Lattice Gas Methods

Author : Gary D. Doolen
Publisher : MIT Press
Page : 356 pages
File Size : 41,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0262540630

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Lattice Gas Methods by Gary D. Doolen Pdf

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 : Dieter A. Wolf-Gladrow
Publisher : Springer
Page : 314 pages
File Size : 42,8 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540465867

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models by Dieter A. Wolf-Gladrow Pdf

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 : Gary Doolen
Publisher : CRC Press
Page : 584 pages
File Size : 40,7 Mb
Release : 2019-03-01
Category : Mathematics
ISBN : 9780429697494

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Lattice Gas Methods For Partial Differential Equations by Gary Doolen Pdf

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 : Anna T. Lawniczak,Raymond Kapral
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 49,5 Mb
Release : 1996
Category : Science
ISBN : 9780821802588

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Pattern Formation and Lattice gas Automata by Anna T. Lawniczak,Raymond Kapral Pdf

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 : Gary D. Doolen
Publisher : Unknown
Page : 554 pages
File Size : 46,6 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:658165346

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Lattice Gas Methods for Partial Differential Equations by Gary D. Doolen Pdf

Author : A. A. Mohamad
Publisher : Springer
Page : 222 pages
File Size : 44,8 Mb
Release : 2019-05-07
Category : Science
ISBN : 9781447174233

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Lattice Boltzmann Method by A. A. Mohamad Pdf

This book introduces readers to the lattice Boltzmann method (LBM) for solving transport phenomena – flow, heat and mass transfer – in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as: • flow in isothermal and non-isothermal lid-driven cavities; • flow over obstacles; • forced flow through a heated channel; • conjugate forced convection; and • natural convection. Diffusion and advection–diffusion equations are discussed, together with applications and examples, and complete computer codes accompany the sections on single and multi-relaxation-time methods. The codes are written in MatLab. However, the codes are written in a way that can be easily converted to other languages, such as FORTRANm Python, Julia, etc. The codes can also be extended with little effort to multi-phase and multi-physics, provided the physics of the respective problem are known. The second edition of this book adds new chapters, and includes new theory and applications. It discusses a wealth of practical examples, and explains LBM in connection with various engineering topics, especially the transport of mass, momentum, energy and molecular species. This book offers a useful and easy-to-follow guide for readers with some prior experience with advanced mathematics and physics, and will be of interest to all researchers and other readers who wish to learn how to apply LBM to engineering and industrial problems. It can also be used as a textbook for advanced undergraduate or graduate courses on computational transport phenomena

Author : Jian Guo Zhou
Publisher : Springer Science & Business Media
Page : 118 pages
File Size : 51,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662082768

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Lattice Boltzmann Methods for Shallow Water Flows by Jian Guo Zhou Pdf

The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geome tries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the micro scopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The av eraged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena. In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows.

Author : Daniel H. Rothman,Stiphane Zaleski
Publisher : Cambridge University Press
Page : 320 pages
File Size : 50,6 Mb
Release : 2004-12-23
Category : Science
ISBN : 0521607604

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Lattice-Gas Cellular Automata by Daniel H. Rothman,Stiphane Zaleski Pdf

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and references are included.

Author : Roberto Monaco
Publisher : World Scientific
Page : 432 pages
File Size : 45,6 Mb
Release : 1989-04-01
Category : Electronic
ISBN : 9789813201415

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Discrete Kinetic Theory, Lattice Gas Dynamics And Foundations Of Hydrodynamics - Proceedings Of The Workshop by Roberto Monaco Pdf

The proceedings will concentrate, with the aim of presenting the most recent results, on the relevant problems in the mathematics and physics of the discrete kinetic theory, lattice gas dynamics and foundations of hydrodynamics. In particular the following three fields will be covered: (i) Mathematical models and applications in discrete kinetic theory; (ii) Lattice gas in two and three dimensions; (iii) Hydrodynamic limit and foundations of fluidodynamics.

Author : Timm Krüger,Halim Kusumaatmaja,Alexandr Kuzmin,Orest Shardt,Goncalo Silva,Erlend Magnus Viggen
Publisher : Springer
Page : 694 pages
File Size : 42,9 Mb
Release : 2016-11-07
Category : Science
ISBN : 9783319446493

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The Lattice Boltzmann Method by Timm Krüger,Halim Kusumaatmaja,Alexandr Kuzmin,Orest Shardt,Goncalo Silva,Erlend Magnus Viggen Pdf

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.

Author : Brosl Hasslacher,Steven A. Orszag,Stephen Wolfram
Publisher : Perseus Books
Page : 554 pages
File Size : 50,9 Mb
Release : 1990
Category : Mathematics
ISBN : 020113232X

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Lattice Gas Methods for Partial Differential Equations by Brosl Hasslacher,Steven A. Orszag,Stephen Wolfram Pdf

Author : Daniel H. Rothman,Stiphane Zaleski
Publisher : Cambridge University Press
Page : 323 pages
File Size : 40,5 Mb
Release : 1997-08-28
Category : Computers
ISBN : 9780521552011

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Lattice-Gas Cellular Automata by Daniel H. Rothman,Stiphane Zaleski Pdf

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

Author : Zhaoli Guo,Chang Shu
Publisher : World Scientific
Page : 419 pages
File Size : 46,8 Mb
Release : 2013
Category : Science
ISBN : 9789814508308

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Lattice Boltzmann Method and Its Applications in Engineering by Zhaoli Guo,Chang Shu Pdf

This book covers the fundamental and practical application of the Lattice Boltzmann method (LBM). This method is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics.

Author : Michael C. Sukop,Daniel T. Thorne
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 47,6 Mb
Release : 2007-04-05
Category : Science
ISBN : 9783540279822

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Lattice Boltzmann Modeling by Michael C. Sukop,Daniel T. Thorne Pdf

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 : J.-P. Rivet,J. P. Boon
Publisher : Cambridge University Press
Page : 312 pages
File Size : 53,6 Mb
Release : 2005-09-15
Category : Science
ISBN : 0521019710

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Lattice Gas Hydrodynamics by J.-P. Rivet,J. P. Boon Pdf

Lattice gas hydrodynamics describes the approach to fluid dynamics using a micro-world constructed as an automaton universe, where the microscopic dynamics is based not on a description of interacting particles, but on the laws of symmetry and invariance of macroscopic physics. We imagine point-like particles residing on a regular lattice, where they move from node to node and undergo collisions when their trajectories meet. If the collisions occur according to some simple logical rules, and if the lattice has the proper symmetry, then the automaton shows global behavior very similar to that of real fluids. This book carries two important messages. First, it shows how an automaton universe with simple microscopic dynamics--the lattice gas--can exhibit macroscopic behavior in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations that capture the essentials of actual fluctuations in real fluids.