Lattice Gas Methods For Partial Differential Equations
Lattice Gas Methods For Partial Differential Equations

Author: Gary Doolen

Publisher: CRC Press

Published: 2019-03-01

Total Pages: 583

ISBN-13: 042969749X

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Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.

Lattice Gas Methods
Lattice Gas Methods

Author: Gary D. Doolen

Publisher: MIT Press

Published: 1991

Total Pages: 356

ISBN-13: 9780262540636

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This volume focuses on progress in applying the lattice gas approach to partial differential equations that arise in simulating the flow of fluids.Lattice gas methods are new parallel, high-resolution, high-efficiency techniques for solving partial differential equations. This volume focuses on progress in applying the lattice gas approach to partial differential equations that arise in simulating the flow of fluids. It introduces the lattice Boltzmann equation, a new direction in lattice gas research that considerably reduces fluctuations.The twenty-seven contributions explore the many available software options exploiting the fact that lattice gas methods are completely parallel, which produces significant gains in speed. Following an overview of work done in the past five years and a discussion of frontiers, the chapters describe viscosity modeling and hydrodynamic mode analyses, multiphase flows and porous media, reactions and diffusion, basic relations and long-time correlations, the lattice Boltzmann equation, computer hardware, and lattice gas applications.Gary D. Doolen is Acting Director of the Center for Nonlinear Studies at Los Alamos National Laboratory.

Lattice-Gas Cellular Automata and Lattice Boltzmann Models
Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Author: Dieter A. Wolf-Gladrow

Publisher: Springer

Published: 2004-10-19

Total Pages: 320

ISBN-13: 3540465863

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Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations
Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Author: Hans G. Kaper

Publisher: CRC Press

Published: 1991-02-25

Total Pages: 290

ISBN-13: 9780585319674

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Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per

Handbook of Differential Equations
Handbook of Differential Equations

Author: Daniel Zwillinger

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 808

ISBN-13: 1483263967

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Handbook of Differential Equations, Second Edition is a handy reference to many popular techniques for solving and approximating differential equations, including numerical methods and exact and approximate analytical methods. Topics covered range from transformations and constant coefficient linear equations to Picard iteration, along with conformal mappings and inverse scattering. Comprised of 192 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.

Lattice-Gas Cellular Automata
Lattice-Gas Cellular Automata

Author: Daniel H. Rothman

Publisher: Cambridge University Press

Published: 1997-08-28

Total Pages: 323

ISBN-13: 052155201X

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A self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases.

The Lattice Boltzmann Method
The Lattice Boltzmann Method

Author: Timm Krüger

Publisher: Springer

Published: 2016-11-07

Total Pages: 705

ISBN-13: 3319446495

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This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.