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Author: J.-P. Rivet Publisher: Cambridge University Press ISBN: 9780521019712 Category : Science Languages : en Pages : 312
Book Description
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.
Author: J.-P. Rivet Publisher: Cambridge University Press ISBN: 9780521019712 Category : Science Languages : en Pages : 312
Book Description
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.
Author: J.-P. Rivet Publisher: Cambridge University Press ISBN: 0521419441 Category : Computers Languages : en Pages : 313
Book Description
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 which capture the essentials of actual fluctuations in real fluids.
Author: Dieter A. Wolf-Gladrow Publisher: Springer ISBN: 3540465863 Category : Mathematics Languages : en Pages : 320
Book Description
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 ISBN: 042969749X Category : Mathematics Languages : en Pages : 583
Book Description
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: Jackson R. Herring Publisher: World Scientific ISBN: 9789971508272 Category : Science Languages : en Pages : 392
Book Description
This book is a formal presentation of lectures given at the 1987 Summer School on Turbulence, held at the National Center for Atmospheric Research under the auspices of the Geophysical Turbulence Program. The lectures present in detail certain of the more challenging and interesting current turbulence research problems in engineering, meteorology, plasma physics, and mathematics. The lecturers-Uriel Frisch (Mathematics), Douglas Lilly (Meteorology), David Montgomery (Plasma Physics), and Hendrik Tennekes (Engineering) ? are distinguished for both their research contributions and their abilities to communicate these to students with enthusiasm. This book is distinguished by its simultaneous focus on the fundamentals of turbulent flows (in neutral and ionized fluids) and on a presentation of current research tools and topics in these fields.
Author: Gary D. Doolen Publisher: MIT Press ISBN: 9780262540636 Category : Mathematics Languages : en Pages : 356
Book Description
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: S. Succi Publisher: Oxford University Press ISBN: 9780198503989 Category : Mathematics Languages : en Pages : 308
Book Description
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: Roberto Monaco Publisher: World Scientific ISBN: 981320141X Category : Languages : en Pages : 432
Book Description
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 Publisher: Springer ISBN: 3319446495 Category : Science Languages : en Pages : 705
Book Description
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: J.-P. Rivet
Author: J.-P. Rivet
Author: Daniel H. Rothman
Author: J.-P. Rivet
Author: Dieter A. Wolf-Gladrow
Author: Gary Doolen
Author: Jackson R. Herring
Author: Gary D. Doolen
Author: S. Succi
Author: Roberto Monaco
Author: Timm Krüger