Lattice Gas Cellular Automata and Lattice Boltzmann Models An Introd
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 researcher
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1725
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1725
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Dieter A. Wolf-Gladrow
Lattice-Gas Cellular Automata and Lattice Boltzmann Models An Introduction
Springer
Author Dieter A. Wolf-Gladrow Alfred Wegener Institute for Polar and Marine Research Postfach 12 01 61 27515 Bremerhaven, Germany E-mail: [email protected]
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Wolf-Gladrow, Dieter: Lattice gas cellular automata and lattice Boltzmann models: an introduction I Dieter A. Wolf-Gladrow. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics.; 1725) ISBN 3-540-66973-6
Mathematics Subject Classification (1991): 35Q30, 58F08, 65C20, 76P05, 82C40 ISSN 0075-8434 ISBN 3-540-66973-6 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution underthe German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author Printed on acid-free paper SPIN: 10700369 41/3143du-543210
Table of Contents
1.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The basic idea of lattice-gas cellular automata and lattice Boltzmann models
4 7
1.3.1 The Navier-Stokes equation . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3.2 The basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3.3 Top-down versus bottom-up . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.4 LGCA versus molecular dynamics . . . . . . . . . . . . . . . . . . 11 2.
Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 What are cellular automata? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 A short history of cellular automata . . . . .
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