computer particle models, including linked-cell method, SPME-method, tree codes, amd multipol technique. It illustrates modeling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. The text offers step-by-step explanations of numerical simulation, providing illustrative code examples. With the description of the algorithms and the presentation of the results of various simulations from fields such as material science, nanotechnology, biochemistry and astrophysics, the reader of this book will learn how to write programs capable of running successful experiments for molecular dynamics.
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Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes

Author: Miguel Cerrolaza,Sandra Shefelbine,Diego Garzón-Alvarado

Publisher: Academic Press

ISBN: 0128117192

Category: Technology & Engineering

Page: 454

View: 9396

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. Provides non-conventional analysis methods for modeling Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) Includes contributions from several world renowned experts in their fields Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems
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Fluid Simulation for Computer Graphics, Second Edition

Author: Robert Bridson

Publisher: CRC Press

ISBN: 1482232847

Category: Computers

Page: 263

View: 1359

A practical introduction, the second edition of Fluid Simulation for Computer Graphics shows you how to animate fully three-dimensional incompressible flow. It covers all the aspects of fluid simulation, from the mathematics and algorithms to implementation, while making revisions and updates to reflect changes in the field since the first edition. Highlights of the Second Edition New chapters on level sets and vortex methods Emphasizes hybrid particle–voxel methods, now the industry standard approach Covers the latest algorithms and techniques, including: fluid surface reconstruction from particles; accurate, viscous free surfaces for buckling, coiling, and rotating liquids; and enhanced turbulence for smoke animation Adds new discussions on meshing, particles, and vortex methods The book changes the order of topics as they appeared in the first edition to make more sense when reading the first time through. It also contains several updates by distilling author Robert Bridson’s experience in the visual effects industry to highlight the most important points in fluid simulation. It gives you an understanding of how the components of fluid simulation work as well as the tools for creating your own animations.
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Computational Methods in Plasma Physics

Author: Stephen Jardin

Publisher: CRC Press

ISBN: 9781439810958

Category: Science

Page: 372

View: 1175

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts necessary for the numerical solution of partial differential equations. Along with discussing numerical stability and accuracy, the author explores many of the algorithms used today in enough depth so that readers can analyze their stability, efficiency, and scaling properties. He focuses on mathematical models where the plasma is treated as a conducting fluid, since this is the most mature plasma model and most applicable to experiments. The book also emphasizes toroidal confinement geometries, particularly the tokamak—a very successful configuration for confining a high-temperature plasma. Many of the basic numerical techniques presented are also appropriate for equations encountered in a higher-dimensional phase space. One of the most challenging research areas in modern science is to develop suitable algorithms that lead to stable and accurate solutions that can span relevant time and space scales. This book provides an excellent working knowledge of the algorithms used by the plasma physics community, helping readers on their way to more advanced study.
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Multiple Time Scales

Author: Jeremiah U. Brackbill,Bruce I. Cohen

Publisher: Academic Press

ISBN: 1483257568

Category: Mathematics

Page: 456

View: 5924

Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.
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Numerical Methods in Astrophysics

An Introduction

Author: Peter Bodenheimer,Gregory P. Laughlin,Michal Rozyczka,Tomasz Plewa,Harold. W Yorke,Harold W. Yorke

Publisher: CRC Press

ISBN: 9780750308830

Category: Science

Page: 344

View: 7234

Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations. This resource indicates which methods are most suitable for particular problems, demonstrates what the accuracy requirements are in numerical simulations, and suggests ways to test for and reduce the inevitable negative effects. After an introduction to the basic equations and derivations, the book focuses on practical applications of the numerical methods. It explores hydrodynamic problems in one dimension, N-body particle dynamics, smoothed particle hydrodynamics, and stellar structure and evolution. The authors also examine advanced techniques in grid-based hydrodynamics, evaluate the methods for calculating the gravitational forces in an astrophysical system, and discuss specific problems in grid-based methods for radiation transfer. The book incorporates brief user instructions and a CD-ROM of the numerical codes, allowing readers to experiment with the codes to suit their own needs. With numerous examples and sample problems that cover a wide range of current research topics, this highly practical guide illustrates how to solve key astrophysics problems, providing a clear introduction for graduate and undergraduate students as well as researchers and professionals.
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Vortex Methods

Theory and Practice

Author: Georges-Henri Cottet,Petros D. Koumoutsakos

Publisher: Cambridge University Press

ISBN: 0521621860

Category: Mathematics

Page: 313

View: 9494

Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
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Smoothed Particle Hydrodynamics

A Meshfree Particle Method

Author: Gui-Rong Liu,M. B. Liu

Publisher: World Scientific

ISBN: 9812384561

Category: Technology & Engineering

Page: 449

View: 9354

This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided and coupling of SPH and molecular dynamics is discussed for multiscale simulation, making this a friendly book for readers and SPH users.
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Computer Simulation Study of Collective Phenomena in Dense Suspensions of Red Blood Cells under Shear

Author: Heinrich Krüger

Publisher: Springer Science & Business Media

ISBN: 3834823767

Category: Science

Page: 165

View: 6084

The rheology of dense red blood cell suspensions is investigated via computer simulations based on the lattice Boltzmann, the immersed boundary, and the finite element methods. The red blood cells are treated as extended and deformable particles immersed in the ambient fluid. In the first part of the work, the numerical model and strategies for stress evaluation are discussed. In the second part, the behavior of the suspensions in simple shear flow is studied for different volume fractions, particle deformabilities, and shear rates. Shear thinning behavior is recovered. The existence of a shear-induced transition from a tumbling to a tank-treading motion is demonstrated. The transition can be parameterized by a single quantity, namely the effective capillary number. It is the ratio of the suspension stress and the characteristic particle membrane stress. At the transition point, a strong increase in the orientational order of the red blood cells and a significant decrease of the particle diffusivity are observed. However, the average cell deformation shows no signature of the transition.
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Particle Methods for Multi-Scale and Multi-physics

Author: Moubin E. T. Al LIU

Publisher: World Scientific

ISBN: 9814571709

Category: Science

Page: 400

View: 2780

Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences --
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An Introduction to Modeling and Simulation of Particulate Flows

Author: T. I. Zohdi

Publisher: SIAM

ISBN: 9780898718928

Category: Granular materials

Page: 176

View: 9675

The relatively recent increase in computational power available for mathematical modeling and simulation raises the possibility that modern numerical methods can play a significant role in the analysis of complex particulate flows. An Introduction to Modeling and Simulation of Particulate Flows focuses on basic models and physically based computational solution strategies for the direct and rapid simulation of flowing particulate media. Its emphasis is primarily on fluidized dry particulate flows in which there is no significant interstitial fluid, although fully coupled fluid-particle systems are discussed as well. An introduction to basic computational methods for ascertaining optical responses of particulate systems also is included. The successful analysis of a wide range of applications requires the simulation of flowing particulate media that simultaneously involves near-field interaction and contact between particles in a thermally sensitive environment. These systems naturally occur in astrophysics and geophysics; powder processing pharmaceutical industries; bio-, micro- and nanotechnologies; and applications arising from the study of spray processes involving aerosols, sputtering, and epitaxy. Audience: written for computational scientists, numerical analysts, and applied mathematicians, it will be of interest to civil and mechanical engineers and materials scientists. It is also suitable for first-year graduate students in the applied sciences, engineering, and applied mathematics who have an interest in the computational analysis of complex particulate flows.
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Numerical Methods in Finance with C++

Author: Maciej J. Capiński,Tomasz Zastawniak

Publisher: Cambridge University Press

ISBN: 0521177162

Category: Business & Economics

Page: 175

View: 9414

Provides aspiring quant developers with the numerical techniques and programming skills needed in quantitative finance. No programming background required.
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Introduction to Computational Methods in Many Body Physics

Author: Michael Bonitz,Dirk Semkat

Publisher: Rinton PressInc

ISBN: N.A

Category: Science

Page: 400

View: 6751

This book is a multi-purpose and "user-friendly" textbook covering both fundamentals (in thermodynamics and statistical mechanics) and numerous applications. The emphasis is on simple derivations of simple results which can be compared with experimental data. The first half of the book covers basic thermodynamics, statistical ensembles, Boltzmann and quantum statistics; and the second half covers magnetism, electrostatic interactions (solutions and plasmas), non-equilibrium statistical mechanics, polymers, superfluidity, renormalization theory, and other specialized topics. This book, while serving well as a reference book for research scientists, is especially suitable as a textbook for a one-year statistical mechanics course for undergraduate students in physics, chemistry, engineering, biology, and material sciences. Alternatively, the first 5 chapters of the book can be used as the textbook for an undergraduate one-semester combined thermodynamics/statistical mechanics course (or statistical thermodynamics).
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Issues in Computation: 2013 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1490109021

Category: Computers

Page: 1200

View: 9250

Issues in Computation / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Computing. The editors have built Issues in Computation: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computing in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
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A Student's Guide to Numerical Methods

Author: Ian H. Hutchinson

Publisher: Cambridge University Press

ISBN: 1107095670

Category: Computers

Page: 221

View: 7880

A plain language style, worked examples and exercises help students to understand the foundations of computational physics and engineering.
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