Lattice-Gas Cellular Automata

Lattice-Gas Cellular Automata
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.

Lattice Gas Dynamics

Lattice Gas Dynamics
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.

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

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.

The Lattice Boltzmann Equation

The Lattice Boltzmann Equation
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.

Lattice Gas Hydrodynamics

Lattice Gas Hydrodynamics
Author: J.-P. Rivet
Publisher: Cambridge University Press
Total Pages: 312
Release: 2005-09-15
Genre: Science
ISBN: 9780521019712

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.

Statistical Mechanics of Lattice Systems

Statistical Mechanics of Lattice Systems
Author: Sacha Friedli
Publisher: Cambridge University Press
Total Pages: 643
Release: 2017-11-23
Genre: Mathematics
ISBN: 1107184827

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Discrete Kinetic Theory, Lattice Gas Dynamics And Foundations Of Hydrodynamics - Proceedings Of The Workshop

Discrete Kinetic Theory, Lattice Gas Dynamics And Foundations Of Hydrodynamics - Proceedings Of The Workshop
Author: Roberto Monaco
Publisher: World Scientific
Total Pages: 432
Release: 1989-04-01
Genre:
ISBN: 981320141X

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.

Lattice Gas Methods For Partial Differential Equations

Lattice Gas Methods For Partial Differential Equations
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.

Lattice Boltzmann Method And Its Application In Engineering

Lattice Boltzmann Method And Its Application In Engineering
Author: Zhaoli Guo
Publisher: World Scientific
Total Pages: 419
Release: 2013-03-25
Genre: Technology & Engineering
ISBN: 9814508314

Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.With these coverage LBM, the book intended to promote its applications, instead of the traditional computational fluid dynamic method.