Lattice Gas Methods For Partial Differential Equations / Edition 1

by Gary Doolen

Overview

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.

Product Details

ISBN-13:	9780367002879
Publisher:	CRC Press
Publication date:	09/13/2019
Pages:	582
Product dimensions:	6.31(w) x 9.38(h) x (d)

About the Author

Stephen Wolfram was born in England in 1959. He was educated at Eton and Oxford, and received his PhD in theoretical physics from Caltech at the age of twenty. Wolfram’s early work in particle physics, cosmology and computer science earned him one of the first MacArthur awards. Wolfram began his work on the problem of complexity in 1981. And after writing the sequence of papers collected in this book, Wolfram founded the first research center and the first journal devoted to the study of complexity. Then in 1986, he formed Wolfram Research, Inc., and began the development of Mathematica. Released in 1988, Mathematica has become the standard software system for technical computation used by scientists, engineers, students and others around the world. Wolfram has been the recipient of many awards for science and business. He now divides his time between basic research and the leadership of his company.

Table of Contents

Preface / Gary D. Doolen — Basic Papers — Calculations Using Lattice Gas Techniques / T. Shimomura, G. D. Doolen, B. Hasslacher and C. Fu — Lattice-Gas Automata for the Navier-Stokes Equation / U. Frisch, B. Hasslacher, and Y. Pomeau — Cellular Automaton Fluids 1: Basic Theory — Stephen Wolfram — Lattice Gas Hydrodynamics in Two and Three Dimensions / Uriel Frisch, Dominique d'Humieres, Brosl Hasslacher, Pierre Lallemand, Yves Pomeau, and Jean-Pierre Rivet — Density and Velocity Dependence of Reynolds Numbers for Several Lattice Gas Models / K. Diemer, K. Hunt, S. Chen, T. Shimomura and G. D. Doolen — Viscosity of a Lattice Gas / Michel Henon — Computer Hardware Papers — Prospects for a Lattice-Gas Computer / A. Despain, C. E. Max, G. Doolen and B. Hasslacher —Cellular Automata Machines / Norman Margo/us and Tommaso Toffoli — RAPl, a Cellular Automaton Machine for Fluid Dynamics / Andre Clouqueur and Dominique d'Humieres — Hydrodynamic Studies and Application Papers — Reynolds Number Scaling of Cellular-Automaton Hydrodynamics / Steven A. Orszag and Victor Yakhot — Immiscible Cellular-Automaton Fluids / Danied H. Rothman and Jeffrey M. Keller — Analogy between Hyperscale Transport and Cellular Automaton Fluid Dynamics / Victor Yakhot, Bruce J. Bayly, and Steven A. Orszag — Use of the Boltzmann Equation to Simulate Lattice-Gas Automata / Guy R. McNamam and Gianluigi Zanetti — Numerical Simulations of Hydrodynamics with Lattice Gas Automata in Two Dimensions / Dominique d'Humieres and Pierre Lallemand — Numerical Experiments on Lattice Gases: Mixtures and Galilean In variance / Dominique d'Humieres, Pierre Lallemand, and Geoffrey Searby — Transport Coefficients for Magnetohydrodynamic Cellular Automata / Tudatsugu Hatori and David Montgomery —The Effect of Galilean N on-Invariance in Lattice Gas Automaton One-Dimensional Flow / Fernand Hayot — A Posieuille Viscometer for Lattice Gas Automata / Leo P. Kadanoff, Guy R. McNamma, and Gianluigi Zanetti — Green-Kubo Formalism for Lattice Gas Hydrodynamics and Monte-Carlo Evaluation of Shear Viscosities / Jean-Pierre Rivet — Cellular Automata for Hydrodynamics with Free Boundaries in Two and Three Dimensions / P. Clavin, D. d'Humieres, P. Lal/emand, and Y. Pomeau — Simulation of 2-D Von Karman Streets using a Lattice Gas / D. d'Humieres, Y. Pomeau and P. Lallemand — Flow of a Lattice Gas between Two Parallel Plates: Development of the Poiseuille Profile / D. d'Humieres and P. Lal/emand — Lattice Gas Hydrodynamics, Green-Kubo Formula / U. Frisch and J. P. Rivet — Lattice Gas Automata in the Boltzmann Approximation / J. P. Rivet and U. Frish —More Partial Differential Equations — New Cellular Automaton Model for Magnetohydrodynamics / Hudong Chen and William H. Matthaeus — Two Cellular Automata for Plasma Computations / David Montgomery a.nd Gary D. Doolen — Numerical Experiments with Lattice Lorentz Gases / P.-M. Binder — A Cellular Automaton for Burgers' Equation / B.M. Boghosian and C. D. Levermore — Simple Lattice Gas Models for Waves / Hudong Chen, Shiyi Chen, G. D. Doolen, and Y. C. Lee — Bibliography / ~ry~~n