Lecture Notes in Mathematics : An Introduction - Dieter A. Wolf-Gladrow

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Lecture Notes in Mathematics

An Introduction

By: Dieter A. Wolf-Gladrow

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Paperback | 18 February 2000

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324 Pages

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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.

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Introduction
Preface
Overview
The basic idea of lattice-gas cellular automata and lattice Boltzmann models
Cellular Automata
What are cellular automata?
A short history of cellular automata
One-dimensional cellular automata
Two-dimensional cellular automata
Lattice-gas cellular automata
The HPP lattice-gas cellular automata
The FHP lattice-gas cellular automata
Lattice tensors and isotropy in the macroscopic limit
Desperately seeking a lattice for simulations in three dimensions
FCHC
The pair interaction (PI) lattice-gas cellular automata
Multi-speed and thermal lattice-gas cellular automata
Zanetti ("staggered") invariants
Lattice-gas cellular automata: What else?
Some statistical mechanics
The Boltzmann equation
Chapman-Enskog: From Boltzmann to Navier-Stokes
The maximum entropy principle
Lattice Boltzmann Models
From lattice-gas cellular automata to lattice Boltzmann models
BGK lattice Boltzmann model in 2D
Hydrodynamic lattice Boltzmann models in 3D
Equilibrium distributions: the ansatz method
Hydrodynamic LBM with energy equation
Stability of lattice Boltzmann models
Simulating ocean circulation with LBM
A lattice Boltzmann equation for diffusion
Lattice Boltzmann model: What else?
Summary and outlook
Appendix
Boolean algebra
FHP: After some algebra one finds ...
Coding of the collision operator of FHP-II and FHP-III in C
Thermal LBM: derivation of the coefficients
SchlA[$$$]fli symbols
Notation, symbols and abbreviations
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Mathematics

An Introduction

At a Glance

Paperback

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