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Pattern Formation and Lattice gas Automata

Pattern Formation and Lattice gas Automata
Author: Anna T. Lawniczak
Publisher: American Mathematical Soc.
Total Pages: 357
Release: 1996
Genre: Computers
ISBN: 0821802585

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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.


Physics Briefs

Physics Briefs
Author:
Publisher:
Total Pages: 916
Release: 1994
Genre: Physics
ISBN:

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Lattice-Gas Cellular Automata and Lattice Boltzmann Models
Author: Dieter A. Wolf-Gladrow
Publisher: Springer
Total Pages: 320
Release: 2004-10-19
Genre: Mathematics
ISBN: 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.


Advanced HPC-based Computational Modeling in Biomechanics and Systems Biology

Advanced HPC-based Computational Modeling in Biomechanics and Systems Biology
Author: Mariano Vázquez
Publisher: Frontiers Media SA
Total Pages: 449
Release: 2019-04-04
Genre:
ISBN: 2889458172

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.


Lattice Boltzmann Method

Lattice Boltzmann Method
Author: Abdulmajeed A. Mohamad
Publisher:
Total Pages: 228
Release: 2019
Genre: Fluid mechanics
ISBN: 9781447174240

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Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.


The Lattice Boltzmann Method

The Lattice Boltzmann Method
Author: Timm Krüger
Publisher: Springer
Total Pages: 705
Release: 2016-11-07
Genre: Science
ISBN: 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.


Analysis of Lattice-Boltzmann Methods

Analysis of Lattice-Boltzmann Methods
Author: Martin Rheinländer
Publisher: GRIN Verlag
Total Pages: 384
Release: 2007
Genre: Mathematics
ISBN: 363879606X

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Doctoral Thesis / Dissertation from the year 2007 in the subject Mathematics - Analysis, University of Constance (Fachbereich Mathematik & Statistik), 69 entries in the bibliography, language: English, abstract: Lattice-Boltzmann algorithms represent a quite novel class of numerical schemes, which are used to solve evolutionary partial differential equations (PDEs). In contrast to other methods (FEM, FVM), lattice-Boltzmann methods rely on a mesoscopic approach. The idea consists in setting up an artificial, grid-based particle dynamics, which is chosen such that appropriate averages provide approximate solutions of a certain PDE, typically in the area of fluid dynamics. As lattice-Boltzmann schemes are closely related to finite velocity Boltzmann equations being singularly perturbed by special scalings, their consistency is not obvious. This work is concerned with the analysis of lattice-Boltzmann methods also focusing certain numeric phenomena like initial layers, multiple time scales and boundary layers. As major analytic tool, regular (Hilbert) expansions are employed to establish consistency. Exemplarily, two and three population algorithms are studied in one space dimension, mostly discretizing the advection-diffusion equation. It is shown how these model schemes can be derived from two-dimensional schemes in the case of special symmetries. The analysis of the schemes is preceded by an examination of the singular limit being characteristic of the corresponding scaled finite velocity Boltzmann equations. Convergence proofs are obtained using a Fourier series approach and alternatively a general regular expansion combined with an energy estimate. The appearance of initial layers is investigated by multiscale and irregular expansions. Among others, a hierarchy of equations is found which gives insight into the internal coupling of the initial layer and the regular part of the solution. Next, the consistency of the model algorithms is considered followed by


Applied Mechanics Reviews

Applied Mechanics Reviews
Author:
Publisher:
Total Pages: 338
Release: 1987
Genre: Mechanics, Applied
ISBN:

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Fluid Mechanics

Fluid Mechanics
Author: L D Landau
Publisher: Elsevier
Total Pages: 556
Release: 2013-09-03
Genre: Technology & Engineering
ISBN: 1483161048

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Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.