Lattice Gas Cellular Automata And Lattice Boltzmann Models
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Author | : Dieter A. Wolf-Gladrow |
Publisher | : Springer |
Total Pages | : 320 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 3540465863 |
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.
Author | : Anna T. Lawniczak |
Publisher | : American Mathematical Soc. |
Total Pages | : 357 |
Release | : 1996 |
Genre | : Computers |
ISBN | : 0821802585 |
Articles review the diverse recent progress in the theory and development of lattice-gas and lattice Boltzmann methods and their applications. It features up-to-date articles, takes an interdisciplinary approach including mathematics, physical chemistry, and geophysics.
Author | : Daniel H. Rothman |
Publisher | : Cambridge University Press |
Total Pages | : 323 |
Release | : 1997-08-28 |
Genre | : Computers |
ISBN | : 052155201X |
A self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases.
Author | : Gary D. Doolen |
Publisher | : MIT Press |
Total Pages | : 356 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780262540636 |
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.
Author | : Michael C. Sukop |
Publisher | : Springer Science & Business Media |
Total Pages | : 178 |
Release | : 2007-04-05 |
Genre | : Science |
ISBN | : 3540279822 |
Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.
Author | : S. Succi |
Publisher | : Oxford University Press |
Total Pages | : 308 |
Release | : 2001-06-28 |
Genre | : Mathematics |
ISBN | : 9780198503989 |
Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.
Author | : Bastien Chopard |
Publisher | : Cambridge University Press |
Total Pages | : 357 |
Release | : 1998-12-10 |
Genre | : Computers |
ISBN | : 0521461685 |
Self-contained, pedagogic introduction to powerful techniques for graduate students and researchers in physics and computer science.
Author | : Gary Doolen |
Publisher | : CRC Press |
Total Pages | : 584 |
Release | : 2019-03-01 |
Genre | : Mathematics |
ISBN | : 0429717504 |
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.
Author | : Jeffrey Yepez |
Publisher | : |
Total Pages | : 226 |
Release | : 1995 |
Genre | : Lattice gas |
ISBN | : |
The theory and computation of lattice gas dynamics for viscous fluid hydrodynamics is presented. Theoretical analysis of these exactly conserved, discrete models is done using the Boltzmann approximation, a mean-field theoretical treatment. Theoretical results are then compared to numerical data arrived by exactly computed simulations of simple lattice-gas systems. The numerical simulations presented were carried out on a prototype lattice-gas machine, the CAM-8, which is a virtual finegrained paralled mesh architecture suitable for discrete modeling in arbitrary dimensions. Single speed and multi-speed lattice gases are treated. The new contribution is an integer lattice gas with many particles per momentum state. Comparisons are made between the mean-field theory and numerical experiments for shear viscosity transport coefficient.
Author | : Timm Krüger |
Publisher | : Springer |
Total Pages | : 705 |
Release | : 2016-11-07 |
Genre | : Science |
ISBN | : 3319446495 |
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.