Lattice-gas cellular automata and lattice Boltzmann models. An introduction
type: Item
instance of: scholarly article
title: Lattice-gas cellular automata and lattice Boltzmann models. An introduction
zbMATH Open document ID: 0999.82054
author: Dieter A. Wolf-Gladrow
published in: Lecture Notes in Mathematics
publication date: 2000-04-16T00:00:00Z
full work available at URL: t1725.htm
review text: Lattice-gas cellular automata are have become alternative tool for the numerical analysis of gas dynamics (Navier-Stokes equation). In contrast to the traditional discretization methods, LGCA's start with a discrete model that has build much of the physically motivated properties of the underlying microsystems, while under suitable scaling is is designed to reproduce the solutions of the desired hydrodynamic equations. This book is an introduction to this field written from the practitioners point of view, providing all the necessary tools to actually implement these methods in concrete algorithms for the simulation of real world problems. This complements in a welcome way other texts on the subject that often spend more time on the underlying physics or mathematics, but less on the concrete problems facing an actual implementation, such as the precise choice of the lattice, collisions rules and specially adapted programming techniques (indeed, the book almost starts with the question: Fortran or C?!). The book is divided into 5 Sections and an Appendix. Section 1 discusses the basic issues of simulation of the Navier-Stokes equations and explains the basic ideas of LGCA's and lattice Boltzmann models. Section 2 reviews some general aspects of Cellular Automata. Here the reader will find the familiar pictures of Wolfram's 1D CA's, Conway's 2D ``game of live'', etc. Section 3 covers LGCA modelling. The reader is introduced to the classical models like the HPP (Hardy, de Pazzis, Pomeau) and FHP (Frisch, Hasslacher, Pomeau) automata. The role of the choice of the underlying lattice in reproducing the proper symmetries of the solutions, the importance of the incorporation of the appropriate conservation laws in order to obtain the desired macroscopic equations are explained carefully. A large part of this chapter is devoted to the question how in three dimension a suitable lattice can be constructed. At the same time the the programming issues of the numerical implement…
reviewed by: Anton Bovier
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 76M28
Mathematics Subject Classification ID: 82-01
Mathematics Subject Classification ID: 76-01
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 76P05
zbMATH DE Number: 1432043
zbMATH Keywords: cellular automata
zbMATH Keywords: lattice gas
zbMATH Keywords: lattice Boltzmann models
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: numerical simulation
describes a project that uses: WolframAlpha
MaRDI profile type: Publication
OpenAlex ID: W2497980095
DOI: 10.1007/B72010
description: scientific article; zbMATH DE number 1432043